Results for 'many-valued logic'

1000+ found
Order:
  1.  49
    Many-Valued And Fuzzy Logic Systems From The Viewpoint Of Classical Logic.Ekrem Sefa Gül - 2018 - Tasavvur - Tekirdag Theology Journal 4 (2):624 - 657.
    The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  2.  61
    Dual Systems of Sequents and Tableaux for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Bulletin of the EATCS 51:192-197.
    The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  3. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2020 - London: College Publications.
    2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive (...)
    Download  
     
    Export citation  
     
    Bookmark  
  4. Many-Valued Logic between the Degrees of Truth and the Limits of Knowledge.Salah Osman - 2002 - Alexandria, Egypt: Al Maaref Establishment Press.
    هو أول كتاب باللغة العربية يعرض لمراحل وآليات تطور المنطق الرمزي المعاصر متعدد القيم بأنساقه المختلفة، مركزًا على مشكلة الغموض المعرفي للإنسان بأبعادها اللغوية والإبستمولوجية والأنطولوجية، والتي تتجلى – على سبيل المثال – فيما تحفل به الدراسات الفلسفية والمنطقية والعلمية من مفارقات تمثل تحديًا قويًا لثنائية الصدق والكذب الكلاسيكية، وكذلك في اكتشاف «هيزنبرج» لمبدأ اللايقين، وتأكيده وعلماء الكمّ على ضرورة التفسيرات الإحصائية في المجال دون الذري، الأمر الذي يؤكد عدم فعالية قانون الثالث المرفوع في التعامل مع معطيات الواقع الفعلي، واستحالة (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5.  48
    Proof Theory of Finite-Valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  6. Approximating Propositional Calculi by Finite-Valued Logics.Matthias Baaz & Richard Zach - 1994 - In 24th International Symposium on Multiple-valued Logic, 1994. Proceedings. Los Alamitos: IEEE Press. pp. 257–263.
    The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices (...)
    Download  
     
    Export citation  
     
    Bookmark  
  7. Systematic Construction of Natural Deduction Systems for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - In Proceedings of The Twenty-Third International Symposium on Multiple-Valued Logic, 1993. Los Alamitos, CA: IEEE Press. pp. 208-213.
    A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  8.  53
    Elimination of Cuts in First-Order Finite-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1994 - Journal of Information Processing and Cybernetics EIK 29 (6):333-355.
    A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  9. Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  10. Aristotle's Many-Sorted Logic.J. Corcoran - 2008 - Bulletin of Symbolic Logic 14 (1):155-156.
    As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  11. Bourne on Future Contingents and Three-Valued Logic.Daisuke Kachi - 2009 - Logic and Logical Philosophy 18 (1):33-43.
    Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of the intermediate (...)
    Download  
     
    Export citation  
     
    Bookmark  
  12. Was Łukasiewicz Wrong? : Three-Valued Logic and Determinism.Daisuke Kachi - 1996 - In Łukasiewicz in Dublin -- An International Conference on the Work of Jan Łukasiewicz.
    Łukasiewicz has often been criticized for his motive for inventing his three-valued logic, namely the avoidance of determinism. First of all, I want to show that almost all of the critcism along this line was wrong. Second I will indicate that he made mistakes, however, in constructing his system, because he had other motives at the same time. Finally I will propose some modification of his system and its interpretation which can attain his original purpose in some sense.
    Download  
     
    Export citation  
     
    Bookmark  
  13. Valuations.Jean-Louis Lenard - manuscript
    Is logic empirical? Is logic to be found in the world? Or is logic rather a convention, a product of conventions, part of the many rules that regulate the language game? Answers fall in either camp. We like the linguistic answer. In this paper, we want to analyze how a linguistic community would tackle the problem of developing a logic and show how the linguistic conventions adopted by the community determine the properties of the local (...). Then show how to move from a notion of logic that varies from community to community to a notion of logic that is in a sense universal. The framework is conventional up to a point: we have sentences, atomic and composite, the connectives are interpreted, values are computed, and the value of a composite sentence is a function of the values of its subsentences. Less conventional is the use of a plurality of truth values, and the sharp distinction we draw between sentences and statements, in the spirit of the distinction between proposition and judgment that one may find in proof theory. The linguistic community will face many choices. What are the good ones, the ones to avoid? Are there, in some sense, optimal choices? These are the kind of issues we are addressing. Where do we end up? With some kind of universal bivalent logic, ironically enough. We start from an arbitrarily large number of truth values, atomic sentences and connectives, construct a generic many-valued logic, recover more or less the usual results and issues, and in the end it all comes down to a positive bivalent logic with two connectives, `and' and `or', as if logic is nothing more than a mere accounting of possibilities. (shrink)
    Download  
     
    Export citation  
     
    Bookmark  
  14.  93
    4. Contradictorial Gradualism Vs. Discontinuism: Two Views On Fuzziness And The Transition Problem.Marcelo VÁsconez - 2006 - Logique Et Analyse 49 (195).
    The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  15. Fuzziness and the Sorites Paradox.Marcelo Vasconez - 2006 - Dissertation, Catholic University of Louvain
    The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  16.  30
    A One-Valued Logic for Non-One-Sidedness.Fabien Schang - 2013 - International Journal of Jaina Studies 9 (1):1-25.
    Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz's mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhangi, i.e. the theory of sevenfold predication. Before arguing for this formalist approach to (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  24
    Paracomplete Logics Which Are Dual to the Paraconsistent Logics L3A and L3B.Alejandro Hernández-Tello, Verónica Borja-Macı́as & Marcelo E. Coniglio - 2020 - LANMR 2019: Proceedings of the 12th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning.
    In 2016 Beziau, introduce a more restricted concept of paraconsistency, namely the genuine paraconsistency. He calls genuine paraconsistent logic those logic rejecting φ, ¬φ |- ψ and |- ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of these logics satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are: |- φ, ¬φ, and ¬(ψ ∨ ¬ψ) |- . We call genuine paracomplete logics those rejecting the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  18.  12
    Negation and Dichotomy.Fabien Schang (ed.) - 2009 - Bydgoszcz: Kazimierz Wielki University Press.
    The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition.
    Download  
     
    Export citation  
     
    Bookmark  
  19.  49
    Une sémantique générale des croyances justifiées.Fabien Schang & Alexandre Costa Leite - 2016 - CLE-Prints 16 (3):1-24.
    Nous proposons une logique épistémique quadrivalente AR4.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  20. (Master Thesis) Of Madness and Many-Valuedness: An Investigation Into Suszko's Thesis.Sanderson Molick - 2015 - Dissertation, UFRN
    Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undeter- mined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third (...)
    Download  
     
    Export citation  
     
    Bookmark  
  21. Effective Finite-Valued Approximations of General Propositional Logics.Matthias Baaz & Richard Zach - 2008 - In Arnon Avron, Nachum Dershowitz & Alexander Rabinovich (eds.), Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Berlin: Springer. pp. 107–129.
    Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways (...)
    Download  
     
    Export citation  
     
    Bookmark  
  22. Trees for a 3-Valued Logic.Fred Johnson - 1984 - Analysis 44 (1):43-6.
    Fred shows how problems with Slater's restriction of the classical propositional logic can be solved.
    Download  
     
    Export citation  
     
    Bookmark  
  23. Ancient Logic and its Modern Interpretations.John Corcoran (ed.) - 1974 - Boston: Reidel.
    This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient (...) texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  24.  72
    A 4-Valued Logic of Strong Conditional.Fabien Schang - 2018 - South American Journal of Logic 3 (1):59-86.
    How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on (...)
    Download  
     
    Export citation  
     
    Bookmark  
  25. Negation on the Australian Plan.Francesco Berto & Greg Restall - 2019 - Journal of Philosophical Logic 48 (6):1119-1144.
    We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  26. The Development of Mathematical Logic From Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  27. One Community or Many? From Logic to Juridical Law, Via Metaphysics [in Kant].Lucas Thorpe - 2011 - In Howard Williams, Sorin Baiasu & Sami Pihlstrom (eds.), Politics and Metaphysics in Kant. Political Philosophy Now: University of Wales Press.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  28. A Three-Valued Interpretation for a Relevance Logic.Fred Johnson - 1976 - The Relevance Logic Newsletter 1 (3):123-128.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  29. Labeled Calculi and Finite-Valued Logics.Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach - 1998 - Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  30. Validity in Simple Partial Logic.Daisuke Kachi - 2002 - Annals of the Japan Association for Philosophy of Science 10 (4):139-153.
    Firstly I characterize Simple Partial Logic (SPL) as the generalization and extension of a certain two-valued logic. Based on the characterization I present two definitions of validity in SPL. Finally I show that given my characterization these two definitions are more appropriate than other definitions that have been prevalent, since both have some desirable semantic properties that the others lack.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  31. Tensed Ontology Based on Simple Partial Logic.Daisuke Kachi - 2002 - Proceedings of Ninth International Symposium on Temporal Representation and Reasoning: TIME-02:141-145.
    Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I compare (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  32. True, Truer, Truest.Brian Weatherson - 2005 - Philosophical Studies 123 (1-2):47-70.
    What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  33.  47
    Epistemic Pluralism.Fabien Schang - 2017 - Logique Et Analyse 239 (60):337-353.
    The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  34. Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
    In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both with (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  35.  48
    Normality Operators and Classical Recapture in Extensions of Kleene Logics.Ciuni Roberto & Massimiliano Carrara - forthcoming - Logic Journal of the IGPL.
    In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a (...)
    Download  
     
    Export citation  
     
    Bookmark  
  36. Jaina Logic and the Philosophical Basis of Pluralism.Jonardon Ganeri - 2002 - History and Philosophy of Logic 23 (4):267-281.
    What is the rational response when confronted with a set of propositions each of which we have some reason to accept, and yet which taken together form an inconsistent class? This was, in a nutshell, the problem addressed by the Jaina logicians of classical India, and the solution they gave is, I think, of great interest, both for what it tells us about the relationship between rationality and consistency, and for what we can learn about the logical basis of philosophical (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  37. The Founding of Logic.John Corcoran - 1994 - Ancient Philosophy 14 (S1):9-24.
    Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  38. 2007. Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski. Eds. C. Martínez Et Al. Current Topics in Logic and Analytic Philosophy / Temas Actuales de Lógica y Filosofía Analítica. Imprenta Univeridade Santiago de Compostela.John Corcoran - 2007 - In C. Martínez (ed.), Current Topics in Logic and Analytic Philosophy /. pp. 145-178.
    Download  
     
    Export citation  
     
    Bookmark  
  39. Aristotle's Logic at the University of Buffalo's Department of Philosophy.John Corcoran - 2009 - Ideas Y Valores 58 (140):99-117.
    We begin with an introductory overview of contributions made by more than twenty scholars associated with the Philosophy Department at the University of Buffalo during the last half-century to our understanding and evaluation of Aristotle's logic. More well-known developments are merely mentioned in..
    Download  
     
    Export citation  
     
    Bookmark  
  40. Track-Down Operations on Bilattices.Damian Szmuc - 2018 - In Robert Wille & Martin Lukac (eds.), Proceedings of the 48th IEEE International Symposium on Multiple-Valued Logic. Los Alamitos, California, EE. UU.: pp. 74-79.
    This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. Finally, two logics of sequential combinations (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  41. Beyond the Fregean Myth: The Value of Logical Values.Fabien Schang - 2010 - In Piotr Stalmaszczyk (ed.), Objects of Inquiry in Philosophy of Language and Linguistics. Frankfurt: Ontos Verlag. pp. 245--260.
    One of the most prominent myths in analytic philosophy is the so- called “Fregean Axiom”, according to which the reference of a sentence is a truth value. In contrast to this referential semantics, a use-based formal semantics will be constructed in which the logical value of a sentence is not its putative referent but the information it conveys. Let us call by “Question Answer Semantics” (thereafter: QAS) the corresponding formal semantics: a non-Fregean many-valued logic, where the meaning of (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  42.  47
    MacColl’s Modes of Modalities.Fabien Schang - 2011 - Philosophia Scientiae 15:149-188.
    Hugh MacColl is commonly seen as a pioneer of modal and many-valued logic, given his introduction of modalities that go beyond plain truth and falsehood. But a closer examination shows that such a legacy is debatable and should take into account the way in which these modalities proceeded. We argue that, while MacColl devised a modal logic in the broad sense of the word, he did not give rise to a many-valued logic in the strict (...)
    Download  
     
    Export citation  
     
    Bookmark  
  43. A Tableau Calculus for Partial Functions.Manfred Kerber Michael Kohlhase - unknown
    Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional logics. However, strong Kleene logic, where quantification is restricted and therefore not truthfunctional, does not fit the framework directly. (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
  44.  39
    A Generalised Model of Judgment Aggregation.Franz Dietrich - 2007 - Social Choice and Welfare 4 (28):529-565.
    The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems (...)
    Download  
     
    Export citation  
     
    Bookmark   57 citations  
  45.  65
    From Bi-Facial Truth to Bi-Facial Proofs.Stefan Wintein & Reinhard A. Muskens - 2015 - Studia Logica 103 (3):545-558.
    In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  46. Sentence, Proposition, Judgment, Statement, and Fact: Speaking About the Written English Used in Logic.John Corcoran - 2009 - In W. A. Carnielli (ed.), The Many Sides of Logic. College Publications. pp. 71-103.
    The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  47. What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, from Consistency to Inconsistency. Springer Verlag.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  48. Aristotle's Demonstrative Logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  49. Dynamic Epistemic Logic and Logical Omniscience.Mattias Skipper Rasmussen - 2015 - Logic and Logical Philosophy 24 (3):377-399.
    Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this paper, (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  50. ARISTOTELIAN LOGIC AND EUCLIDEAN GEOMETRY.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (1):131-2.
    John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
1 — 50 / 1000