Academic literature on the topic 'Mathematical Logic and Formal Languages'
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Journal articles on the topic "Mathematical Logic and Formal Languages"
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Gopal, Тadepalli. "Learning Computational Logic through Geometric Reasoning." Innovative STEM Education 5, no. 1 (July 24, 2023): 7–12. http://dx.doi.org/10.55630/stem.2023.0501.
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Computers control everyday things ranging from the heart pacemakers to voice controlled devices that form an integral part of many appliances. Failures related to computers regularly cause disruption, damage and occasionally death. Computational logic establishes the facts in a logical formalism. It attempts to understand the nature of mathematical reasoning with a wide variety of formalisms, techniques and technologies. Formal verification uses mathematical and logical formalisms to prove the correctness of designs. Formal methods provide the maturity and agility to assimilate the future concepts, languages, techniques and tools for computational methods and models. The quest for simplification of formal verification is never ending. This summary report advocates the use of geometry to construct quick conclusions by the human mind that can be formally verified if necessary.
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Park, Sewon. "Continuous Abstract Data Types for Verified Computation." Bulletin of Symbolic Logic 27, no. 4 (December 2021): 531. http://dx.doi.org/10.1017/bsl.2021.51.
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AbstractWe devise imperative programming languages for verified real number computation where real numbers are provided as abstract data types such that the users of the languages can express real number computation by considering real numbers as abstract mathematical entities. Unlike other common approaches toward real number computation, based on an algebraic model that lacks implementability or transcendental computation, or finite-precision approximation such as using double precision computation that lacks a formal foundation, our languages are devised based on computable analysis, a foundation of rigorous computation over continuous data. Consequently, the users of the language can easily program real number computation and reason about the behaviours of their programs, relying on their mathematical knowledge of real numbers without worrying about artificial roundoff errors. As the languages are imperative, we adopt precondition–postcondition-style program specification and Hoare-style program verification methodologies. Consequently, the users of the language can easily program a computation over real numbers, specify the expected behaviour of the program, including termination, and prove the correctness of the specification. Furthermore, we suggest extending the languages with other interesting continuous data, such as matrices, continuous real functions, et cetera.Abstract taken directly from the thesis.E-mail: sewonpark17@gmail.comURL: https://sewonpark.com/thesis
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Moschovakis, Yiannis N. "The formal language of recursion." Journal of Symbolic Logic 54, no. 4 (December 1989): 1216–52. http://dx.doi.org/10.1017/s0022481200041086.
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This is the first of a sequence of papers in which we will develop a foundation for the theory of computation based on a precise, mathematical notion of abstract algorithm. To understand the aim of this program, one should keep in mind clearly the distinction between an algorithm and the object (typically a function) computed by that algorithm. The theory of computable functions (on the integers and on abstract structures) is obviously relevant to this work, but we will focus on making rigorous and identifying the mathematical properties of the finer (intensional) notion of algorithm.It is characteristic of this approach that we take recursion to be a fundamental (primitive) process for constructing algorithms, not a derived notion which must be reduced to others—e.g. iteration or application and abstraction, as in the classical λ-calculus. We will model algorithms by recursors, the set-theoretic objects one would naturally choose to represent (syntactically described) recursive definitions. Explicit and iterative algorithms are modelled by (appropriately degenerate) recursors.The main technical tool we will use is the formal language of recursion, FLR, a language of terms with two kinds of semantics: on each suitable structure, the denotation of a term t of FLR is a function, while the intension of t is a recursor (i.e. an algorithm) which computes the denotation of t. FLR is meant to be intensionally complete, in the sense that every (intuitively understood) “algorithm” should “be” (faithfully modelled, in all its essential properties by) the intension of some term of FLR on a suitably chosen structure.
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Gelsema, Tjalling. "The Logic of Aggregated Data." Acta Cybernetica 24, no. 2 (November 3, 2019): 211–48. http://dx.doi.org/10.14232/actacyb.24.2.2019.4.
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A notion of generalization-specialization is introduced that is more expressive than the usual notion from, e.g., the UML or RDF-based languages. This notion is incorporated in a typed formal language for modeling aggregated data. Soundness with respect to a sets-and-functions semantics is shown subsequently. Finally, a notion of congruence is introduced. With it terms in the language that have identical semantics, i.e., synonyms, can be discovered. The resulting formal language is well-suited for capturing faithfully aggregated data in such a way that it can serve as the foundation for corporate metadata management in a statistical office.
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Kutsak, Nina Yu, and Vladislav V. Podymov. "Formal Verification of Three-Valued Digital Waveforms." Modeling and Analysis of Information Systems 26, no. 3 (September 28, 2019): 332–50. http://dx.doi.org/10.18255/1818-1015-2019-3-332-350.
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We investigate a formal verification problem (mathematically rigorous correctness checking) for digital waveforms used in practical development of digital microelectronic devices (digital circuits) at early design stages. According to modern methodologies, a digital circuit design starts at high abstraction levels provided by hardware description languages (HDLs). One of essential steps of an HDLbased circuit design is an HDL code debug, similar to the same step of program development in means and importance. A popular way of an HDL code debug is based on extraction and analysis of a waveform, which is a collection of plots for digital signals: functional descriptions of value changes related to selected circuit places in real time. We propose mathematical means for automation of correctness checking for such waveforms based on notions and methods of formal verification against temporal logic formulae, and focus on such typical featues of HDL-related digital signals and corresponding (informal) properties, such as real time, three-valuededness, and presence of signal edges. The three-valuededness means that at any given time, besides basic logical values 0 and 1, a signal may have a special undefined value: one of the values 0 and 1, but which one of them is either not known, or not important. An edge point of a signal is a time point at which the signal changes its value. The main results are mathematical notions, propositions, and algorithms which allow to formalize and solve a formal verification problem for considered waveforms, including: definitions for signals and waveforms which the mentioned typical digital signal features; a temporal logic suitable for formalization of waveform correctness properties, and a related verification problem statement; a solution technique for the verification problem, which is based on reduction to signal transfromation and analysis; a corresponding verification algorithm together with its correctness proof and “reasonable” complexity bounds.
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Vanderveken, Daniel. "Towards a Formal Pragmatics of Discourse." International Review of Pragmatics 5, no. 1 (2013): 34–69. http://dx.doi.org/10.1163/18773109-13050102.
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Could we enrich speech-act theory to deal with discourse? Wittgenstein and Searle pointed out difficulties. Most conversations lack a conversational purpose, they require collective intentionality, their background is indefinitely open, irrelevant and infelicitous utterances do not prevent conversations to continue, etc. Like Wittgenstein and Searle I am sceptic about the possibility of a general theory of all kinds of language-games. In my view, the single primary purpose of discourse pragmatics is to analyse the structure and dynamics of language-games whose type is provided with an internal conversational goal. Such games are indispensable to any kind of discourse. They have a descriptive, deliberative, declaratory or expressive conversational goal corresponding to a possible direction of fit between words and things. Logic can analyse felicity-conditions of such language-games because they are conducted according to systems of constitutive rules. Speakers often speak non-literally or non-seriously. The real units of conversation are therefore attempted illocutions whether literal, serious or not. I will show how to construct speaker-meaning from sentence-meaning, conversational background and conversational maxims. I agree with Montague that we need the resources of formalisms (proof, model- and game-theories) and of mathematical and philosophical logic in pragmatics. I will explain how to further develop propositional and illocutionary logics, the logic of attitudes and of action in order to characterize our ability to converse. I will also compare my approach to others (Austin, Belnap, Grice, Montague, Searle, Sperber and Wilson, Kamp, Wittgenstein) as regards hypotheses, methodology and other issues.
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Kanamori, Akihiro. "The Empty Set, The Singleton, and the Ordered Pair." Bulletin of Symbolic Logic 9, no. 3 (September 2003): 273–98. http://dx.doi.org/10.2178/bsl/1058448674.
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For the modern set theorist the empty set Ø, the singleton {a}, and the ordered pair 〈x, y〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement, and Choice are broached in the formal elaboration of the ‘set of’f {} operation. So it is surprising that, while these notions are unproblematic today, they were once sources of considerable concern and confusion among leading pioneers of mathematical logic like Frege, Russell, Dedekind, and Peano. In the development of modern mathematical logic out of the turbulence of 19th century logic, the emergence of the empty set, the singleton, and the ordered pair as clear and elementary set-theoretic concepts serves as amotif that reflects and illuminates larger and more significant developments in mathematical logic: the shift from the intensional to the extensional viewpoint, the development of type distinctions, the logical vs. the iterative conception of set, and the emergence of various concepts and principles as distinctively set-theoretic rather than purely logical. Here there is a loose analogy with Tarski's recursive definition of truth for formal languages: The mathematical interest lies mainly in the procedure of recursion and the attendant formal semantics in model theory, whereas the philosophical interest lies mainly in the basis of the recursion, truth and meaning at the level of basic predication. Circling back to the beginning, we shall see how central the empty set, the singleton, and the ordered pair were, after all.
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LADYMAN, JAMES, ØYSTEIN LINNEBO, and RICHARD PETTIGREW. "IDENTITY AND DISCERNIBILITY IN PHILOSOPHY AND LOGIC." Review of Symbolic Logic 5, no. 1 (November 17, 2011): 162–86. http://dx.doi.org/10.1017/s1755020311000281.
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AbstractQuestions about the relation between identity and discernibility are important both in philosophy and in model theory. We show how a philosophical question about identity and discernibility can be ‘factorized’ into a philosophical question about the adequacy of a formal language to the description of the world, and a mathematical question about discernibility in this language. We provide formal definitions of various notions of discernibility and offer a complete classification of their logical relations. Some new and surprising facts are proved; for instance, that weak discernibility corresponds to discernibility in a language with constants for every object, and that weak discernibility is the most discerning nontrivial discernibility relation.
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Kuzmin, Egor V. "LTL-Specification of Counter Machines." Modeling and Analysis of Information Systems 28, no. 1 (March 24, 2021): 104–19. http://dx.doi.org/10.18255/1818-1015-2021-1-104-119.
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The article is written in support of the educational discipline “Non-classical logics”. Within the framework of this discipline, the objects of study are the basic principles and constructive elements, with the help of which the formal construction of various non-classical propositional logics takes place. Despite the abstractness of the theory of non-classical logics, in which the main attention is paid to the strict mathematical formalization of logical reasoning, there are real practical areas of application of theoretical results. In particular, languages of temporal modal logics are widely used for modeling, specification, and verification (correctness analysis) of logic control program systems. This article demonstrates, using the linear temporal logic LTL as an example, how abstract concepts of non-classical logics can be reƒected in practice in the field of information technology and programming. We show the possibility of representing the behavior of a software system in the form of a set of LTL-formulas and using this representation to verify the satisfiability of program system properties through the procedure of proving the validity of logical inferences, expressed in terms of the linear temporal logic LTL. As program systems, for the specification of the behavior of which the LTL logic will be applied, Minsky counter machines are considered. Minsky counter machines are one of the ways to formalize the intuitive concept of an algorithm. They have the same computing power as Turing machines. A counter machine has the form of a computer program written in a high-level language, since it contains variables called counters, and conditional and unconditional jump operators that allow to build loop constructions. It is known that any algorithm (hypothetically) can be implemented in the form of a Minsky three-counter machine.
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RABE, FLORIAN. "A logical framework combining model and proof theory." Mathematical Structures in Computer Science 23, no. 5 (March 1, 2013): 945–1001. http://dx.doi.org/10.1017/s0960129512000424.
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Mathematical logic and computer science have driven the design of a growing number of logics and related formalisms such as set theories and type theories. In response to this population explosion, logical frameworks have been developed as formal meta-languages in which to represent, structure, relate and reason about logics.Research on logical frameworks has diverged into separate communities, often with conflicting backgrounds and philosophies. In particular, two of the most important logical frameworks are the framework of institutions, from the area of model theory based on category theory, and the Edinburgh Logical Framework LF, from the area of proof theory based on dependent type theory. Even though their ultimate motivations overlap – for example in applications to software verification – they have fundamentally different perspectives on logic.In the current paper, we design a logical framework that integrates the frameworks of institutions and LF in a way that combines their complementary advantages while retaining the elegance of each of them. In particular, our framework takes a balanced approach between model theory and proof theory, and permits the representation of logics in a way that comprises all major ingredients of a logic: syntax, models, satisfaction, judgments and proofs. This provides a theoretical basis for the systematic study of logics in a comprehensive logical framework. Our framework has been applied to obtain a large library of structured and machine-verified encodings of logics and logic translations.
Dissertations / Theses on the topic "Mathematical Logic and Formal Languages"
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Almeida, João Marcos de 1974. "Logics of Formal Inconsistency." Phd thesis, Instituições portuguesas -- UTL-Universidade Técnica de Lisboa -- IST-Instituto Superior Técnico -- -Departamento de Matemática, 2005. http://dited.bn.pt:80/29635.
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According to the classical consistency presupposition, contradictions have an explosive character: Whenever they are present in a theory, anything goes, and no sensible reasoning can thus take place. A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense. The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level. As a consequence, the LFIs are able to recapture consistent reasoning by the addition of appropriate consistency assumptions.
The present monograph introduces the LFIs and provides several illustrations of them and of their properties, showing that such logics constitute in fact the majority of interesting paraconsistent systems in the literature. Several ways of performing the recapture of consistent reasoning inside such inconsistent systems are also illustrated. In each case, interpretations in terms of many-valued, possible-translations, or modal semantics are provided, and the problems related to providing algebraic counterparts to such logics are surveyed. A formal abstract approach is proposed to all related definitions and an extended investigation is made into the logical principles and the positive and negative properties of negation.
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Toninho, Bernardo Parente Coutinho Fernandes. "A Logic and tool for local reasoning about security protocols." Master's thesis, FCT - UNL, 2009. http://hdl.handle.net/10362/2307.
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Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaThis thesis tackles the problem of developing a formal logic and associated model-checking techniques to verify security properties, and its integration in the Spatial Logic Model Checker(SLMC) tool. In the areas of distributed system design and analysis, there exists a substantial amount of work related to the verification of correctness properties of systems, in which the work aimed at the verification of security properties mostly relies on precise yet informal methods of reasoning. This work follows a line of research that applies formal methodologies to the verification of security properties in distributed systems, using formal tools originally developed for the study of concurrent and distributed systems in general. Over the years, several authors have proposed spatial logics for local and compositional reasoning about algebraic models of distributed systems known as process calculi. In this work, we present a simplification of a process calculus known as the Applied - calculus, introduced by Abadi and Fournet, designed for the study of security protocols. We then develop a spatial logic for this calculus, extended with knowledge modalities, aimed at reasoning about security protocols using the concept of local knowledge of processes. Furthermore, we conclude that the extensions are sound and complete regarding their intended semantics and that they preserve decidability, under reasonable assumptions. We also present a model-checking algorithm and the proof of its completeness for a large class of processes. Finally, we present an OCaml implementation of the algorithm, integrated in the Spatial Logic Model Checker tool, developed by Hugo Vieira and Luis Caires, thus producing the first tool for security protocol analysis that employs spatial logics.
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Reis, Teofilo de Souza. "Conectivos flexíveis : uma abordagem categorial às semânticas de traduções possíveis." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278896.
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Orientador: Marcelo Esteban ConiglioDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: Neste trabalho apresentamos um novo formalismo de decomposição de Lógicas, as Coberturas por Traduções Possíveis, ou simplesmente CTPs. As CTPs constituem uma versão formal das Semânticas de Traduções Possíveis, introduzidas por W. Carnielli em 1990. Mostramos como a adoção de um conceito mais geral de morfismo de assinaturas proposicionais (usando multifunções no lugar de funções) nos permite definir uma categoria Sig?, na qual os conectivos, ao serem traduzidos de uma assinatura para outra, gozam de grande flexibilidade. A partir de Sig?, contruímos a categoria Log? de lógicas tarskianas e morfismos (os quais são funções obtidas a partir de um morfismo de assinaturas, isto é, de uma multifunção). Estudamos algumas características de Sig? e Log?, afim de verificar que estas categorias podem de fato acomodar as construções que pretendemos apresentar. Mostramos como definir em Log? o conjunto de traduções possíveis de uma fórmula, e a partir disto definimos a noção de CTP para uma lógica L. Por fim, exibimos um exemplo concreto de utilização desta nova ferramenta, e discutimos brevemente as possíveis abordagens para uma continuação deste trabalho.
Abstract: We present a general study of a new formalism of decomposition of logics, the Possible- Translations Coverings (in short PTC 's) which constitute a formal version of Possible-Translations Semantics, introduced by W. Carnielli in 1990. We show how the adoption of a more general notion of propositional signatures morphism allows us to define a category Sig?, in which the connectives, when translated from a signature to another one, enjoy of great flexibility. Essentially, Sig? -morphisms will be multifunctions instead of functions. From Sig? we construct the category Log? of tarskian logics and morphisms between them (these .are functions obtained from signature morphisms, that is, from multifunctions) . We show how to define in Log? the set of possible translations of a given formula, and we define the notion of a PTC for a logic L. We analyze some properties of PTC 's and give concrete examples of the above mentioned constructions. We conclude with a discussion of the approaches to be used in a possible continuation of these investigations.
Mestrado
Mestre em Filosofia
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Silvestrini, Luiz Henrique da Cruz. "Uma nova abordagem para a noção de quase-verdade." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/280594.
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Orientador: Marcelo Esteban ConiglioTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Mikenberg, da Costa e Chuaqui (1986) introduziram a noção de quase-verdade por meio da noção de estruturas parciais, e para tanto, conceberam os predicados como ternas. O arcabouço conceitual resultante proporcionou o emprego de estruturas parciais na ciência, pois, em geral, não sabemos tudo a respeito de um determinado domínio de conhecimento. Generalizamos a noção de predicados como ternas para fórmulas complexas. A partir desta nova abordagem, obtemos uma definição de quase-verdade via noção de satisfação pragmática de uma fórmula A em uma estrutura parcial E. Introduzimos uma lógica subjacente à nossa nova definição de quase-verdade, a saber, a lógica paraconsistente trivalente LPT1, a qual possui uma axiomática de primeira ordem. Relacionamos a noção de quase-verdade com algumas lógicas paraconsistentes já existentes. Defendemos que a formalização das Sociedades Abertas, introduzidas por Carnielli e Lima-Marques (1999), quando combinada com quantificadores modulados, introduzidos por Grácio (1999), constitui uma alternativa para capturar a componente indutiva presente na atividade científica, e mostramos, a partir disso, que a proposta original de da Costa e colaboradores pode ser explicada em termos da nova noção de sociedades moduladas
Abstract: Newton da Costa and his collaborators have introduced the notion of quasi-truth by means of partial structures, and for this purpose, they conceived the predicates as ordered triples: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively (the latter represents lack of information). This approach provides a conceptual framework to analyse the use of (first-order) structures in science in contexts of informational incompleteness. In this Thesis, the notion of predicates as triples is extended recursively to any complex formula of the first-order object language. From this, a new definition of quasi-truth via the notion of pragmatic satisfaction is obtained. We obtain the proof-theoretic counterpart of the logic underlying our new definition of quasi-truth, namely, the three-valued paraconsistent logic LPT1, which is presented axiomatically in a first-order language. We relate the notion of quasi-truth with some existing paraconsistent logics. We defend that the formalization of (open) society semantics when combined with the modulated quantifiers constitutes an alternative to capture the inductive component present in scientific activity, and show, from this, that the original proposal of da Costa and collaborators can be explained in terms of the new concept of modulated societies
Doutorado
Filosofia
Doutor em Filosofia
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Bueno-Soler, Juliana 1976. "Multimodalidades anodicas e catodicas : a negação controlada em logicas multimodais e seu poder expressivo." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/280387.
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Orientador: Itala Maria Loffredo D'OttavianoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: O presente trabalho tem por objetivo investigar o papel da negação no âmbito das modalidades, de forma a poder esclarecer até que ponto a negação pode ser atenuada, controlada ou mesmo totalmente eliminada em favor da melhor expressabilidade lógica de certas teorias, asserções ou raciocínios que sofrem os efeitos da negação. Contudo, atenuar ou eliminar a negação tem um alto preço: métodos tradicionais em lógica podem deixar de ser válidos e certos resultados, como teoremas de completude para sistemas lógicos, podem ser derrogados. Do ponto de vista formal, a questão central que investigamos aqui e até que ponto tais métodos podem ser restabelecidos. Com tal finalidade, iniciamos nosso estudo a partir do que denominamos sistemas anódicos" (sem negação) e, a posteriori, introduzimos gradativamente o elemento catódico" (negações, com diversas gradações e diferentes características) nos sistemas modais por meio de combinações com certas lógicas paraconsistentes, as chamadas lógicas da inconsistência formal (LFIs). Todos os sistemas tratados são semanticamente caracterizados por semânticas de mundos possíveis; resultados de incompletude são também obtidos e discutidos. Obtemos ainda semânticas modais de traduções possíveis para diversos desses sistemas. Avançamos na direção das multimodalidades, investigando os assim chamados sistemas multimodais anódicos e catódicos. Finalmente, procuramos avaliar criticamente o alcance e o interesse dos resultados obtidos na direção da racionalidade sensível à negação.
Abstract: The present work aims to investigate the role of negations in the scope of modalities and in the reasoning expressed by modalities. The investigation starts from what we call anodic" systems (without any form of negation) and gradually reaches the cathodic" elements, where negations are introduced by means of combining modal logics with certain paraconsistent logics known as logics of formal inconsistency (LFIs). We obtain completeness results for all treated systems, and also show that certain incompleteness results can be obtained. The class of the investigated systems includes all normal modal logics that are extended by means of the schema Gk;l;m;n due to E. J. Lemmon and D. Scott combined with LFIs. We also tackle the question of obtaining modal possible-translations semantics for these systems. Analogous results are analyzed in the scope of multimodalities, where anodic as much as cathodic logics are studied. Finally, we advance a critical evaluation of the reach and scope of all the results obtained to what concerns expressibility of reasoning considered to be sensible to negation. We also critically assess the obtained results in contrast with problems of rationality that are sensible to negation.
Doutorado
Doutor em Filosofia
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Rodrigues, Tarcísio Genaro. "Sobre os fundamentos de programação lógica paraconsistente." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278897.
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Orientador: Marcelo Esteban ConiglioDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: A Programação Lógica nasce da interação entre a Lógica e os fundamentos da Ciência da Computação: teorias de primeira ordem podem ser interpretadas como programas de computador. A Programação Lógica tem sido extensamente utilizada em ramos da Inteligência Artificial tais como Representação do Conhecimento e Raciocínio de Senso Comum. Esta aproximação deu origem a uma extensa pesquisa com a intenção de definir sistemas de Programação Lógica paraconsistentes, isto é, sistemas nos quais seja possível manipular informação contraditória. Porém, todas as abordagens existentes carecem de uma fundamentação lógica claramente definida, como a encontrada na programação lógica clássica. A questão básica é saber quais são as lógicas paraconsistentes subjacentes a estas abordagens. A presente dissertação tem como objetivo estabelecer uma fundamentação lógica e conceitual clara e sólida para o desenvolvimento de sistemas bem fundados de Programação Lógica Paraconsistente. Nesse sentido, este trabalho pode ser considerado como a primeira (e bem sucedida) etapa de um ambicioso programa de pesquisa. Uma das teses principais da presente dissertação é que as Lógicas da Inconsistência Formal (LFI's), que abrangem uma enorme família de lógicas paraconsistentes, proporcionam tal base lógica. Como primeiro passo rumo à definição de uma programação lógica genuinamente paraconsistente, demonstramos nesta dissertação uma versão simplificada do Teorema de Herbrand para uma LFI de primeira ordem. Tal teorema garante a existência, em princípio, de métodos de dedução automática para as lógicas (quantificadas) em que o teorema vale. Um pré-requisito fundamental para a definição da programação lógica é justamente a existência de métodos de dedução automática. Adicionalmente, para a demonstração do Teorema de Herbrand, são formuladas aqui duas LFI's quantificadas através de sequentes, e para uma delas demonstramos o teorema da eliminação do corte. Apresentamos também, como requisito indispensável para os resultados acima mencionados, uma nova prova de correção e completude para LFI's quantificadas na qual mostramos a necessidade de exigir o Lema da Substituição para a sua semântica
Abstract: Logic Programming arises from the interaction between Logic and the Foundations of Computer Science: first-order theories can be seen as computer programs. Logic Programming have been broadly used in some branches of Artificial Intelligence such as Knowledge Representation and Commonsense Reasoning. From this, a wide research activity has been developed in order to define paraconsistent Logic Programming systems, that is, systems in which it is possible to deal with contradictory information. However, no such existing approaches has a clear logical basis. The basic question is to know what are the paraconsistent logics underlying such approaches. The present dissertation aims to establish a clear and solid conceptual and logical basis for developing well-founded systems of Paraconsistent Logic Programming. In that sense, this text can be considered as the first (and successful) stage of an ambitious research programme. One of the main thesis of the present dissertation is that the Logics of Formal Inconsistency (LFI's), which encompasses a broad family of paraconsistent logics, provide such a logical basis. As a first step towards the definition of genuine paraconsistent logic programming we shown, in this dissertation, a simplified version of the Herbrand Theorem for a first-order LFI. Such theorem guarantees the existence, in principle, of automated deduction methods for the (quantified) logics in which the theorem holds, a fundamental prerequisite for the definition of logic programming over such logics. Additionally, in order to prove the Herbrand Theorem we introduce sequent calculi for two quantified LFI's, and cut-elimination is proved for one of the systems. We also present, as an indispensable requisite for the above mentioned results, a new proof of soundness and completeness for first-order LFI's in which we show the necessity of requiring the Substitution Lemma for the respective semantics
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Palacios, Pastrana Florencio Edmundo. "Etude des rapports entre linguistique et logique concernant la dimension temporelle : un modèle de transition." Université Joseph Fourier (Grenoble), 1998. http://www.theses.fr/1998GRE10273.
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Le but general de cette these est de developper un langage formel susceptible de modeliser certains traits du langage naturel ayant une relation forte avec le temps. En particulier nous sommes interesse par la notion linguistique de l'aspect et de ses consequences logiques possibles. Nous basons notre analyse sur deux perspectives : linguistique et logique. Pour la premiere nous analysons les concepts pertinents lies a la categorie grammaticale de l'aspect, qui, avec la categorie du temps grammatical, a une relation directe avec la notion de temps. Pour la seconde perspective, nous analysons les notions logiques mises en jeu dans des systemes formels deductifs et leur relations avec le temps : la logique temporelle. Comme il est etabli, les langages formels bases sur les notions definies par frege ne sont pas suffisants pour exprimer toutes les composantes temporelles du langage naturel. Toutefois il y a d'autres formalismes etendus qui prennent en compte certains concepts linguistiques comme l'aspect. Une telle proposition a ete faite par galton qui introduit des operateurs pour certaines des notions aspectuelles les plus courantes en anglais comme la perfectivite et la progressivite. Notre proposition introduit des notions topologiques pour representer la structure de l'ensemble dans lequel un enonce prend une certaine valeur de verite. De plus nous traitons aussi du concept de sigma-signification pour representer certains concepts theoriques non ensemblistes en rapport avec la signification des enonces.
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Yim, Austin Vincent. "On Galois correspondences in formal logic." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b47d1dda-8186-4c81-876c-359409f45b97.
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This thesis examines two approaches to Galois correspondences in formal logic. A standard result of classical first-order model theory is the observation that models of L-theories with a weak form of elimination of imaginaries hold a correspondence between their substructures and automorphism groups defined on them. This work applies the resultant framework to explore the practical consequences of a model-theoretic Galois theory with respect to certain first-order L-theories. The framework is also used to motivate an examination of its underlying model-theoretic foundations. The model-theoretic Galois theory of pure fields and valued fields is compared to the algebraic Galois theory of pure and valued fields to point out differences that may hold between them. The framework of this logical Galois correspondence is also applied to the theory of pseudoexponentiation to obtain a sketch of the Galois theory of exponential fields, where the fixed substructure of the complex pseudoexponential field B is an exponential field with the field Qrab as its algebraic subfield. This work obtains a partial exponential analogue to the Kronecker-Weber theorem by describing the pure field-theoretic abelian extensions of Qrab, expanding upon work in the twelfth of Hilbert’s problems. This result is then used to determine some of the model-theoretic abelian extensions of the fixed substructure of B. This work also incorporates the principles required of this model-theoretic framework in order to develop a model theory over substructural logics which is capable of expressing this Galois correspondence. A formal semantics is developed for quantified predicate substructural logics based on algebraic models for their propositional or nonquantified fragments. This semantics is then used to develop substructural forms of standard results in classical first-order model theory. This work then uses this substructural model theory to demonstrate the Galois correspondence that substructural first-order theories can carry in certain situations.
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Dumbravă, Ştefania-Gabriela. "Formalisation en Coq de Bases de Données Relationnelles et Déductives -et Mécanisation de Datalog." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS525/document.
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Cette thèse présente une formalisation en Coq des langages et des algorithmes fondamentaux portant sur les bases de données. Ainsi, ce fourni des spécifications formelles issues des deux approches différentes pour la définition des modèles de données: une basée sur l’algèbre et l'autre basée sur la logique.A ce titre, une première contribution de cette thèse est le développement d'une bibliothèque Coq pour le modèle relationnel. Cette bibliothèque contient les modélisations de l’algèbre relationnelle et des requêtes conjonctives. Il contient aussi une mécanisation des contraintes d'intégrité et de leurs procédures d'inférence. Nous modélisons deux types de contraintes: les dépendances, qui sont parmi les plus courantes: les dépendances fonctionnelles et les dépendances multivaluées, ainsi que leurs axiomatisations correspondantes. Nous prouvons formellement la correction de leurs algorithmes d'inférence et, pour le cas de dépendances fonctionnelles, aussi la complétude.Ces types de dépendances sont des instances de contraintes plus générales : les dépendances génératrices d'égalité (equality generating dependencies, EGD) et, respectivement, les dépendances génératrices de tuples (tuple generating dependencies, TGD), qui appartiennent a une classe encore plus large des dépendances générales (general dependencies). Nous modélisons ces dernières et leur procédure d'inférence, i.e, "the chase", pour lequel nous établissons la correction. Enfin, on prouve formellement les théorèmes principaux des bases de données, c'est-à-dire, les équivalences algébriques, la théorème de l' homomorphisme et la minimisation des requêtes conjonctives.Une deuxième contribution consiste dans le développement d'une bibliothèque Coq/ssreflect pour la programmation logique, restreinte au cas du Datalog. Dans le cadre de ce travail, nous donnons la première mécanisations d'un moteur Datalog standard et de son extension avec la négation. La bibliothèque comprend une formalisation de leur sémantique en theorie des modelés ainsi que de leur sémantique par point fixe, implémentée par une procédure d'évaluation stratifiée. La bibliothèque est complétée par les preuves de correction, de terminaison et de complétude correspondantes. Cette plateforme ouvre la voie a la certification d' applications centrées donnéesThis thesis presents a formalization of fundamental database theories and algorithms. This furthers the maturing state of the art in formal specification development in the database field, with contributions stemming from two foundational approches to database models: relational and logic based.As such, a first contribution is a Coq library for the relational model. This contains a mechanization of integrity constraints and of their inference procedures. We model two of the most common dependencies, namely functional and multivalued, together with their corresponding axiomatizations. We prove soundness of their inference algorithms and, for the case of functional ones, also completeness. These types of dependencies are instances of equality and, respectively, tuple generating dependencies, which fall under the yet wider class of general dependencies. We model these and their inference procedure,i.e, the chase, for which we establish soundness.A second contribution consists of a Coq/Ssreflect library for logic programming in the Datalog setting. As part of this work, we give (one of the) first mechanizations of the standard Datalog language and of its extension with negation. The library includes a formalization of their model theoretical semantics and of their fixpoint semantics, implemented through bottom-up and, respectively, through stratified evaluation procedures. This is complete with the corresponding soundness, termination and completeness proofs. In this context, we also construct a preliminary framework for dealing with stratified programs. This work paves the way towards the certification of data-centric applications
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Cholodovskis, Ana Flávia de Faria 1988. "Lógicas de inconsistência formal e não-monotonicidade." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/279773.
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Orientador: Walter Alexandre CarnielliDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Existem diversas razões para justificar o desenvolvimento de lógicas não-clássicas tais como a expressividade destas linguagens e como elas poderiam ajudar a formalizar o pensamento humano. Neste sentido, as lógicas não-monotônicas foram desenvolvidas em prol de formalizar raciocínios cotidianos baseados na premissa de que nós deveríamos ser capazes de retratar conclusões previamente obtidas quando confrontadas com novas informações. Algumas lógicas não-monotônicas utilizam a noção de pensamento default para formalizar raciocínios cotidianos. Por outro lado, as lógicas paraconsistentes são aquelas lógicas que estudam teorias não-explosivas e foram desenvolvidas em prol de lidar com contradições. Sobre as lógicas paraconsistentes, existe uma classe de sistemas que se mostram realmente interessantes, particularmente: as Lógicas de Inconsistência Formal (LIFs). LIFs são um tipo especial de lógicas paraconsistentes que são gentilmente explosivas e internalizam o conceito de consistência no nível da linguagem-objeto utilizando o operador de consistência ? . A questão inicial Poderia a Paraconsistência substituir a Não-Monotonicidade? nos guiou à formalização de uma pergunta mais específica, entretanto, mais intrigante: É possível desenvolver uma lógica não-monotônica gentilmente explosiva?. No intuito de buscar responder a essa questão, é importante investigar conceitual e filosoficamente a relevância e as problemáticas de se desenvolver tal lógica. Este trabalho visa justificar a importância de uma lógica não-monotônica paraconsistente baseada nas Lógicas de Inconsistência Formal a partir de uma análise intuitiva dos conceitos e das noções envolvidas em tais sistemas formais considerando, ainda, abordagens possíveis a partir das chamadas Lógicas Adaptativas de Inconsistência e das Lógicas Moduladas
Abstract: There are many reasons to justify the development of non-classical logics such as the expressivity of those languages and how they could help to formulate human reasoning. In that sense, nonmonotonic logics were developed in order to formalize everyday reasoning based on the premise that we should be able to retract conclusions previously obtained in face of new information. Some nonmonotonic logics uses the notion of default reasoning to formalize everyday reasoning. On the other hand, paraconsistent logics are those logics that studies non-explosive theories and were developed in order to deal with contradictions. About paraconsistent logics, there is a class of systems that has shown to be really interesting, particularly: the Logics of Formal Inconsistency [LFIs]. LFIs are a special kind of paraconsistent logics that are gently explosive and internalize the concept of consistency at the object-language level using the consistency operator ?. The initial question Can Paraconsistency replace Nonmonotonicity? guided us to the formulation of a more specific yet intriguing question: Is it possible to develop a gently explosive nonmonotonic logic?. In order to answer that question, it is important to investigate both conceptual and philosophical relevance and problems of developing such logic. This work intends to justify the importance of a non-monotonic paraconsistent logic based on Logics of Formal Inconsistency from an intuitive analysis of concepts and notions involved in such formal systems, also considering possible approaches from the so called Adaptive Logics of Inconsistency an Modulated Logics
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Books on the topic "Mathematical Logic and Formal Languages"
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Srivastava, S. M. A Course on Mathematical Logic. 2nd ed. New York, NY: Springer New York, 2013.
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Casadio, C. Logic for grammar: Developments in linear logic and formal linguistics. Roma: Bulzoni, 2002.
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Colloquium on Logic, Language, Mathematics Linguistics (3rd 1991 Brașov, Romania). Proceedings of the Third Colloquium on Logic, Language, Mathematics Linguistics, Brasov, 23-25 mai 1991. Brasov: Transilvania University of Brasov, Faculty of Sciences, Dept. of Mathematics, 1991.
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Larrazabal, Jesús M. Logic Colloquium' 96: Proceedings of the Colloquium held in San Sebastián, Spain, July 9-15, 1996. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998.
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service), SpringerLink (Online, ed. Logica: Metodo Breve. Milano: Springer Milan, 2011.
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1953-, Delzell Charles N., ed. Mathematical logic and model theory: A brief introduction. London: Springer, 2011.
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A, Carnielli Walter, ed. Analysis and synthesis of logics: How to cut and paste reasoning systems. Dordrecht: Springer, 2008.
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International Colloquium on Grammatical Inference (10th 2010 Valencia, Spain). Grammatical inference: theoretical results and applications: 10th international colloquium ; proceedings. Berlin: Springer, 2010.
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International Colloquium on Grammatical Inference (9th 2008 Saint-Malo, France). Grammatical inference: Algorithms and applications : 9th international colloquium, ICGI 2008, Saint-Malo, France, September 22-24, 2008 : proceedings. [New York]: Springer-Verlag Berlin Heidelberg, 2008.
Find full textBook chapters on the topic "Mathematical Logic and Formal Languages"
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Csirmaz, Laszlo, and Zalán Gyenis. "Formal Languages and Automata." In Mathematical Logic, 13–18. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-79010-3_3.
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Manin, Yu I. "Introduction to Formal Languages." In A Course in Mathematical Logic for Mathematicians, 3–18. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0615-1_1.
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Reghiş, Mircea, and Eugene Roventa. "The Formal Language of Propositional Logic." In Classical and Fuzzy Concepts in Mathematical Logic and Applications, 23–35. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003067924-3.
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Reghiş, Mircea, and Eugene Roventa. "The Formal Language of Predicate Logic." In Classical and Fuzzy Concepts in Mathematical Logic and Applications, 197–204. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003067924-13.
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van Benthem, Johan. "Mathematical Logic and Natural Language: Life at the border." In Foundations of the Formal Sciences II, 25–38. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0395-6_2.
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Ingram, David. "2. Knowledge, Language and Reason." In Health Care in the Information Society, 69–192. Cambridge, UK: Open Book Publishers, 2023. http://dx.doi.org/10.11647/obp.0335.02.
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The story starts long ago, with the gradual conceptualization of knowledge as an encyclopaedia—a circle of learning. This chapter traces a path from the invention of medicine in classical times, through philosophy, language and logic, and through mathematics, natural science and computer science into the modern era of information technology and health care. It follows the librarian’s dilemma over the ages—discovering how best to position books and documents within collections and search them in pursuit of learning. The chapter proceeds to consider languages as expressions of knowledge, and the different forms they take—spoken, written, artistic, mathematical, logical and computational. This sets the scene for introducing computational discipline that grew from endeavours to formulate rigorous logical foundations of mathematics, in earlier times, and the development of formal logic in support of rigorous reasoning. From there, the computer has become integral to how we express and reason with knowledge, and to problem solving and the discovery of new knowledge. These are twenty-first-century frontiers of machine learning and artificial intelligence. Moving to the complex world of medical language and terminology, used in representing knowledge about medicine and health care, the chapter discusses difficulties faced in evolving their corpora of terms and classifications, from pragmatic organizations into reliably computable forms. Notable pioneering initiatives and their leaders are profiled, highlighting some ideas that have acquired staying power and others that have not, looking for patterns of success and failure. Finally, the chapter moves to a discussion of some pioneering computer-based systems for capturing, storing and reasoning with medical knowledge, such as for guiding the prescription of antimicrobial drugs. It closes with a light-hearted take on how we use the terms knowledge, information and data, and a reflection on the traction that is needed in the unfolding of new knowledge and its application in practical contexts.
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Aliferis, Constantin, and Gyorgy Simon. "Foundations and Properties of AI/ML Systems." In Health Informatics, 33–94. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-39355-6_2.
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AbstractThe chapter provides a broad introduction to the foundations of health AI and ML systems and is organized as follows: (1) Theoretical properties and formal vs. heuristic systems: computability, incompleteness theorem, space and time complexity, exact vs. asymptotic complexity, complexity classes and how to establish complexity of problems even in the absence of known algorithms that solve them, problem complexity vs. algorithm and program complexity, and various other properties. Moreover, we discuss the practical implications of complexity for system tractability, the folly of expecting Moore’s Law and large-scale computing to solve intractable problems, and common techniques for creating tractable systems that operate in intractable problem spaces. We also discuss the distinction between heuristic and formal systems and show that they exist on a continuum rather than in separate spaces. (2) Foundations of AI including logics and logic based systems (rule based systems, semantic networks, planning systems search, NLP parsers), symbolic vs. non-symbolic AI, Reasoning with Uncertainty, Decision Making theory, Bayesian Networks, and AI/ML programming languages. (3) Foundations of Computational Learning Theory: ML as search, ML as geometrical construction and function optimization, role of inductive biases, PAC learning, VC dimension, Theory of Feature Selection, Theory of Causal Discovery. Optimal Bayes Classifier, No Free Lunch Theorems, Universal Function Approximation, generative vs. discriminative models; Bias-Variance Decomposition of error and essential concepts of mathematical statistics.
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Li, Wei. "Formal Inference Systems." In Mathematical Logic, 45–70. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9977-1_3.
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Li, Wei. "Formal Inference Systems." In Mathematical Logic, 55–81. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0862-0_3.
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Li, Wei. "Sequences of Formal Theories." In Mathematical Logic, 117–37. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9977-1_6.
Full textConference papers on the topic "Mathematical Logic and Formal Languages"
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Simko, Gabor, Tihamer Levendovszky, Sandeep Neema, Ethan Jackson, Ted Bapty, Joseph Porter, and Janos Sztipanovits. "Foundation for Model Integration: Semantic Backplane." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70534.
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One of the primary goals of the Adaptive Vehicle Make (AVM) program of DARPA is the construction of a model-based design flow and tool chain, META, that will provide significant productivity increase in the development of complex cyber-physical systems. In model-based design, modeling languages and their underlying semantics play fundamental role in achieving compositionality. A significant challenge in the META design flow is the heterogeneity of the design space. This challenge is compounded by the need for rapidly evolving the design flow and the suite of modeling languages supporting it. Heterogeneity of models and modeling languages is addressed by the development of a model integration language – CyPhy – supporting constructs needed for modeling the interactions among different modeling domains. CyPhy targets simplicity: only those abstractions are imported from the individual modeling domains to CyPhy that are required for expressing relationships across sub-domains. This “semantic interface” between CyPhy and the modeling domains is formally defined, evolved as needed and verified for essential properties (such as well-formedness and invariance). Due to the need for rapid evolvability, defining semantics for CyPhy is not a “one-shot” activity; updates, revisions and extensions are ongoing and their correctness has significant implications on the overall consistency of the META tool chain. The focus of this paper is the methods and tools used for this purpose: the META Semantic Backplane. The Semantic Backplane is based on a mathematical framework provided by term algebra and logics, incorporates a tool suite for specifying, validating and using formal structural and behavioral semantics of modeling languages, and includes a library of metamodels and specifications of model transformations.
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Huang, K. S., B. K. Jenkins, and A. A. Sawchuk. "Binary Image Algebra and Digital Optical Cellular Image Processors." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/optcomp.1987.mb5.
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Image processing and image analysis tasks have large data processing requirements and inherent parallelism and are well suited to implementation on digital optical processors because of the parallelism and free interconnection capabilities of optical systems [1][2]. Recently, several techniques for constructing optical cellular logic processors for image processing have been proposed [2]-[5]. Through parallel studies of architectures, algorithms, mathematical structures, and optics we have found that: 1) cellular automata are appropriate models for parallel image processing machines [6]; 2) an image algebra extending from mathematical morphology [7] [8] can lead to a formal parallel language approach to the design of image processing algorithms; 3) the algebraic structure serves as a framework for both algorithms and architectures of parallel image processing; and 4) optical computing techniques are able to efficiently implement image algebra based on cellular logic architectures (e.g. cellular array, cellular hypercube etc.). Here we will first discuss image algebra and then architectures for its implementation.
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Elleuch, Maissa, Yassine Aydi, and Mohamed Abid. "Formal specification of delta MINs for MPSOC in the ACL2 logic." In Design Languages (FDL). IEEE, 2008. http://dx.doi.org/10.1109/fdl.2008.4641461.
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Habiballa, Hashim, and Radek Jendryscik. "Formal logic rewrite system bachelor in teaching mathematical informatics." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992228.
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Nakamura, Masaki, and Kazutoshi Sakakibara. "Formal Verification and Mathematical Optimization for Autonomous Vehicle Group Controllers." In 2019 ACM/IEEE 22nd International Conference on Model Driven Engineering Languages and Systems Companion (MODELS-C). IEEE, 2019. http://dx.doi.org/10.1109/models-c.2019.00111.
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Bertot, Yves. "Fixed Precision Patterns for the Formal Verification of Mathematical Constant Approximations." In POPL '15: The 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2676724.2693172.
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Belle, Vaishak. "Logic meets Probability: Towards Explainable AI Systems for Uncertain Worlds." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/733.
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Logical AI is concerned with formal languages to represent and reason with qualitative specifications; statistical AI is concerned with learning quantitative specifications from data. To combine the strengths of these two camps, there has been exciting recent progress on unifying logic and probability. We review the many guises for this union, while emphasizing the need for a formal language to represent a system's knowledge. Formal languages allow their internal properties to be robustly scrutinized, can be augmented by adding new knowledge, and are amenable to abstractions, all of which are vital to the design of intelligent systems that are explainable and interpretable.
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Tolk, Andreas, Saikou Y. Diallo, and Charles D. Turnitsa. "Mathematical models towards self-organizing formal federation languages based on conceptual models of information exchange capabilities." In 2008 Winter Simulation Conference (WSC). IEEE, 2008. http://dx.doi.org/10.1109/wsc.2008.4736163.
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Gollapudi, Chandra, and Dawn Tilbury. "Logic Control Design and Implementation for a Machining Line Testbed Using Petri Nets." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/dsc-24594.
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Abstract Historically, logic control for machining systems has been programmed in ladder logic. Although this language is very intuitive at a low level, it is difficult to understand the sequencing in a large and complex program. Recently, several different formal languages, such as Petri nets, finite state machines, and real-time temporal logic, have been proposed for logic control design. These languages allow the logic to be formally verified to be correct before it is implemented. The proofs of correctness rely on a set of explicit and implicit assumptions. By implementing these methods on a testbed system, the advantages and limitations can be more easily seen. This paper describes an implementation of a formal method for logic control design using Petri nets on a small-scale testbed at the University of Michigan using software developed at the University of Kentucky.
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Adamovich, Alexei Igorevich, and Andrei Valentinovich Klimov. "On theories of names and references in formal languages and implications for functional and object-oriented programming." In 23rd Scientific Conference “Scientific Services & Internet – 2021”. Keldysh Institute of Applied Mathematics, 2021. http://dx.doi.org/10.20948/abrau-2021-30.
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The long-standing problem of adequate formalization of local names in mathematical formulae and semantics of references in object-oriented languages taken “as is” without objects, is discussed. Reasons why the existing approaches cannot be considered suitable solutions, are explained. An introduction to the relatively recent works on the theories of names and references of the group headed by Andrew Pitts, is given. The notion of referential transparency, in which contextual equivalence is used instead of the usual equality of values, is analyzed. This is the main property, which these theories are based upon: it is preserved when a purely functional language is extended with names and references as data. It is argued that such referential transparency, along with many others, can be preserved for mutable objects that change to a limited extent. This leads to a model of computation between functional and object-oriented ones, allowing for a deterministic parallel implementation.
Reports on the topic "Mathematical Logic and Formal Languages"
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Baader, Franz, and Ralf Küsters. Unification in a Description Logic with Transitive Closure of Roles. Aachen University of Technology, 2001. http://dx.doi.org/10.25368/2022.115.
Full textAbstract:
Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL₀, which allows for conjunction, value restriction, and the top concept only, is already ExpTime-complete. The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles. It also shows that matching (which is polynomial in FL₀) is PSpace-complete in the extended description logic. These results are proved via a reduction to linear equations over regular languages, which are then solved using automata. The obtained results are also of interest in formal language theory.
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Baader, Franz, and Benjamin Zarrieß. Verification of Golog Programs over Description Logic Actions. Technische Universität Dresden, 2013. http://dx.doi.org/10.25368/2022.198.
Full textAbstract:
High-level action programming languages such as Golog have successfully been used to model the behavior of autonomous agents. In addition to a logic-based action formalism for describing the environment and the effects of basic actions, they enable the construction of complex actions using typical programming language constructs. To ensure that the execution of such complex actions leads to the desired behavior of the agent, one needs to specify the required properties in a formal way, and then verify that these requirements are met by any execution of the program. Due to the expressiveness of the action formalism underlying Golog (situation calculus), the verification problem for Golog programs is in general undecidable. Action formalisms based on Description Logic (DL) try to achieve decidability of inference problems such as the projection problem by restricting the expressiveness of the underlying base logic. However, until now these formalisms have not been used within Golog programs. In the present paper, we introduce a variant of Golog where basic actions are defined using such a DL-based formalism, and show that the verification problem for such programs is decidable. This improves on our previous work on verifying properties of infinite sequences of DL actions in that it considers (finite and infinite) sequences of DL actions that correspond to (terminating and non-terminating) runs of a Golog program rather than just infinite sequences accepted by a Büchi automaton abstracting the program.