Relevant bibliographies by topics / Algebraic logic

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Algebraic logic'

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Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Algebraic logic"

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Rota, Gian-Carlo. "Algebraic logic." Advances in Mathematics 61, no. 2 (August 1986): 184. http://dx.doi.org/10.1016/0001-8708(86)90075-7.

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Yang, Eunsuk. "Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics." Axioms 10, no. 4 (October 25, 2021): 273. http://dx.doi.org/10.3390/axioms10040273.

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Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear Urquhart-style and Fine-style Routley–Meyer semantics, for them as algebraic Routley–Meyer-style semantics.
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De Araujo Feitosa, Hércules, Mariana Matulovic, and Ana Claudia de J. Golzio. "A basic epistemic logic and its algebraic model." INTERMATHS 4, no. 2 (December 30, 2023): 28–37. http://dx.doi.org/10.22481/intermaths.v4i2.14133.

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In this paper we propose an algebraic model for a modal epistemic logic. Although it is known the existence of algebraic models for modal logics, considering that there are so many different modal logics, so it is not usual to give an algebraic model for each such system. The basic epistemic logic used in the paper is bimodal and we can show that the epistemic algebra introduced in the paper is an adequate model for it.
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Höfner, Peter, and Bernhard Möller. "Algebraic Neighbourhood Logic." Journal of Logic and Algebraic Programming 76, no. 1 (May 2008): 35–59. http://dx.doi.org/10.1016/j.jlap.2007.10.004.

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Dang, H. H., P. Höfner, and B. Möller. "Algebraic separation logic." Journal of Logic and Algebraic Programming 80, no. 6 (August 2011): 221–47. http://dx.doi.org/10.1016/j.jlap.2011.04.003.

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Maddux, Roger D. "Finitary Algebraic Logic." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 35, no. 4 (1989): 321–32. http://dx.doi.org/10.1002/malq.19890350405.

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Hsiang, Jieh, and Anita Wasilewska. "Automating Algebraic Proofs in Algebraic Logic." Fundamenta Informaticae 28, no. 1,2 (1996): 129–40. http://dx.doi.org/10.3233/fi-1996-281208.

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van Alten, C. J. "The finite model property for knotted extensions of propositional linear logic." Journal of Symbolic Logic 70, no. 1 (March 2005): 84–98. http://dx.doi.org/10.2178/jsl/1107298511.

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AbstractThe logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: . It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property with respect to its algebraic semantics and hence that the logic is decidable.
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Font, Josep Maria, and Miquel Rius. "An abstract algebraic logic approach to tetravalent modal logics." Journal of Symbolic Logic 65, no. 2 (June 2000): 481–518. http://dx.doi.org/10.2307/2586552.

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AbstractThis paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their “A General Algebraic Semantics for Sentential Logics”. The logics studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo. Landini and Ziliani, at the suggestion of the late Antonio Monteiro.
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ALBUQUERQUE, HUGO, JOSEP MARIA FONT, and RAMON JANSANA. "COMPATIBILITY OPERATORS IN ABSTRACT ALGEBRAIC LOGIC." Journal of Symbolic Logic 81, no. 2 (June 2016): 417–62. http://dx.doi.org/10.1017/jsl.2015.39.

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AbstractThis paper presents a unified framework that explains and extends the already successful applications of the Leibniz operator, the Suszko operator, and the Tarski operator in recent developments in abstract algebraic logic. To this end, we refine Czelakowski’s notion of an S-compatibility operator, and introduce the notion of coherent family of S-compatibility operators, for a sentential logic S. The notion of coherence is a restricted property of commutativity with inverse images by surjective homomorphisms, which is satisfied by both the Leibniz and the Suszko operators. We generalize several constructions and results already existing for the mentioned operators; in particular, the well-known classes of algebras associated with a logic through each of them, and the notions of full generalized model of a logic and a special kind of S-filters (which generalizes the less-known notion of Leibniz filter). We obtain a General Correspondence Theorem, extending the well-known one from the theory of protoalgebraic logics to arbitrary logics and to more general operators, and strengthening its formulation. We apply the general results to the Leibniz and the Suszko operators, and obtain several characterizations of the main classes of logics in the Leibniz hierarchy by the form of their full generalized models, by old and new properties of the Leibniz operator, and by the behaviour of the Suszko operator. Some of these characterizations complete or extend known ones, for some classes in the hierarchy, thus offering an integrated approach to the Leibniz hierarchy that uncovers some new, nice symmetries.
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Dissertations / Theses on the topic "Algebraic logic"

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Albuquerque, Hugo Cardoso. "Operators and strong versions of sentential logics in Abstract Algebraic Logic." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/394003.

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This dissertation presents the results of our research on some recent devel-opments in Abstract Algebraic Logic (AAL), namely on the Suszko operator, the Leibniz filters, and truth-equational logics. Part I builts and develops an abstract framework which unifies under a common treatment the study of the Leibniz, Suszko, and Frege operators in AAL. Part II generalizes the theory of the strong version of protoalgebraic logics, started in, to arbitrary sentential logics. The interplay between several Leibniz- and Suszko-related notions led us to consider a general framework based upon the notion of S-operator (inspired by that of "mapping compatible with S-filters" of Czelakowski), which encompasses the Leibniz, Suszko, and Frege operators. In particular, when applied to the Leibniz and Suszko operators, new notions of Leibniz and Suszko S-filters arise as instances of more general concepts inside the abstract framework built. The former generalizes the existing notion of Leibniz filter for protoalgebraic logics to arbitrary logics, while the latter is introduced here for the first time. Sev-eral results, both known and new, follow quite naturally inside this framework, again by instantiating it with the Leibniz and Suszko operators. Among the main new results, we prove a General Correspondence Theorem (Theorem ??), which generalizes Blok and Pigozzi's well-known Correspondence Theorem for protoalgebraic logics, as well as Czelakowski's less known Correspondence The-orem for arbitrary logics. We characterize protoalgebraic logics in terms of the Suszko operator as those logics in which the Suszko operator commutes with inverse images by surjective homomorphisms (Theorem ??). We characterize truth-equational logics in terms of their (Suszko) S-filters (Theorem ??), in terms of their full g-models (Corollary ??), and in terms of the Suszko operator, a characterization which strengthens that of Raftery, as those logics in which the Suszko operator is a structural representation from the set of S-filters to the set of AIg(S)-relative congruences, on arbitrary algebras (Theorem ??). Finally, we prove a new Isomorphism Theorem for protoalgebraic logics (Theorem ??), in the same spirit of the famous one for algebraizable logics and for weakly algebraizable logics. Endowed with a notion of Leibniz filter applicable to any logic, we are able to generalize the theory of the strong version of a protoalgebraic logic developed by Font and Jansana to arbitrary sentential logics. Given a sentential logic 5, its strong version St is the logic induced by the class of matrices whose truth set is Leibniz filter. We study three definability criteria of Leibniz filters: equational, explicit and logical definability. Under (any of) these assumptions, we prove that the St-filters coincide with Leibniz S-filters on arbitrary algebras. Finally, we apply the general theory developed to a wealth of non-protoalgebraic log-ics covered in the literature. Namely, we consider Positive Modal Logic P,A4,C, Belnap's logic B, the subintuitionistic logics w1C, and Visser's logic VP,C, and Lukasiewicz's infinite-valued logic preserving degrees of truth. We also consider the generalization of the last example mentioned to logics preserving degrees of truth from varieties of integral commutative residuated lattices, and further generalizations to the non-integral case, as well as to the case without multi-plicative constant. We classify all the examples investigated inside the Leibniz and Frege hierarchies. While none of the logics studied is protoalgebraic, all the respective strong versions are truth-equational.
Aquesta dissertació presenta els resultats de la nostra recerca sobre alguns temes recents en Lògica Algebraica Abstracta (LAA), concretament, l'operador de Suszko, els filtres de Leibniz, i les lògiques truth-equacionals. La interacció entre vàries nocións relacionades amb els operadors de Leibniz i de Suszko ens va portar a considerar un marc general basat en la noció de S-operador, que abasta els operadors de Leibniz, de Suszko, i de Frege, unificant així aquests tres operadors paradigmàtics de la LAA sota un mateix tractament.
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Engstrom, Ronald W. Retzer Kenneth A. "The effects of logic on achievement in intermediate algebra." Normal, Ill. : Illinois State University, 1988. http://www.mlb.ilstu.edu/articles/dissertations/8818710.PDF.

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Thesis (D.A.)--Illinois State University, 1988.
Title from title page screen, viewed Oct. 13, 2004. Dissertation Committee: Kenneth A. Retzer (chair), Lynn H. Brown, John A. Dossey, Lotus D. Hershberger, Albert D. Otto, Walter D. Pierce. Includes bibliographical references (leaves 97-102) and abstract. Also available in print.
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Esteban, María. "Duality Theory and Abstract Algebraic Logic." Doctoral thesis, Universitat de Barcelona, 2013. http://hdl.handle.net/10803/125336.

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In this thesis we present the results of our research on duality theory for non-classical logics under the point of view of Abstract Algebraic Logic (AAL). Firstly, we propose an abstract Spectral-like duality and an abstract Priestley-style duality for every filter distributive finitary congruential logic with theorems. This proposal aims to unify the various dualities for concrete logics that we find in the literature, by showing the abstract template in which all of them fit. Secondly, the dual correspondence of some logical properties is examined. This serves to reveal the connection between our abstract dualities and the concrete dualities related wot concrete logics. We apply those results to get new dualities for suitable expansions of a well-known logic: the implicative fragment of intuitionistic logic. Finally, we develop a new strategy that can be modularly applied to simplify some of the dualities obtained. The first part of the dissertation is devoted to introduce the preliminaries and the basic notation. In Chapter 1 we fix the mathematical concepts that we assume the reader is familiar with. Of particular interest is the section in which we introduce the basic concepts of AAL, such as "S-filter" or "S-algebra". The notion of "closure operator" plays a fundamental role in AAL, as well as in our dissertation. The notions of filter and ideal associated with a closure operator, and the separation lemmas between them are studied in detail in Chapter 2. Moreover, we briefly review the literature on duality theory for non classical logics in Chapter 3. In the second part of the dissertation we present an abstract view of the duality theory for non-classical logics. In Chapter 4 we review previous works on this topic, in which our work relies, and we introduce the notions of "referential algebra", "irreducible and optimal S-filter" and "S-semilattice". This lead us to identify a set of necessary conditions that a logic should satisfy in order to develop a Spectra-like/Priestley-style duality for it. These conditions are: "filter distributivity","congruentiality", "finitarity" and "having theorems". Moreover, we carry out a brief digression in which we argue how those notions can also be used to develop an abstract theory of canonical extensions. The core of the proposed theory consists of the definitions of dual objects and morphisms, for the category of S-algebras and homomorphisms, for any logic S that satisfies the mentioned properties. In Chapter 5 we define a Spectral-like duality and a Priestley-style duality for filter distributive finitary congruential logics with theorems, and we prove the respective duality theorems. Due to the abstraction of our approach, we obtain that the objects of both categories involved in the duality posses algebraic nature. However, through the analysis of the dual correspondence of several well-known logical properties, we can simplify the definitions of the dual categories, provided the logic under consideration satisfies such good logical properties. This analysis is interesting under the point of view of AAL, since our results can be regarded as bridge theorems between logical properties and properties of a Kripke-style semantics. And it is also interesting under the point of view of duality theory, since it confirms the strength of duality theory, that can be developed in a modular way beyond the distributive lattice setting. Moreover, our analysis shows the connection of the general theory proposed with the concrete results that we find in the literature, and lead us to explore the applications of such general theory to obtain new dualities.
En esta tesis se presentan los resultados de nuestra investigación acerca de la teoría de la dualidad para lógicas no clásicas desde el punto de vista de la Lógica Algebráica Abstracta (LAA). Un estudio preliminar de las distintas nociones de filtros e ideales lógicos asociados a las álgebras de una lógica cualquiera, y los lemas de separación entre dichas nociones nos lleva a proponer una dualidad abstracta de tipo espectral, y otra de tipo Priestley, para cada lógica congruencial, filtro distributiva, finitaria y con teoremas. Esta propuesta pretende unificar las distintas dualidades de tipo espectral y de tipo Priestley para lógicas no clásicas que encontramos en la literatura, mostrando el esquema abstracto en el que todas ellas encajan e identificando. En segundo lugar es examinada la correspondencia dual de algunas propiedades lógicas, como la propiedad de la conjunción, la propiedad de la disyunción, el teorema de deducción, la propiedad del elemento inconsistente o la propiedad de introducción de la modalidad. Esto sirve, por una parte, para revelar la conexión que existe entre las dualidades abstractas propuestas y las dualidades concretas relacionadas con lógicas no clásicas que habían sido estudiadas previamente, y por otra parte, para obtener nuevas dualidades. Centrándonos en el fragmento implicativo de la lógica intuicionista y en sus expansiones que son filtro distributivas, congruenciales, finitarias y con teoremas, mostramos cómo las dualidades que habían sido estudiadas para algunas de esas lógicas se pueden obtener como casos particulares de la teoría general. Además obtenemos nuevas dualidades para varias de dichas expansiones, algunas de las cuales pueden ser simplificadas dado que las lógicas tienen buenas propiedades. Finalmente, desarrollamos una nueva estrategia que puede ser aplicada de forma modular para simplificar algunas de las dualidades obtenidas. En conclusión, en esta tesis se muestra que la Lógica Algebráica Abstracta provee un marco general teórico apropiado para desarrollar una teoría abstracta de la dualidad para lógicas no clásicas. Dicha teoría uniformiza los diferentes resultados de la literatura, y de ella se deducen nuevos resultados.
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Pretnar, Matija. "Logic and handling of algebraic effects." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4611.

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In the thesis, we explore reasoning about and handling of algebraic effects. Those are computational effects, which admit a representation by an equational theory. Their examples include exceptions, nondeterminism, interactive input and output, state, and their combinations. In the first part of the thesis, we propose a logic for algebraic effects. We begin by introducing the a-calculus, which is a minimal equational logic with the purpose of exposing distinct features of algebraic effects. Next, we give a powerful logic, which builds on results of the a-calculus. The types and terms of the logic are the ones of Levy’s call-by-push-value framework, while the reasoning rules are the standard ones of a classical multi-sorted first-order logic with predicates, extended with predicate fixed points and two principles that describe the universality of free models of the theory representing the effects at hand. Afterwards, we show the use of the logic in reasoning about properties of effectful programs, and in the translation of Moggi’s computational ¸-calculus, Hennessy-Milner logic, and Moggi’s refinement of Pitts’s evaluation logic. In the second part of the thesis, we introduce handlers of algebraic effects. Those not only provide an algebraic treatment of exception handlers, but generalise them to arbitrary algebraic effects. Each such handler corresponds to a model of the theory representing the effects, while the handling construct is interpreted by the homomorphism induced by the universal property of the free model. We use handlers to describe many previously unrelated concepts from both theory and practice, for example CSS renaming and hiding, stream redirection, timeout, and rollback.
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Townsend, Brian E. "Examining secondary students algebraic reasoning flexibility and strategy use /." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4131.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2005.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 14, 2006) Vita. Includes bibliographical references.
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Lu, Weiyun. "Topics in Many-valued and Quantum Algebraic Logic." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35173.

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Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how the partiality of their operations cause things to be vastly more complicated than their totally defined classical analogues. In the final chapter, we discuss coordinatization of MV algebras and prove some new theorems and construct some new concrete examples, connecting these structures up (requiring a detour through effect algebras!) to boolean inverse semigroups.
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Phillips, Caitlin. "An algebraic approach to dynamic epistemic logic." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=86767.

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In reasoning about multi-agent systems, it is important to look beyond the realm of propositional logic and to reason about the knowledge of agents within the system, as what they know about the environment will affect how they behave. A useful tool for formalizing and analyzing what agents know is epistemic logic, a modal logic developed by philosophers in the early 1960s. Epistemic logic is key to understanding knowledge in multi-agent systems, but insufficient if one wishes to study how the agents' knowledge changes over time. To do this, it is necessary to use a logic that combines dynamic and epistemic modalities, called dynamic epistemic logic. Some formalizations of dynamic epistemic logic use Kripke semantics for the states and actions, while others take a more algebraic approach, and use order-theoretic structures in their semantics. We discuss several of these logics, but focus predominantly on the algebraic framework for dynamic epistemic logic.
Past approaches to dynamic epistemic logic have typically been focused on actions whose primary purpose is to communicate information from one agent to another. These actions are unable to alter the valuation of any proposition within the system. In fields such as security and economics, it is easy to imagine situations in which this sort of action would be insufficient. Instead, we expand the framework to include both communication actions and actions that change the state of the system. Furthermore, we propose a new modality which captures both epistemic and propositional changes that result from the agents' actions.
En raisonnement sur les systemes multi-agents, il est important de regarder au-dela du domaine de la logique propositionnelle et de raisonner sur les con- naissances des agents au sein du syst`eme, parce que ce qu'ils savent au sujet de l'environnement influe sur la mani`ere dont ils se comportent. Un outil utile pour l'analyse et la formalisation de ce que les agents savent, est la logique epistemique, une logique modale developpee par les philosophes du debut des annees 1960. La logique epistemique est la cle de la comprehension des connaissances dans les systemes multi-agents, mais elle est insuffisante si l'on veut etudier la facon dont la connaissance des agents evolue a travers le temps. Pour ce faire, il est necessaire de recourir a une logique qui allie des modalites dynamiques et epistemiques, appele la logique epistemique dynamique. Certaines formalisations de la logique epistemique dynamique utilisent la semantique de Kripke pour les etats et les actions, tandis que d'autres prennent une approche algebrique, et utilisent les structures ordonne dans leur semantique. Nous discutons plusieurs de ces logiques, mais nous nous concentrons principalement sur le cadre algebrique pour la logique epistemique dynamique.
Les approches adoptees dans le passe a la logique epistemique dynamique ont generalement ete axe sur les actions dont l'objectif principal est de communiquer des informations d'un agent a un autre. Ces actions sont dans l'impossibilite de modifier l' evaluation de toute proposition au sein du systeme. Dans des domaines tels que la securite et l' economie, il est facile d'imaginer des situations dans lesquelles ce type d'action serait insuffisante. Au lieu de cela, nous etendons le cadre algebrique pour inclure a la fois des actions de communication et des actions qui changent l' etat du systeme. En outre, nous proposons une nouvelle modalite qui permet de capturer a la fois les changements epistemiques et les changements propositionels qui resultent de l'action des agents.
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Silva, Thiago Nascimento da. "Algebraic semantics for Nelson?s logic S." PROGRAMA DE P?S-GRADUA??O EM SISTEMAS E COMPUTA??O, 2018. https://repositorio.ufrn.br/jspui/handle/123456789/24823.

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Al?m da mais conhecida l?gica de Nelson (?3) e da l?gica paraconsistente de Nelson (?4), David Nelson introduziu no artigo de 1959 "Negation and separation of concepts in constructive systems", com motiva??es de aritm?tica e construtividade, a l?gica que ele chamou de "?". Naquele trabalho, a l?gica ? definida por meio de um c?lculo (que carece crucialmente da regra de contra??o) tendo infinitos esquemas de regras, e nenhuma sem?ntica ? fornecida. Neste trabalho n?s tomamos o fragmento proposicional de ?, mostrando que ele ? algebriz?vel (de fato, implicativo) no sentido de Blok & Pigozzi com respeito a uma classe de reticulados residuados involutivos. Assim, fornecemos a primeira sem?ntica para ? (que chamamos de ?-?lgebras), bem como um c?lculo estilo Hilbert finito equivalente ? apresenta??o de Nelson. Fornecemos um algoritmo para construir ?-?lgebras a partir de ?-?lgebras ou reticulados implicativos e demonstramos alguns resultados sobre a classe de ?lgebras que introduzimos. N?s tamb?m comparamos ? com outras l?gicas da fam?lia de Nelson, a saber, ?3 e ?4.
Besides the better-known Nelson logic (?3) and paraconsistent Nelson logic (?4), in Negation and separation of concepts in constructive systems (1959) David Nelson introduced a logic that he called ?, with motivations of arithmetic and constructibility. The logic was defined by means of a calculus (crucially lacking the contraction rule) having infinitely many rule schemata, and no semantics was provided for it. We look in the present dissertation at the propositional fragment of ?, showing that it is algebraizable (in fact, implicative) in the sense of Blok and Pigozzi with respect to a class of involutive residuated lattices. We thus provide the first known algebraic semantics for ?(we call them of ?-algebras) as well as a finite Hilbert-style calculus equivalent to Nelson?s presentation. We provide an algorithm to make ?-algebras from ?-algebras or implicative lattices and we prove some results about the class of algebras which we have introduced. We also compare ? with other logics of the Nelson family, that is, ?3 and ?4.
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PERUZZI, LUISA. "Algebraic approach to paraconsistent weak Kleene logic." Doctoral thesis, Università degli Studi di Cagliari, 2018. http://hdl.handle.net/11584/255936.

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The starting point of this work is the analysis of the logic known as Paraconsistent Weak Kleene (PWK), the 3-valued logic with two designated values defined through the weak Kleene tables. Some philosophical assumptions stand behind the introduction of non-classical logics, which is, basically allowing logics to deal with partial predicates. Despite different non-classical formalisms have found lots more success than PWK logic, this thesis highlights a very surprising connection (which can be further generalized) between such a logic on one side, and the purely algebraic theory of regular varieties, on the other. The latter has been studied in universal algebra since the '60, but had found no application in logic before. In particular, the present work is divided in two different parts, each of which makes use of different machineries and techniques: one is more logically oriented and regards the study of Paraconsistent Weak Kleene logic, under the perspective of Abstract Algebraic Logic, while the other part involves a closer study of the algebraic semantics of the mentioned logic.
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BONZIO, STEFANO. "Algebraic structures from quantum and fuzzy logics." Doctoral thesis, Università degli Studi di Cagliari, 2016. http://hdl.handle.net/11584/266667.

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This thesis concerns the wide research area of logic. In particular, the first part is devoted to analyze different kinds of relational systems (orthogonal and residuated), by investigating the properties of the algebras associated to them. The second part is focused on algebras of logic, in particular, the relationship between prominent quantum and fuzzy structures with certain semirings is proved. The last chapter concerns an application of group theory to some well known mathematical puzzles.
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Books on the topic "Algebraic logic"

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Gindikin, S. G. Algebraic Logic. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5.

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H, Andréka, Monk J. Donald 1930-, and Németi I, eds. Algebraic logic. Amsterdam: New York, 1991.

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Andréka, Hajnal, Zalán Gyenis, István Németi, and Ildikó Sain. Universal Algebraic Logic. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-14887-3.

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Kirchner, Hélène, and Giorgio Levi, eds. Algebraic and Logic Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0013814.

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Hanus, Michael, Jan Heering, and Karl Meinke, eds. Algebraic and Logic Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0026998.

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Grabowski, J., P. Lescanne, and W. Wechler, eds. Algebraic and Logic Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/3-540-50667-5.

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Kirchner, Hélène, and Wolfgang Wechler, eds. Algebraic and Logic Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/3-540-53162-9.

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Levi, Giorgio, and Mario Rodríguez-Artalejo, eds. Algebraic and Logic Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58431-5.

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Hanus, Michael, and Mario Rodríguez-Artalejo, eds. Algebraic and Logic Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61735-3.

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1947-, Blass Andreas, Zhang, Yi, 1964 Aug. 22-, and Workshop on Combinatorial Set Theory, Excellent Classes, and Schanuel Conjecture (2003 : University of Michigan), eds. Logic and its applications. Providence, R.I: American Mathematical Society, 2005.

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Book chapters on the topic "Algebraic logic"

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Kempf, George R. "Logic." In Algebraic Structures, 144–49. Wiesbaden: Vieweg+Teubner Verlag, 1995. http://dx.doi.org/10.1007/978-3-322-80278-1_19.

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Andréka, H., I. Németi, and I. Sain. "Algebraic Logic." In Handbook of Philosophical Logic, 133–247. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-017-0452-6_3.

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Gindikin, S. G. "Predicate Logic." In Algebraic Logic, 316–42. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5_12.

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Klement, Erich Peter, Radko Mesiar, and Endre Pap. "Algebraic aspects." In Trends in Logic, 21–51. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9540-7_2.

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Vingron, Shimon P. "Algebraic Minimisation." In Logic Circuit Design, 79–88. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-40673-7_7.

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Vingron, Shimon P. "Algebraic Minimisation." In Logic Circuit Design, 75–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27657-6_7.

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Gindikin, S. G. "Operations on Propositions." In Algebraic Logic, 1–21. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5_1.

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Gindikin, S. G. "Elements of Probabilistic Logic." In Algebraic Logic, 238–99. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5_10.

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Gindikin, S. G. "Multi-Valued Logics." In Algebraic Logic, 300–315. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5_11.

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Gindikin, S. G. "Logical Functions. Normal Forms." In Algebraic Logic, 22–56. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5_2.

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Conference papers on the topic "Algebraic logic"

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Liang, Fei, and Zhe Lin. "On the Decidability of Intuitionistic Tense Logic without Disjunction." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/249.

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Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.
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PAL'CHUNOV, D. E., and G. E. YAKHYAEVA. "INTERVAL FUZZY ALGEBRAIC SYSTEMS." In Proceedings of the 9th Asian Logic Conference. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772749_0014.

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Plotkin, Gordon, and Matija Pretnar. "A Logic for Algebraic Effects." In 2008 23rd Annual IEEE Symposium on Logic in Computer Science (LICS 2008). IEEE, 2008. http://dx.doi.org/10.1109/lics.2008.45.

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DOWNEY, ROD. "COMPUTABILITY, DEFINABILITY AND ALGEBRAIC STRUCTURES." In 7th and 8th Asian Logic Conferences. CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, 2003. http://dx.doi.org/10.1142/9789812705815_0004.

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Gomes, Joel Felipe Ferreira, and Vitor Rodrigues Greati. "Notes on the Logic of Perfect Paradefinite Algebras." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/wbl.2021.15777.

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This work introduces the variety of perfect paradefinite algebras (PPalgebras), consisting of De Morgan algebras enriched with a perfect operator o, which turns out to be equivalent to the variety of involutive Stone algebras (IS-algebras). The corresponding order-preserving logic PP≤ is a Logic of Formal Inconsistency, a Logic of Formal Undeterminedness, a C-system and a D-system, some of these features being evident in the proposed axiomatization of PP-algebras. After proving the mentioned algebraic equivalence, we show how to axiomatize, by means of Hilbert-style calculi, certain extensions of De Morgan algebras with a perfect operator and, in particular, the logic PP≤.
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Mardare, Radu, Prakash Panangaden, and Gordon Plotkin. "Quantitative Algebraic Reasoning." In LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2933575.2934518.

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Bogaerts, Bart, Joost Vennekens, and Marc Denecker. "Safe Inductions: An Algebraic Study." 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.2017/119.

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In many knowledge representation formalisms, a constructive semantics is defined based on sequential applications of rules or of a semantic operator. These constructions often share the property that rule applications must be delayed until it is safe to do so: until it is known that the condition that triggers the rule will remain to hold. This intuition occurs for instance in the well-founded semantics of logic programs and in autoepistemic logic. In this paper, we formally define the safety criterion algebraically. We study properties of so-called safe inductions and apply our theory to logic programming and autoepistemic logic. For the latter, we show that safe inductions manage to capture the intended meaning of a class of theories on which all classical constructive semantics fail.
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Lima Neto, Clodomir Silva, Thiago Nascimento da Silva, and Umberto Rivieccio. "Quasi-N4-lattices and their logic." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação, 2022. http://dx.doi.org/10.5753/wbl.2022.222852.

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The variety of quasi-N4-lattices (QN4) was recently introduced as a non-involutive generalization of N4-lattices (algebraic models of Nelson's paraconsistent logic). While research on these algebras is still at a preliminary stage, we know that QN4 is an arithmetical variety which possesses a ternary as well as a quaternary deductive term, enjoys equationally definable principal congruences and the strong congruence extension property. We furthermore have recently introduced an algebraizable logic having QN4 as its equivalent semantics. In this contribution we report on the results obtained so far on this class of algebras and on its logical counterpart.
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YUUICHI, KAWAGUCHI. "A COMMON STRUCTURE OF LOGICAL AND ALGEBRAIC ALGORITHMS." In 7th and 8th Asian Logic Conferences. CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, 2003. http://dx.doi.org/10.1142/9789812705815_0009.

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Beffara, Emmanuel. "An Algebraic Process Calculus." In 2008 23rd Annual IEEE Symposium on Logic in Computer Science (LICS 2008). IEEE, 2008. http://dx.doi.org/10.1109/lics.2008.40.

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Reports on the topic "Algebraic logic"

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IOWA STATE UNIV AMES DEPT OF MATHEMATICS. Applications of Algebraic Logic and Universal Algebra to Computer Science. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada210556.

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Obua, Steven. Abstraction Logic. Recursive Mind, November 2021. http://dx.doi.org/10.47757/abstraction.logic.2.

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Abstraction Logic is introduced as a foundation for Practical Types and Practal. It combines the simplicity of first-order logic with direct support for variable binding constants called abstractions. It also allows free variables to depend on parameters, which means that first-order axiom schemata can be encoded as simple axioms. Conceptually abstraction logic is situated between first-order logic and second-order logic. It is sound with respect to an intuitive and simple algebraic semantics. Completeness holds for both intuitionistic and classical abstraction logic, and all abstraction logics in between and beyond.
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Obua, Steven. Abstraction Logic. Steven Obua (as Recursive Mind), October 2021. http://dx.doi.org/10.47757/abstraction.logic.1.

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Abstraction Logic is introduced as a foundation for Practical Types and Practal. It combines the simplicity of first-order logic with direct support for variable binding constants called abstractions. It also allows free variables to depend on parameters, which means that first-order axiom schemata can be encoded as simple axioms. Conceptually abstraction logic is situated between first-order logic and second-order logic. It is sound and complete with respect to an intuitive and simple algebraic semantics.
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Baader, Franz. Concept Descriptions with Set Constraints and Cardinality Constraints. Technische Universität Dresden, 2017. http://dx.doi.org/10.25368/2022.232.

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We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of ALCQ. To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than ALCQ, we are able to show that the complexity of reasoning in it is the same as in ALCQ, both without and with TBoxes.
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Baader, Franz, Silvio Ghilardi, and Cesare Tinelli. A New Combination Procedure for the Word Problem that Generalizes Fusion Decidability Results in Modal Logics. Technische Universität Dresden, 2003. http://dx.doi.org/10.25368/2022.130.

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Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics - which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics.
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Barnett, Janet Heine. Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce. Washington, DC: The MAA Mathematical Sciences Digital Library, July 2013. http://dx.doi.org/10.4169/loci003997.

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