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Journal articles on the topic 'Classical or Formal Logic'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Kakas, Antonis. "Informalizing Formal Logic." Informal Logic 39, no. 2 (2019): 169–204. http://dx.doi.org/10.22329/il.v39i2.5169.

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This paper presents a way in which formal logic can be understood and reformulated in terms of argumentation that can help us unify formal and informal reasoning. Classical deductive reasoning will be expressed entirely in terms of notions and concepts from argumentation so that formal logical entailment is equivalently captured via the arguments that win between those supporting concluding formulae and arguments supporting contradictory formulae. This allows us to go beyond Classical Logic and smoothly connect it with human reasoning, thus providing a uniform argumentation-based view of both

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Карниэлли, У. "Formal polynomials, heuristics and proofs in logic." Logical Investigations 16 (April 7, 2010): 280–94. http://dx.doi.org/10.21146/2074-1472-2010-16-0-280-294.

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This note surveys some previous results on the role of formal polynomials as a representation method for logical derivation in classical and non-classical logics, emphasizing many-valued logics, paraconsistent logics and modal logics. It also discusses the potentialities of formal polynomials as heuristic devices in logic and for expressing certain meta-logical properties, as well as pointing to some promising generalizations towards algebraic geometry.

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Kazumi, Inoue. "Dialectical Contradictions and Classical Formal Logic." International Studies in the Philosophy of Science 28, no. 2 (2014): 113–32. http://dx.doi.org/10.1080/02698595.2014.932526.

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Oliveira, Kleidson Êglicio Carvalho da Silva. "Paraconsistent Logic Programming in Three and Four-Valued Logics." Bulletin of Symbolic Logic 28, no. 2 (2022): 260. http://dx.doi.org/10.1017/bsl.2021.34.

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AbstractFrom the interaction among areas such as Computer Science, Formal Logic, and Automated Deduction arises an important new subject called Logic Programming. This has been used continuously in the theoretical study and practical applications in various fields of Artificial Intelligence. After the emergence of a wide variety of non-classical logics and the understanding of the limitations presented by first-order classical logic, it became necessary to consider logic programming based on other types of reasoning in addition to classical reasoning. A type of reasoning that has been well stu

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Raikhert, Kostiantyn. "LOGIC, RHETORIC, AND HEURISTIC AS ARGUMENTATION THEORIES: AN OUTLINE." Doxa, no. 1(41) (June 27, 2024): 17–25. https://doi.org/10.18524/2410-2601.2024.1(41).316155.

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The study speculates about logic, rhetoric and heuristics as kinds of argumentation theory. Contemporary argumentation theories are informal logics, and it takes work to distinguish between them. The ultimate aim of traditional formal logic is to study proofs and refutations as logical forms, i.e., argumentation, so traditional logic can be seen as an argumentation theory. Classical and non-classical formal logics have traditional formal logic at their core. It allows them to be seen as argumentation theories. Rhetoric uses argumentation as a means of persuasion, and argument is understood muc

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Ciuni, Roberto, and Massimiliano Carrara. "Normality operators and classical recapture in many-valued logic." Logic Journal of the IGPL 28, no. 5 (2018): 657–83. http://dx.doi.org/10.1093/jigpal/jzy055.

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AbstractIn this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some (or all) of the three properties, namely subclassicality and two properties that we call fixed-point negation property and conservativeness. In the second part of the

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Angel, Garrido, and Yuste Piedad. "BRAIN Journal - Controversies about the Introduction of Non-Classical Logics." BRAIN - Broad Research in Artificial Intelligence and Neuroscience 5, no. 1-5 (2014): 34–45. https://doi.org/10.5281/zenodo.1044117.

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ABSTRACT Logic is a set of well-formed formulae, along with an inference relation. But the Classical Logic is bivalent; for this reason, very limited to solve problems with uncertainty on the data. It is well-known that Artificial Intelligence requires Logic. Because its Classical version shows too many insufficiencies, it is very necessary to introduce more sophisticated tools, as may be NonClassical Logics; amongst them, Fuzzy Logic, Modal Logic, Non-Monotonic Logic, Para-consistent Logic, and so on. All them in the same line: against the dogmatism and the dualistic vision of the world: abso

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BRAUER, ETHAN. "RELEVANCE FOR THE CLASSICAL LOGICIAN." Review of Symbolic Logic 13, no. 2 (2018): 436–57. http://dx.doi.org/10.1017/s1755020318000382.

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AbstractAlthough much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to an argument when it contributes to the validity of that argument. I then argue that the sequents which best embod

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Ciuciura, Janusz. "Intuitionistic Implication and Logics of Formal Inconsistency." Axioms 13, no. 11 (2024): 738. http://dx.doi.org/10.3390/axioms13110738.

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Logics of Formal Inconsistency (LFI for short) are a class of paraconsistent logics that validate the principle of gentle explosion, meaning that any formula can be derived from the set of formulas: ∘α, α and ∼α. A unique feature of LFI is the use of the symbol ‘∘’ to represent notions of consistency at the object-language level. These logics are simple in essence, built upon all the axiom schemas of positive classical logic, axioms for negation and the so-called ‘consistency operator’ ∘, with the only inference rule being detachment. In this paper, we propose an alternative foundation for LFI

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Sherry, David. "Formal Logic for Informal Logicians." Informal Logic 26, no. 2 (2008): 199. http://dx.doi.org/10.22329/il.v26i2.444.

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Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without

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Yurkevych, Olena. "LOGIC IN PHILOSOPHICAL REASONING. PHILOSOPHICAL LOGIC." Bulletin of Yaroslav Mudryi National Law University. Series: philosophy, philosophy of law, political science, sociology : The collection of scientific papers 1, no. 60 (2024): 42–55. https://doi.org/10.21564/2663-5704.60.299625.

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<em>The article is devoted to the study of the problem of the relationship between logic and philosophy in the historical-philosophical context and at the current stage of the development of science. Features of the development of traditional and classical formal and non-classical informal logic, corresponding metalogical argumentation are considered. The stage of the formation of philosophical logic is determined, conclusions are drawn regarding the methodological significance of philosophical logic for the development of philosophical knowledge.</em>

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CARNIELLI, WALTER, MARCELO E. CONIGLIO, RODRIGO PODIACKI, and TARCÍSIO RODRIGUES. "ON THE WAY TO A WIDER MODEL THEORY: COMPLETENESS THEOREMS FOR FIRST-ORDER LOGICS OF FORMAL INCONSISTENCY." Review of Symbolic Logic 7, no. 3 (2014): 548–78. http://dx.doi.org/10.1017/s1755020314000148.

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AbstractThis paper investigates the question of characterizing first-orderLFIs (logics of formal inconsistency) by means of two-valued semantics.LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logicQmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent logics, supplying

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Bala, Romi, and Hemant Pandey. "Mathematical Logic: Foundations and Beyond." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9, no. 3 (2018): 1405–11. http://dx.doi.org/10.61841/turcomat.v9i3.14599.

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Mathematical logic serves as the cornerstone of formal reasoning, providing precise tools for analyzing the structure and validity of arguments. This paper offers a comprehensive exploration of key topics in mathematical logic, spanning from classical propositional and predicate logic to modal logic and non-classical logics. It examines the syntactic and semantic aspects of various logical systems, delves into proof theory and computational complexity, and explores applications in diverse fields such as mathematics, computer science, philosophy, and linguistics. By elucidating the fundamental

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Seldin, Jonathan P. "On the role of implication in formal logic." Journal of Symbolic Logic 65, no. 3 (2000): 1076–114. http://dx.doi.org/10.2307/2586689.

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AbstractEvidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a “classical” version of the system. They can also be extended to a system with a restricted set of rules for implication: the result is a system of in

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Mendonça, Bruno R., and Walter A. Carnielli. "Fraïssé’s theorem for logics of formal inconsistency." Logic Journal of the IGPL 28, no. 5 (2018): 1060–72. http://dx.doi.org/10.1093/jigpal/jzy073.

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Abstract We prove that the minimal Logic of Formal Inconsistency (LFI) $\mathsf{QmbC}$ (basic quantified logic of formal inconsistency) validates a weaker version of Fraïssé’s theorem (FT). LFIs are paraconsistent logics that relativize the Principle of Explosion only to consistent formulas. Now, despite the recent interest in LFIs, their model-theoretic properties are still not fully understood. Our aim in this paper is to investigate the situation. Our interest in FT has to do with its fruitfulness; the preservation of FT indicates that a number of other classical semantic properties can be

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Antunes, Henrique. "Enthymematic classical recapture 1." Logic Journal of the IGPL 28, no. 5 (2018): 817–31. http://dx.doi.org/10.1093/jigpal/jzy061.

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AbstractPriest (2006, Ch.8, 2nd edn. Oxford University Press), argues that classical reasoning can be made compatible with his preferred (paraconsistent) logical theory by proposing a methodological maxim authorizing the use of classical logic in consistent situations. Although Priest has abandoned this proposal in favour of the one in G. Priest (1991, Stud. Log., 50, 321–331), I shall argue that due to the fact that the derivability adjustment theorem holds for several logics of formal (in)consistency (cf. W. A. Carnielli and M. E. Coniglio, 2016, Springer), these paraconsistent logics are pa

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Kolotilova, Nataliia. "FORMAL AND INFORMAL LOGIC IN THE SPOD АND VUCA WORLDS". Politology bulletin, № 93 (2024): 54–63. https://doi.org/10.17721/2415-881x.2024.93.54-63.

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The article deals with the formation and development of classical, nonclassical, informal logic and argumentation theory in the context of concepts SPOD and VUCA world. It has been established that modern formal logic (classical and non-classical) can act as a model of both SPOD world and VUCA world. It has been found that the means of classical logic, primarily the fundamental principle of twovalued, allow us to describe the SPOD world with its steady, predictable, ordinary and definite. It has been revealed that the theories of non-classical logic, in particular many-valued and modal, alread

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Coniglio, Marcelo E., Aldo Figallo-Orellano, and Ana C. Golzio. "First-order swap structures semantics for some logics of formal inconsistency." Journal of Logic and Computation 30, no. 6 (2020): 1257–90. http://dx.doi.org/10.1093/logcom/exaa027.

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Abstract The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous approaches to quantified LFIs presented in the literature. The case of QmbC, the simpler quantified LFI e

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Restovic, Ivan. "Feminist Logic, Literally." Australasian Journal of Logic 20, no. 2 (2023): 318–47. http://dx.doi.org/10.26686/ajl.v29i2.8291.

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   I this paper, I discuss Plumwood’s feminist logic program. I argue both in favor of her general stance in feminist philosophy of logic and her more specific feminist critique of classical logic. Plumwood’s general position is in opposition with (I think it’s safe to say) the prevailing view in analytic philosophy about the relation between formal logic and feminist theory, according to which feminist theory cannot say anything about or against logic proper, since the issues of oppression are external to logic as a (formal) discipline. Connected to this externalism is a non

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Japaridze, Giorgi, and Bikal Lamichhane. "Cirquent Calculus in a Nutshell." Logical Investigations 28, no. 1 (2022): 125–41. http://dx.doi.org/10.21146/2074-1472-2022-28-1-125-141.

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This paper is a brief presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility of sharing of subexpressions/subresources between different expressions/resources. This is achieved by dealing with circuit-style constructs, termed cirquents, instead of formulas, sequents or other tree-like structures. The approach exhibits greater expressiveness, flexibility and efficiency compared to the more traditional proof-theoretic approaches. The need for substa

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Valentini, Silvio. "Every countably presented formal topology is spatial, classically." Journal of Symbolic Logic 71, no. 2 (2006): 491–500. http://dx.doi.org/10.2178/jsl/1146620155.

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Carnielli, Walter, Marcelo E. Coniglio, and Abilio Rodrigues. "Recovery operators, paraconsistency and duality." Logic Journal of the IGPL 28, no. 5 (2019): 624–56. http://dx.doi.org/10.1093/jigpal/jzy054.

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Abstract There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics of formal inconsistency (LFIs) and by the logics of formal undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the validity of the principle of excluded middle in a

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23

Basti, Gianfranco. "The Philosophy of Nature of the Natural Realism. The Operator Algebra from Physics to Logic." Philosophies 7, no. 6 (2022): 121. http://dx.doi.org/10.3390/philosophies7060121.

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This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both of the “extensional” logics of the pur

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Picollo, Lavinia. "Truth in a Logic of Formal Inconsistency: How classical can it get?" Logic Journal of the IGPL 28, no. 5 (2018): 771–806. http://dx.doi.org/10.1093/jigpal/jzy059.

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AbstractWeakening classical logic is one of the most popular ways of dealing with semantic paradoxes. Their advocates often claim that such weakening does not affect non-semantic reasoning. Recently, however, Halbach and Horsten (2006) have shown that this is actually not the case for Kripke’s fixed-point theory based on the Strong Kleene evaluation scheme. Feferman’s axiomatization $\textsf{KF}$ in classical logic is much stronger than its paracomplete counterpart $\textsf{PKF}$, not only in terms of semantic but also in arithmetical content. This paper compares the proof-theoretic strength o

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Japaridze, Giorgi. "Computability logic: Giving Caesar what belongs to Caesar." Logical Investigations 25, no. 1 (2019): 100–119. http://dx.doi.org/10.21146/2074-1472-2019-25-1-100-119.

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The present article is a brief informal survey o$\textit {computability logic}$ (CoL). This relatively young and still evolving nonclassical logic can be characterized as a formal theory of computability in the same sense as classical logic is a formal theory of truth. In a broader sense, being conceived semantically rather than proof-theoretically, CoL is not just a particular theory but an ambitious and challenging long-term project for redeveloping logic.   In CoL, logical operators stand for operations on computational problems, formulas represent such problems, and their "trut

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Petik, Jaroslav. "PHILOSOPHICAL PROBLEMS OF THE MENTALISTIC LOGIC." Sophia. Human and Religious Studies Bulletin 14, no. 2 (2019): 38–43. http://dx.doi.org/10.17721/sophia.2019.14.9.

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Paper deals with philosophical problems of mentalistic logic. Mentalistic logic is a formal system that concentrates on underpinning processes of mental life instead of certain elements of extrinsic rational behavior as most of existing logics (like BDI calculi) do. The project is compared to the existing logics of actions. Mentalistic logic is patually a formal system and partually phenomenological study of human mind. We presume formal signs such as propositions and modal operators refer to mental states and can describe the general structure of mental activity. That is purely the approach o

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Hernández Ortiz, Héctor. "A real argument to defy classical logic." Principia: an international journal of epistemology 28, no. 1 (2024): 7–13. http://dx.doi.org/10.5007/1808-1711.2024.e96699.

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In this paper, an argument by Fisher (2004) is formalized and evaluated by means of some tools of classical logic. The argument presented by Fisher is a version of a piece of reasoning of great historical importance known as Pascal’s Wager. According to Fisher, “this is a fascinating piece of reasoning. It is complex and important and hard to handle”. Here is shown that, although formal logical analysis has limitations to evaluate everyday deductive arguments, it is perfectly capable to formalize and evaluate Fisher’s argument. This should show that its usefulness is undeniable.

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Karpenko, Ivan. "Consistency and Some Other Requirements of a Formal Theory in the Context of Multiverse Models." Studia Humana 13, no. 4 (2024): 23–34. http://dx.doi.org/10.2478/sh-2024-0022.

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Abstract The paper is devoted to the problem of describing reality in the language of mathematics and logic in connection with intellectual intuition. The question raised is how the basic requirements of mathematical theory and logic will change if some of the multiverse models of modern physics are taken as the basis. Mathematics is considered in the context of various historical approaches. It is shown that some of the well-known requirements of a formal theory (such as consistency) may begin to play a different role if the multiverse hypothesis is accepted. In the framework of theories base

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Japaridze, Giorgi. "Towards applied theories based on computability logic." Journal of Symbolic Logic 75, no. 2 (2010): 565–601. http://dx.doi.org/10.2178/jsl/1268917495.

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AbstractComputability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, “truth” means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with respect to the semantics of CL. Conservatively exte

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SCHECHTER, JOSHUA. "WEAKLY CLASSICAL THEORIES OF IDENTITY." Review of Symbolic Logic 4, no. 4 (2011): 607–44. http://dx.doi.org/10.1017/s1755020311000220.

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AbstractThere are well-known quasi-formal arguments that identity is a “strict” relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard classical theory but which does not validate the formal analogues of (1)–(3). The core idea is simple:

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Kuzmin, Egor V. "LTL-Specification of Counter Machines." Modeling and Analysis of Information Systems 28, no. 1 (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 widel

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Kosilova, Elena V. "UNDERSTANDING IN MATHEMATICS: FROM CLASSICS TO NON-CLASSICS AND POST-NON-CLASSICS. PART ONE." RSUH/RGGU Bulletin. Series Philosophy. Social Studies. Art Studies 1, no. 1 (2022): 10–22. http://dx.doi.org/10.28995/2073-6401-2022-1-10-22.

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The article deals with an issue of understanding in the classical, non-classical and post-non-classical tradition by the example of understanding mathematics. The prime part of the article looks at the matter of classical and post-non-classical science and poses an issue of understanding. Mathematics itself can be classical or non-classical, as well as logic. Classical logic and mathematics were characterized by intuitive clarity and connection with the world, whether it be the surrounding world or the world of thought. Non-classical logic and mathematics are “sciences-in-themselves”, the only

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Friedman, Harvey M., and Andrej Ščedrov. "On the quantificational logic of intuitionistic set theory." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 1 (1986): 5–10. http://dx.doi.org/10.1017/s0305004100063854.

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Formal propositional logic describing the laws of constructive (intuitionistic) reasoning was first proposed in 1930 by Heyting. It is obtained from classical pro-positional calculus by deleting the Law of Excluded Middle, and it is usually referred to as Heyting's (intuitionistic) propositional calculus ([9], §§23, 19) (we write HPP in short). Formal logic involving predicates and quantifiers based on HPP is called Heyting's (intuitionistic) predicate calculus ([9], §§31, 19) (we write HPR in short).

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Cieśliński, Cezary. "Interpreting the compositional truth predicate in models of arithmetic." Archive for Mathematical Logic 60, no. 6 (2021): 749–70. http://dx.doi.org/10.1007/s00153-020-00758-z.

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AbstractWe present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.

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KHALED, MOHAMED, GERGELY SZÉKELY, KOEN LEFEVER, and MICHÈLE FRIEND. "DISTANCES BETWEEN FORMAL THEORIES." Review of Symbolic Logic 13, no. 3 (2019): 633–54. http://dx.doi.org/10.1017/s1755020319000558.

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AbstractIn the literature, there have been several methods and definitions for working out whether two theories are “equivalent” (essentially the same) or not. In this article, we do something subtler. We provide a means to measure distances (and explore connections) between formal theories. We introduce two natural notions for such distances. The first one is that of axiomatic distance, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of conceptual distance which measures the minimum number of concepts that distinguish two theories.

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Khomenko, Iryna, and Yaroslav Shramko. "LOGIC AND PHILOSOPHY: LINES OF INTERACTION." Bulletin of Taras Shevchenko National University of Kyiv. Philosophy, no. 4 (2021): 14–23. http://dx.doi.org/10.17721/2523-4064.2021/4-2/12.

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In this paper, we argue in favour of the applicability of logical tools for the analysis of various philosophical issues. Different systems of the modern non-classical (philosophical) logic are considered, and a promising approach of research represented by informal logic. We conclude with some remarks about the prospects for a fruitful interaction of modern formal and informal logic with philosophical knowledge.

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Huang, Qifan, Li Zhou, Wang Fang, Mengyu Zhao, and Mingsheng Ying. "Efficient Formal Verification of Quantum Error Correcting Programs." Proceedings of the ACM on Programming Languages 9, PLDI (2025): 1068–93. https://doi.org/10.1145/3729293.

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Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion logic and a program logic specifically crafted for QEC programs and establish a sound proof system. We then develop an efficient method for handling verification conditions (VCs) of QEC programs: for Pauli errors, the VCs are reduced to classical assertions that can be solved by SMT solvers, and for non-Pauli errors, we provide a heuristic algorithm. We form

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Liu, Chanjuan, Ruining Zhang, Yu Zhang, and Enqiang Zhu. "A Formal Representation for Intelligent Decision-Making in Games." Mathematics 11, no. 22 (2023): 4567. http://dx.doi.org/10.3390/math11224567.

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The study of intelligent game-playing has gained tremendous attention in the past few decades. The recent development of artificial intelligence (AI) players (e.g., the Go player AlphaGo) has made intelligent game-playing even more prominent in both academia and industry. The performance of state-of-the-art AI players benefits greatly from machine learning techniques, based on which, players can make estimations and decisions even without understanding the games. Although AI machines show great superiority over humans in terms of data processing and complex computation, there remains a vast di

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Poythress, Vern. "A semiotic analysis of multiple systems of logic: using tagmemic theory to assess the usefulness and limitations of formal logics, and to produce a mathematical lattice model including multiple systems of logic." Semiotica 2022, no. 244 (2022): 145–62. http://dx.doi.org/10.1515/sem-2020-0051.

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Abstract Tagmemic theory as a semiotic theory can be used to analyze multiple systems of logic and to assess their strengths and weaknesses. This analysis constitutes an application of semiotics and also a contribution to understanding of the nature of logic within the context of human meaning. Each system of logic is best adapted to represent one portion of human rationality. Acknowledging this correlation between systems and their targets helps explain the usefulness of more than one system. Among these systems, the two-valued system of classical logic takes its place. All the systems of log

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Sadeghi, Ahmad. "Fuzzy Logic for Scientific Discoveries in Fuzziological Epistemology." International Journal of Philosophy 12, no. 2 (2024): 27–37. http://dx.doi.org/10.11648/j.ijp.20241202.13.

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All types of logic started with Aristotle and have been corrected as a traditional, formal, conditional, classical logic and even modern logic carry the main problems of Aristotelian logic. Despite their important differences, because of these core commonalities they are all called &lt;i&gt;Classical Logic&lt;/i&gt;. The fundamental limitations of classical logic make it impossible to advance the knowledge necessary to solve growing human problems. All human knowledge, especially scientific knowledge is based on the logical principles that seem to hinder the knowledge of realit

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Moschovakis, Yiannis N. "The formal language of recursion." Journal of Symbolic Logic 54, no. 4 (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 cha

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Freytes, Hector, Roberto Giuntini, and Giuseppe Sergioli. "Holistic Type Extension for Classical Logic via Toffoli Quantum Gate." Entropy 21, no. 7 (2019): 636. http://dx.doi.org/10.3390/e21070636.

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A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, where also irreversible transformations are taken into account. Formal aspects of this new logical system are detailed: in particular, the concepts of tautology and contradiction are investigated in this extension. These concepts turn out to receive substantial changes due to the non-separability of some quantum states; as an example, Werner states emerge as particular cases of “holistic" contradiction.

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PABIJUTAITĖ, Živilė, and Pranciškus GRICIUS. "Aristotelian Roots of Contemporary Tense Logic." Studia Universitatis Babeș-Bolyai Philosophia 69, no. 2 (2024): 65–79. http://dx.doi.org/10.24193/subbphil.2024.2.04.

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Tense logic is a branch of contemporary logic which includes formal devices that allow us to deal with the temporal relations between propositions. The aim of our paper is threefold: 1) to reveal how Aristotelian philosophical ideas about time, truth, possibility and necessity were reinterpreted by the founder of contemporay tense logic Arthur Prior; 2) to discuss what novel solutions to the classical problem of future contingents are available using Priorean invention; 3) to describe how the tools of tense logic have transcended their original theoretical purposes. Keywords: Tense Logic, Sea-

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DROSTE, MANFRED, and BUNDIT PIBALJOMMEE. "WEIGHTED NESTED WORD AUTOMATA AND LOGICS OVER STRONG BIMONOIDS." International Journal of Foundations of Computer Science 25, no. 05 (2014): 641–66. http://dx.doi.org/10.1142/s0129054114500269.

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Nested words have been introduced by Alur and Madhusudan as a model for e.g. recursive programs or XML documents and have received much recent interest. In this paper, we investigate a quantitative automaton model and a quantitative logic for nested words. The behavior resp. the semantics map nested words to weights which are taken from a strong bimonoid. Strong bimonoids can be viewed as semirings without requiring the distributivity assumption which was essential in the classical theory of formal power series; strong bimonoids include e.g. all bounded lattices and many other structures from

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Karpenko, Ivan. "Some Remarks on the Requirements for Scientific Theory in the Context of Many-worlds Models." Voprosy Filosofii, no. 5 (July 2024): 140–46. http://dx.doi.org/10.21146/0042-8744-2024-5-140-146.

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The article discusses the problem of a correct description of reality in science and philosophy, taking into account the acceptance of the many-world hypothesis. Many-worlds are understood as modern physical hypotheses that allow the existence of other universes (many-world interpretation, chaotic inflation, string landscape, and others). It is shown that these models are likely to challenge the traditional intellectual intuition on which classical science is built: they require new methodological approaches, and perhaps a new epistemology in general. Some requirements of classical logic, ba

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Semenova, V. A., and S. V. Smirnov. "Extended methodology for deriving formal concepts." Journal of Physics: Conference Series 2099, no. 1 (2021): 012026. http://dx.doi.org/10.1088/1742-6596/2099/1/012026.

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Abstract Two methodologies for formal concepts derivation are considered: the classical one, which focuses on the posterior analysis of the object’s properties of the studied knowledge domain, and non-classical, the cornerstone of which is the a priori formation of the set of measured object’s properties and the determination of existential relations on this set. In the article, firstly, a position is fixed in the technological chain of the target transformation of the source data, where the difference between considered methodologies shows itself. Secondly, the commonality of these two approa

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Belluce, L. P. "Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory." Canadian Journal of Mathematics 38, no. 6 (1986): 1356–79. http://dx.doi.org/10.4153/cjm-1986-069-0.

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In classical two-valued logic there is a three way relationship among formal systems, Boolean algebras and set theory. In the case of infinite-valued logic we have a similar relationship among formal systems, MV-algebras and what is called Bold fuzzy set theory. The relationship, in the latter case, between formal systems and MV-algebras has been known for many years while the relationship between MV-algebras and fuzzy set theory has hardly been studied. This is not surprising. MV-algebras were invented by C. C. Chang [1] in order to provide an algebraic proof of the completeness theorem of th

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Barrio, Eduardo Alejandro. "Models & Proofs: LFIs Without a Canonical Interpretations." Principia: an international journal of epistemology 22, no. 1 (2018): 87–112. http://dx.doi.org/10.5007/1808-1711.2018v22n1p87.

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In different papers, Carnielli, W. & Rodrigues, A. (2012), Carnielli, W. Coniglio, M. & Rodrigues, A. (2017) and Rodrigues & Carnielli, (2016) present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE (the Basic Logic of Evidence) and the second—that is a conservative extension of BLE—is named LETJ (the Logic of Evidence and Truth). Roughly, BLE and LETJ are two non-classical (paraconsistent and paracomplete) logics in which the Laws of Explosion (EXP) and Excluded Middle (PEM) are not admissible. LETJ is built on to

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Sorina, G. V. "Logic. Logicians. Fate." Политическая концептология: журнал метадисциплинарных исследований, no. 4 (December 30, 2022): 113–35. http://dx.doi.org/10.18522/2218-5518.2022.4.113135.

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The article considers peculiarities of communicative processes, social and personal, in the fate of two generations of logics of Moscow University: the sixties and seventies. It is shown that in the general system movement of the sixties in our country its special place was occupied by the logic and methodology of science. The Logicians-Sixties were in fact fighting for the right to exist in the country of classical formal logic and at the same time for the right to correspond to the current level of development of logic. The influence of the Sixties on the formation of intellectual biographie

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Delgrande, James P. "A Knowledge Level Account of Forgetting." Journal of Artificial Intelligence Research 60 (December 30, 2017): 1165–213. http://dx.doi.org/10.1613/jair.5530.

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Forgetting is an operation on knowledge bases that has been addressed in different areas of Knowledge Representation and with respect to different formalisms, including classical propositional and first-order logic, modal logics, logic programming, and description logics. Definitions of forgetting have been expressed in terms of manipulation of formulas, sets of postulates, isomorphisms between models, bisimulations, second-order quantification, elementary equivalence, and others. In this paper, forgetting is regarded as an abstract belief change operator, independent of the underlying logic.

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