Results for 'logical rules'

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  1. Chapter 5. Constructing a Demonstration of Logical Rules, or How to Use Kant’s Logic Corpus.Huaping Lu-Adler - 2015 - In Robert R. Clewis (ed.), Reading Kant's Lectures. Boston: De Gruyter. pp. 137-158.
    In this chapter, I discuss some problems of Kant’s logic corpus while recognizing its richness and potential value. I propose and explain a methodic way to approach it. I then test the proposal by showing how we may use various mate- rials from the corpus to construct a Kantian demonstration of the formal rules of thinking (or judging) that lie at the base of Kant’s Metaphysical Deduction. The same proposal can be iterated with respect to other topics. The said (...)
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  2. Exceptional Logic.Bruno Whittle - forthcoming - Review of Symbolic Logic:1-37.
    The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these (...)
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  3. On rules of inference and the meanings of logical constants.Panu Raatikainen - 2008 - Analysis 68 (4):282-287.
    In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of (...)
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  4. The Rules of Logic Composition for the Bayesian Epistemic e-Values.Wagner Borges & Julio Michael Stern - 2007 - Logic Journal of the IGPL 15 (5-6):401-420.
    In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, Hj, j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev, is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to (...)
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  5. Axiomatizations with context rules of inference in modal logic.Valentin Goranko - 1998 - Studia Logica 61 (2):179-197.
    A certain type of inference rules in modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.
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  6. Limiting logical pluralism.Suki Finn - 2019 - Synthese 198 (Suppl 20):4905-4923.
    In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens and Universal Instantiation. I (...)
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  7. Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules.Nils Kürbis - 2021 - Synthese 199 (5-6):14223-14248.
    This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that (...)
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  8. Internal Set Theory IST# Based on Hyper Infinitary Logic with Restricted Modus Ponens Rule: Nonconservative Extension of the Model Theoretical NSA.Jaykov Foukzon - 2022 - Journal of Advances in Mathematics and Computer Science 37 (7): 16-43.
    The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion of Tarski’s axiom (...)
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  9. (1 other version)Book "Set theory INC^# based on intuitionistic logic with restricted modus ponens rule".Jaykov Foukzon - 2021 - LAP LAMBERT Academic Publishing.
    In this book set theory INC# based on intuitionistic logic with restricted modus ponens rule is proposed. It proved that intuitionistic logic with restricted modus ponens rule can to safe Cantor naive set theory from a triviality.
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  10. Correction regarding 'Normalisation and Subformula Property for a System of Classical Logic with Tarski's Rule'.Nils Kürbis - manuscript
    This note corrects an error in my paper 'Normalisation and Subformula Property for a System of Classical Logic with Tarski's Rule' (Archive for Mathematical Logic 61 (2022): 105-129, DOI 10.1007/s00153-021-00775-6): Theorem 2 is mistaken, and so is a corollary drawn from it as well as a corollary that was concluded by the same mistake. Luckily this does not affect the main result of the paper.
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  11. Normalisation and subformula property for a system of classical logic with Tarski’s rule.Nils Kürbis - 2021 - Archive for Mathematical Logic 61 (1):105-129.
    This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule (...)
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  12. (1 other version)Inferential Quantification and the ω-rule.Constantin C. Brîncuş - 2024 - In Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction. Springer Verlag. pp. 345--372.
    Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the (...)
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  13. Propositional Logic – A Primer.Leslie Allan - manuscript
    This tutorial is for beginners wanting to learn the basics of propositional logic; the simplest of the formal systems of logic. Leslie Allan introduces students to the nature of arguments, validity, formal proofs, logical operators and rules of inference. With many examples, Allan shows how these concepts are employed through the application of three different methods for proving the formal validity of arguments.
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  14. Logical Inference and Its Dynamics.Carlotta Pavese - 2016 - In Olivier Roy, Allard Tamminga & Malte Willer (eds.), Deontic Logic and Normative Systems. London, UK: College Publications. pp. 203-219.
    This essay advances and develops a dynamic conception of inference rules and uses it to reexamine a long-standing problem about logical inference raised by Lewis Carroll’s regress.
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  15. Set Theory INC# Based on Intuitionistic Logic with Restricted Modus Ponens Rule (Part. I).Jaykov Foukzon - 2021 - Journal of Advances in Mathematics and Computer Science 36 (2):73-88.
    In this article Russell’s paradox and Cantor’s paradox resolved successfully using intuitionistic logic with restricted modus ponens rule.
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  16. Logic: The Stoics (Part Two).Susanne Bobzien - 1999 - In Keimpe Algra, Jonathan Barnes, Jaap Mansfeld & Malcolm Schofield (eds.), The Cambridge History of Hellenistic Philosophy. New York: Cambridge University Press.
    ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction can (...)
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  17. Rules of Belief and the Normativity of Intentional Content.Derek Green - 2021 - Acta Analytica 36 (2):159-69.
    Mental content normativists hold that the mind’s conceptual contents are essentially normative. Many hold the view because they think that facts of the form “subject S possesses concept c” imply that S is enjoined by rules concerning the application of c in theoretical judgments. Some opponents independently raise an intuitive objection: even if there are such rules, S’s possession of the concept is not the source of the enjoinment. Hence, these rules do not support mental content normativism. (...)
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  18. Hilpinen's rules of acceptance and inductive logic.Alex C. Michalos - 1971 - Philosophy of Science 38 (2):293-302.
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  19. 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 of Stoic (...)
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  20. Semantic Rules, Modal Knowledge, and Analyticity.Antonella Mallozzi - 2023 - In Duško Prelević & Anand Vaidya (eds.), Epistemology of Modality and Philosophical Methodology. New York, NY: Routledge.
    According to Amie Thomasson's Modal Normativism (MN), knowledge of metaphysical modality is to be explained in terms of a speaker’s mastery of semantic rules, as opposed to one’s epistemic grasp of independent modal facts. In this chapter, I outline (MN)'s account of modal knowledge (§1) and argue that more than semantic mastery is needed for knowledge of metaphysical modality. Specifically (§2), in reasoning aimed at gaining such knowledge, a competent speaker needs to further deploy essentialist principles and information. In (...)
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    Rules, Practices and Principles.Phil Hutchinson & Doug Hardman - 2023 - Journal of Evaluation in Clinical Practice 29 (7):1095-1099.
    Bioethics seems preoccupied with establishing, debating, promoting and sometimes debunking principles. While these tasks trade on the status of the word ‘principle’ in our ordinary language, scant attention is paid to the way principles operate in language. In this paper, we explore how principles relate to rules and practices so as to better understand their logic. We argue that principles gain their sense and power from the practices which give them sense. While general principles can be, and are, establishable (...)
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  22. Against Logical Inferentialism.Nick Zangwill - 2021 - Logique Et Analyse 255 (255):275-287.
    I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objectionthe Mushroom Omelette Objectionis that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those (...)
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  23. Paraconsistency: Logic and Applications.Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) - 2013 - Dordrecht, Netherland: Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems (...)
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  24. Logical information and epistemic space.Mark Jago - 2009 - Synthese 167 (2):327 - 341.
    Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains (...)
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  25. Molecularity in the Theory of Meaning and the Topic Neutrality of Logic.Bernhard Weiss & Nils Kürbis - 2024 - In Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction. Springer Verlag. pp. 187-209.
    Without directly addressing the Demarcation Problem for logic—the problem of distinguishing logical vocabulary from others—we focus on distinctive aspects of logical vocabulary in pursuit of a second goal in the philosophy of logic, namely, proposing criteria for the justification of logical rules. Our preferred approach has three components. Two of these are effectively Belnap’s, but with a twist. We agree with Belnap’s response to Prior’s challenge to inferentialist characterisations of the meanings of logical constants. Belnap (...)
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  26. Descartes' Rules and the Workings of the Mind.Eric Palmer - 1997 - North American Kant Society:269-282.
    I briefly consider why Descartes stopped work on the _Rules_ towards the end of my paper. My main concern is to accurately characterize the project represented in the _Rules_, especially in its relation to early-modern logic.
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  27. Set Theory INC_{∞^{#}}^{#} Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part III).Hyper inductive definitions. Application in transcendental number theory.Jaykov Foukzon - 2021 - Journal of Advances in Mathematics and Computer Science 36 (8):43.
    Main results are: (i) number e^{e} is transcendental; (ii) the both numbers e+π and e-π are irrational.
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  28. Logical Conventionalism.Jared Warren - unknown - In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger (eds.), Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press.
    Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific (...)
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  29. Propositions, Dispositions and Logical Knowledge.Corine Besson - 2010 - In M. Bonelli & A. Longo (eds.), Quid Est Veritas? Essays in Honour of Jonathan Barnes. Bibliopolis.
    This paper considers the question of what knowing a logical rule consists in. I defend the view that knowing a logical rule is having propositional knowledge. Many philosophers reject this view and argue for the alternative view that knowing a logical rule is, at least at the fundamental level, having a disposition to infer according to it. To motivate this dispositionalist view, its defenders often appeal to Carroll’s regress argument in ‘What the Tortoise Said to Achilles’. I (...)
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  30. A Logical Approach to Reasoning by Analogy.Todd R. Davies & Stuart J. Russell - 1987 - In John P. McDermott (ed.), Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI'87). Morgan Kaufmann Publishers. pp. 264-270.
    We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata (...)
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  31. One-step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.
    This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...)
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  32. The Logical Space of Democracy.Christian List - 2011 - Philosophy and Public Affairs 39 (3):262-297.
    Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; at most (...)
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  33. Three rules of distribution: one counterexample.John Corcoran - 1987 - Journal of Symbolic Logic 52:886-887.
    This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's (...)
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  34. Logical and Moral Aliens Within Us: Kant on Theoretical and Practical Self-Conceit.G. Anthony Bruno - 2023 - In Jens Pier (ed.), Limits of Intelligibility: Issues from Kant and Wittgenstein. London: Routledge.
    This chapter intervenes in recent debates in Kant scholarship about the possibility of a general logical alien. Such an alien is a thinker whose laws of thinking violate ours. She is third-personal as she is radically unlike us. Proponents of the constitutive reading of Kant’s conception of general logic accordingly suggest that Kant rules out the possibility of such an alien as unthinkable. I add to this an often-overlooked element in Kant’s thinking: there is reason to think that (...)
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  35. A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics.David Ellerman - 2024 - Entropy Special Issue: Information-Theoretic Concepts in Physics 26 (2).
    The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, (...)
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  36. Logic and Gambling.Stephen Spielman - manuscript
    This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic (...)
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  37. The Free Choice Permission as a Default Rule.Daniela Glavaničová - 2018 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 25 (4):495-516.
    It is quite plausible to say that you may read or write implies that you may read and you may write (though possibly not both at once). This so-called free choice principle is well-known in deontic logic. Sadly, despite being so intuitive and seemingly innocent, this principle causes a lot of worries. The paper briefly but critically examines leading accounts of free choice permission present in the literature. Subsequently, the paper suggests to accept the free choice principle, but only as (...)
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  38. A Simple Logical Matrix and Sequent Calculus for Parry’s Logic of Analytic Implication.Damian E. Szmuc - 2021 - Studia Logica 109 (4):791-828.
    We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.
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  39. The Adoption Problem and Anti-Exceptionalism about Logic.Suki Finn - 2019 - Australasian Journal of Logic 16 (7):231.
    Anti-exceptionalism about logic takes logic to be, as the name suggests, unexceptional. Rather, in naturalist fashion, the anti-exceptionalist takes logic to be continuous with science, and considers logical theories to be adoptable and revisable accordingly. On the other hand, the Adoption Problem aims to show that there is something special about logic that sets it apart from scientific theories, such that it cannot be adopted in the way the anti-exceptionalist proposes. In this paper I assess the damage the Adoption (...)
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  40. Logics for modelling collective attitudes.Daniele Porello - 2018 - Fundamenta Informaticae 158 (1-3):239-27.
    We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities (...)
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  41. Normalisation for Bilateral Classical Logic with some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem (...)
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  42. The Logic of Analogy.Avi Sion - 2023 - USA: Amazon/Kindle.
    The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.
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  43. Logical Form and the Limits of Thought.Manish Oza - 2020 - Dissertation, University of Toronto
    What is the relation of logic to thinking? My dissertation offers a new argument for the claim that logic is constitutive of thinking in the following sense: representational activity counts as thinking only if it manifests sensitivity to logical rules. In short, thinking has to be minimally logical. An account of thinking has to allow for our freedom to question or revise our commitments – even seemingly obvious conceptual connections – without loss of understanding. This freedom, I (...)
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  44. Set Theory INC# Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part.II) Hyper inductive definitions.Jaykov Foukzon - 2021 - Journal of Advances in Mathematics and Computer Science 36 (4):22.
    In this paper intuitionistic set theory INC# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.
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  45. Update rules and semantic universals.Luca Incurvati & Giorgio Sbardolini - 2023 - Linguistics and Philosophy 46 (2):259-289.
    We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. (...)
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  46. Supervaluationism, Modal Logic, and Weakly Classical Logic.Joshua Schechter - 2024 - Journal of Philosophical Logic 53 (2):411-61.
    A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of (...) consequence according to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)
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  47. Generalized logical operations among conditional events.Angelo Gilio & Giuseppe Sanfilippo - 2019 - Applied Intelligence 49:79-102.
    We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...)
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  48. Cathoristic Logic.Richard Evans - manuscript
    Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a number of results such as compactness, a semantic characterisa- tion of elementary equivalence, the existence of a quadratic-time decision pro- cedure, and Brandom’s incompatibility semantics property. We demonstrate the usefulness of the logic as a language for knowledge representation.
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  49. Relevant Logics, Counterfactual Worlds, and the Understanding of Narrative.Luis Galván - 2019 - In Matei Chihaia & Katharina Rennhak (eds.), Relevance and Narrative Research. Lexington Books. pp. 37-60.
    The aim of this paper is to explore what insights relevant logics may provide for the understanding of literary fictional narrative. To date, hardly anyone has reflected on the intersection of relevant logics and narratology, and some could think that there is good reason for it. On the one hand, relevance has been a prominent issue in pragmatics, in the tradition of Grice, and Sperber and Wilson; thus framed, relevance is highly context-sensitive, so it seems unsuitable for formal analysis. On (...)
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  50. Understanding the Logical Constants and Dispositions.Corine Besson - 2009 - The Baltic International Yearbook of Cognition, Logic and Communication 5:1-24.
    Many philosophers claim that understanding a logical constant (e.g. ‘if, then’) fundamentally consists in having dispositions to infer according to the logical rules (e.g. Modus Ponens) that fix its meaning. This paper argues that such dispositionalist accounts give us the wrong picture of what understanding a logical constant consists in. The objection here is that they give an account of understanding a logical constant which is inconsistent with what seem to be adequate manifestations of such (...)
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