Results for 'Logic'

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  1.  72
    Truthmaker Semantics for Relevant Logic.Mark Jago - forthcoming - Journal of Philosophical Logic.
    I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I (...)
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  2.  62
    Formalizing Kant's Rules: A Logic of Conditional Imperatives and Permissives.Richard Evans, Andrew Stephenson & Marek Sergot - forthcoming - Journal of Philosophical Logic.
    This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...)
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  3.  74
    Intuitionism and the Modal Logic of Vagueness.Susanne Bobzien & Ian Rumfitt - forthcoming - Journal of Philosophical Logic.
    ABSTRACT: Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any (...)
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  4. Logic and Semantics for Imperatives.Nate Charlow - 2014 - Journal of Philosophical Logic 43 (4):617-664.
    In this paper I will develop a view about the semantics of imperatives, which I term Modal Noncognitivism, on which imperatives might be said to have truth conditions (dispositionally, anyway), but on which it does not make sense to see them as expressing propositions (hence does not make sense to ascribe to them truth or falsity). This view stands against “Cognitivist” accounts of the semantics of imperatives, on which imperatives are claimed to express propositions, which are then enlisted in explanations (...)
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  5. Logic for Exact Entailment.Kit Fine & Mark Jago - 2018 - Review of Symbolic Logic:1-21.
    An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion (...)
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  6. 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 (...)
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  7.  64
    Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
    This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much (...)
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  8. Deontic Logic.Paul McNamara - 2006 - In Dov Gabbay & John Woods (eds.), The Handbook of the History of Logic, vol. 7: Logic and the Modalities in the Twentieth Century. Elsevier Press. pp. 197-288.
    Overview of fundamental work in deontic logic.
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  9. An Introduction to Partition Logic.David Ellerman - 2014 - Logic Journal of the IGPL 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the (...)
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  10.  68
    Laws of Thought and Laws of Logic After Kant.Lydia Patton - 2018 - In Sandra Lapointe (ed.), Logic from Kant to Russell. New York: Routledge. pp. 123-137.
    George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of (...)
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  11. What is the Correct Logic of Necessity, Actuality and Apriority?Peter Fritz - 2014 - Review of Symbolic Logic 7 (3):385-414.
    This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives (...)
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  12.  75
    On an Intuitionistic Logic for Pragmatics.Gianluigi Bellin, Massimiliano Carrara & Daniele Chiffi - 2018 - Journal of Logic and Computation 50 (28):935–966..
    We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a (...) of assertions and conjectures: looking at the S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)
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  13. Neo-Logicism and its Logic.Panu Raatikainen - forthcoming - History and Philosophy of Logic.
    The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions, and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the “logic” assumed rather than from Hume’s principle. It is shown that Hume’s principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only few rudimentary (...)
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  14. Second-Order Logic.John Corcoran - 2001 - In M. Zeleny (ed.), Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. KLUKER. pp. 61–76.
    “Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our (...)
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  15.  93
    Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
    We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...)
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  16. A Norm-Giver Meets Deontic Action Logic.Robert Trypuz & Piotr Kulicki - 2011 - Logic and Logical Philosophy 20 (1-2):2011.
    In the paper we present a formal system motivated by a specific methodology of creating norms. According to the methodology, a norm-giver before establishing a set of norms should create a picture of the agent by creating his repertoire of actions. Then, knowing what the agent can do in particular situations, the norm-giver regulates these actions by assigning deontic qualifications to each of them. The set of norms created for each situation should respect (1) generally valid deontic principles being the (...)
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  17.  13
    A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (2):81-97.
    This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
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  18. 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 (...)
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  19.  78
    Non-Analytic Tableaux for Chellas's Conditional Logic CK and Lewis's Logic of Counterfactuals VC.Richard Zach - 2018 - Australasian Journal of Logic 15 (3):609-628.
    Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.
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  20. A Logic of Justification and Truthmaking.Alessandro Giordani - 2013 - Review of Symbolic Logic 6 (2):323-342.
    In the present paper we propose a system of propositional logic for reasoning about justification, truthmaking, and the connection between justifiers and truthmakers. The logic of justification and truthmaking is developed according to the fundamental ideas introduced by Artemov. Justifiers and truthmakers are treated in a similar way, exploiting the intuition that justifiers provide epistemic grounds for propositions to be considered true, while truthmakers provide ontological grounds for propositions to be true. This system of logic is then (...)
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  21. 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, (...)
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  22.  70
    What Isn’T Obvious About ‘Obvious’: A Data-Driven Approach to Philosophy of Logic.Moti Mizrahi - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Press. pp. 201-224.
    It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, (...)
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  23. Logic in the Tractatus.Max Weiss - 2017 - Review of Symbolic Logic 10 (1):1-50.
    I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is (...)
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  24. Completeness of an Ancient Logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the (...)
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  25. The Logic of Partitions: Introduction to the Dual of the Logic of Subsets: The Logic of Partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as (...)
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  26. Logic is Metaphysics.Daniel Durante Pereira Alves - 2011 - Principia: An International Journal of Epistemology 15 (1):31-42.
    Analyzing the position of two philosophers whose views are recognizably divergent, W. O. Quine and M. Dummett, we intend to support a striking point of agreement between them: the idea that our logical principles constitute our principles about what there is, and therefore, that logic is metaphysics.
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  27. Proofnets for S5: Sequents and Circuits for Modal Logic.Greg Restall - 2007 - In C. Dimitracopoulos, L. Newelski & D. Normann (eds.), Logic Colloquium 2005. Cambridge: Cambridge University Press. pp. 151-172.
    In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is (...)
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  28. Basic Action Deontic Logic.Alessandro Giordani & Ilaria Canavotto - 2016 - In O. Roy, T. Allard & W. Malte (eds.), Deontic Logic and Normative Systems. College Publications. pp. 80-92.
    The aim of this paper is to introduce a system of dynamic deontic logic in which the main problems related to the de finition of deontic concepts, especially those emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law, are solved. The basic idea is to introduce two crucial distinctions allowing us to differentiate (i) what is ideal with respect to a given code, which fixes the (...)
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  29. Heinrich Behmann’s 1921 Lecture on the Decision Problem and the Algebra of Logic.Paolo Mancosu & Richard Zach - 2015 - Bulletin of Symbolic Logic 21 (2):164-187.
    Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important (...)
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  30. Logic and/of Truthmaking.Jamin Asay - 2016 - In Syraya Chin-Mu Yang, Duen-Min Deng & Hanti Lin (eds.), Structural Analysis of Non-Classical Logics: The Proceedings of the Second Taiwan Philosophical Logic Colloquium. Springer Verlag.
    The purpose of this paper is to explore the question of how truthmaker theorists ought to think about their subject in relation to logic. Regarding logic and truthmaking, I defend the view that considerations drawn from advances in modal logic have little bearing on the legitimacy of truthmaker theory. To do so, I respond to objections Timothy Williamson has lodged against truthmaker theory. As for the logic of truthmaking, I show how the project of understanding the (...)
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  31.  63
    Enriching Deontic Logic.Ilaria Canavotto & Alessandro Giordani - 2018 - Journal of Logic and Computation 1:1-23.
    It is well known that systems of action deontic logic emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law are subject to paradoxes. In general, paradoxes are acknowledged as such if we have intuitions telling us that things should be different. The aim of this paper is to introduce a paradox-free deontic action system by (i) identifying the basic intuitions leading to the emergence of the (...)
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  32.  64
    Convergence, Continuity and Recurrence in Dynamic Epistemic Logic.Dominik Klein & Rasmus K. Rendsvig - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). Springer. pp. 108-122.
    The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced (...)
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  33.  93
    Higher Order Modal Logic.Reinhard Muskens - 2006 - In Patrick Blackburn, Johan Van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Elsevier. pp. 621-653.
    A logic is called higher order if it allows for quantification over higher order objects, such as functions of individuals, relations between individuals, functions of functions, relations between functions, etc. Higher order logic began with Frege, was formalized in Russell [46] and Whitehead and Russell [52] early in the previous century, and received its canonical formulation in Church [14].1 While classical type theory has since long been overshadowed by set theory as a foundation of mathematics, recent decades have (...)
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  34.  58
    Force, Content and Logic.Michael Schmitz - 2018 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics, Contributions of the Austrian Ludwig Wittgenstein Society, Vol. XXVI 41th International Wittgenstein Symposium Kirchberg am Wechsel. pp. 221-223.
    The Frege point to the effect that e.g. the clauses of conditionals are not asserted and therefore cannot be assertions is often taken to establish a dichotomy between the content of a speech act, which is propositional and belongs to logic and semantics, and its force, which belongs to pragmatics. Recently this dichotomy has been questioned by philosophers such as Peter Hanks and Francois Recanati, who propose act-theoretic accounts of propositions, argue that we can’t account for propositional unity independently (...)
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  35. Logical Consequence in Modal Logic II: Some Semantic Systems for S4.George Weaver - 1974 - Notre Dame Journal of Formal Logic 15:370.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...)
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  36. Vagueness and Intuitionistic Logic.Ian Rumfitt - forthcoming - In Alexander Miller (ed.), Language, Logic,and Mathematics: Themes from the Philosophy of Crispin Wright. Oxford University Press.
    In his essay ‘“Wang’s Paradox”’, Crispin Wright proposes a solution to the Sorites Paradox (in particular, the form of it he calls the ‘Paradox of Sharp Boundaries’) that involves adopting intuitionistic logic when reasoning with vague predicates. He does not give a semantic theory which accounts for the validity of intuitionistic logic (and the invalidity of stronger logics) in that area. The present essay tentatively makes good the deficiency. By applying a theorem of Tarski, it shows that intuitionistic (...)
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  37. The Logic of Joint Ability in Two-Player Tacit Games.Peter Hawke - 2017 - Review of Symbolic Logic 10 (3):481-508.
    Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where (...)
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  38. Logic of Implicit and Explicit Justifiers.Alessandro Giordani - 2016 - In L. Felline, A. Ledda, F. Paoli & E. Rossanese (eds.), New Directions in Logic and the Philosophy of Science. College Publications. pp. 119-131.
    The aim of this paper is to provide an intuitive semantics for systems of justification logic which allows us to cope with the distinction between implicit and explicit justifiers. The paper is subdivided into three sections. In the first one, the distinction between implicit and explicit justifiers is presented and connected with a proof-theoretic distinction between two ways of interpreting sequences of sentences; that is, as sequences of axioms in a certain set and as sequences proofs constructed from that (...)
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  39. Logic or Reason?Penelope Rush - 2012 - Logic and Logical Philosophy 21 (2):127-163.
    This paper explores the question of what logic is not. It argues against the wide spread assumptions that logic is: a model of reason; a model of correct reason; the laws of thought, or indeed is related to reason at all such that the essential nature of the two are crucially or essentially co-illustrative. I note that due to such assumptions, our current understanding of the nature of logic itself is thoroughly entangled with the nature of reason. (...)
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  40.  68
    Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic.Matthias Baaz & Richard Zach - 2000 - In Peter G. Clote & Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Berlin: Springer. pp. 187– 201.
    Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system (...)
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  41. Modal Logic S4 as a Paraconsistent Logic with a Topological Semantics.Marcelo E. Coniglio & Leonardo Prieto-Sanabria - 2017 - In Carlos Caleiro, Francisco Dionisio, Paula Gouveia, Paulo Mateus & João Rasga (eds.), Logic and Computation: Essays in Honour of Amilcar Sernadas. London, UK: College Publications. pp. 171-196.
    In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological (...)
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  42. Logic, Ontological Neutrality, and the Law of Non-Contradiction.Achille C. Varzi - 2014 - In Elena Ficara (ed.), Contradictions. Logic, History, Actuality. De Gruyter. pp. 53–80.
    Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification (...)
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  43. 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 (...)
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  44. Ancient Indian Logic and Analogy.J. B. Paris & A. Vencovska - 2017 - In S. Ghosh & S. Prasad (eds.), Logic and its Applications, Lecture Notes in Computer Science 10119. Springer. pp. 198-210.
    B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.
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  45.  43
    Means or End? On the Valuation of Logic Diagrams.Jens Lemanski - 2016 - Logic-Philosophical Studies 14:98-122.
    From the beginning of the 16th century to the end of the 18th century, there were not less than ten philosophers who focused extensively on Venn’s ostensible analytical diagrams, as noted by modern historians of logic (Venn, Gardner, Baron, Coumet et al.). But what was the reason for early modern philosophers to use logic or analytical diagrams? Among modern historians of logic one can find two theses which are closely connected to each other: M. Gardner states that (...)
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  46.  99
    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 (...)
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  47. Review: Karel Lambert, Meinong and the Principle of Independence. Its Place in Meinong's Theory of Objects and Its Significance in Contemporary Philosophical Logic[REVIEW]William J. Rapaport - 1986 - Journal of Symbolic Logic 51 (1):248-252.
    Review of Karel Lambert, Meinong and the Principle of Independence: Its Place in Meinong's Theory of Objects and Its Significance in Contemporary Philosophical Logic.
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  48. Deontic Logic as a Study of Conditions of Rationality in Norm-Related Activities.Berislav Žarnić - 2016 - In Olivier Roy, Allard Tamminga & Malte Willer (eds.), Deontic Logic and Normative Systems. College Publications. pp. 272-287.
    The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational norm-giving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of set-theoretic approach and extended to a two-sets model which allows for the separate treatment of obligation-norms and permission norms. The three translation functions connecting the language of deontic logic with (...)
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  49.  92
    Second Order Inductive Logic and Wilmers' Principle.M. S. Kliess & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
    We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.
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  50.  59
    Tableau-Based Decision Procedure for the Multiagent Epistemic Logic with All Coalitional Operators for Common and Distributed Knowledge.M. Ajspur, V. Goranko & D. Shkatov - 2013 - Logic Journal of the IGPL 21 (3):407-437.
    We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi\-agent epistemic logic \CMAELCD\ with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for \CMAELCD\ and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input set (...)
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