Results for 'Modal logic'

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  1. 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 (...)
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  2. Modal Logic and Philosophy.Sten Lindström & Krister Segerberg - 2007 - In Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Amsterdam, the Netherlands: Elsevier. pp. 1149-1214.
    Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the (...)
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  3.  62
    Modal Logic. An Introduction.Zia Movahed - 2002 - Tehran: Hermes Publishers.
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  4. Quine and Quantified Modal Logic – Against the Received View.Adam Tamas Tuboly - 2015 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 22 (4):518-545.
    The textbook-like history of analytic philosophy is a history of myths, re-ceived views and dogmas. Though mainly the last few years have witnessed a huge amount of historical work that aimed to reconsider our narratives of the history of ana-lytic philosophy there is still a lot to do. The present study is meant to present such a micro story which is still quite untouched by historians. According to the received view Kripke has defeated all the arguments of Quine against quantified (...)
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  5. First-Order Modal Logic in the Necessary Framework of Objects.Peter Fritz - 2016 - Canadian Journal of Philosophy 46 (4-5):584-609.
    I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes (...)
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  6. 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 (...) vocabulary—is directly motivated in terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)
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  7. 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 (...)
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  8.  83
    The Modal Logic of the Countable Random Frame.Valentin Goranko & Bruce Kapron - 2003 - Archive for Mathematical Logic 42 (3):221-243.
    We study the modal logic M L r of the countable random frame, which is contained in and `approximates' the modal logic of almost sure frame validity, i.e. the logic of those modal principles which are valid with asymptotic probability 1 in a randomly chosen finite frame. We give a sound and complete axiomatization of M L r and show that it is not finitely axiomatizable. Then we describe the finite frames of that (...) and show that it has the finite frame property and its satisfiability problem is in EXPTIME. All these results easily extend to temporal and other multi-modal logics. Finally, we show that there are modal formulas which are almost surely valid in the finite, yet fail in the countable random frame, and hence do not follow from the extension axioms. Therefore the analog of Fagin's transfer theorem for almost sure validity in first-order logic fails for modal logic. (shrink)
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  9. Chrysippus' Modal Logic and Its Relation to Philo and Diodorus.Susanne Bobzien - 1993 - In K. Doering & Th Ebert (eds.), Dialektiker und Stoiker. Franz Steiner. pp. 63--84.
    ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and (...) theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy. (shrink)
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  10. Regression in Modal Logic.Robert Demolombe, Andreas Herzig & Ivan Varzinczak - 2003 - Journal of Applied Non-Classical Logics 13 (2):165-185.
    In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.
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  11.  84
    Refutation Systems in Modal Logic.Valentin Goranko - 1994 - Studia Logica 53 (2):299 - 324.
    Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refutation systems.
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  12. 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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  13.  82
    Hegel, Modal Logic, and the Social Nature of Mind.Paul Redding - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (5):586-606.
    ABSTRACTHegel's Phenomenology of Spirit provides a fascinating picture of individual minds caught up in “recognitive” relations so as to constitute a realm—“spirit”—which, while necessarily embedded in nature, is not reducible to it. In this essay I suggest a contemporary path for developing Hegel's suggestive ideas in a way that broadly conforms to the demands of his own system, such that one moves from logic to a philosophy of mind. Hence I draw on Hegel's “subjective logic”, understood in the (...)
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  14. Ockhamism and Quantified Modal Logic.Andrea Iacona - 2015 - Logique Et Analyse 58:353-370.
    This paper outlines a formal account of tensed sentences that is consistent with Ockhamism, a view according to which future contingents are either true or false. The account outlined substantively differs from the attempts that have been made so far to provide a formal apparatus for such a view in terms of some expressly modified version of branching time semantics. The system on which it is based is the simplest quantified modal logic.
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  15.  75
    Hyperboolean Algebras and Hyperboolean Modal Logic.Valentin Goranko & Dimiter Vakarelov - 1999 - Journal of Applied Non-Classical Logics 9 (2):345-368.
    Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it (...)
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  16. On the Expressive Power of First-Order Modal Logic with Two-Dimensional Operators.Alexander Kocurek - 2018 - Synthese 195 (10):4373-4417.
    Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of (...)
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  17. Essentialism Vis-À-Vis Possibilia, Modal Logic, and Necessitism.Sonia Roca-Royes - 2011 - Philosophy Compass 6 (1):54-64.
    Pace Necessitism – roughly, the view that existence is not contingent – essential properties provide necessary conditions for the existence of objects. Sufficiency properties, by contrast, provide sufficient conditions, and individual essences provide necessary and sufficient conditions. This paper explains how these kinds of properties can be used to illuminate the ontological status of merely possible objects and to construct a respectable possibilist ontology. The paper also reviews two points of interaction between essentialism and modal logic. First, we (...)
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  18. Modal Logic Vs. Ontological Argument.Andrezej Biłat - 2012 - European Journal for Philosophy of Religion 4 (2):179--185.
    The contemporary versions of the ontological argument that originated from Charles Hartshorne are formalized proofs based on unique modal theories. The simplest well-known theory of this kind arises from the b system of modal logic by adding two extra-logical axioms: “If the perfect being exists, then it necessarily exists‘ and “It is possible that the perfect being exists‘. In the paper a similar argument is presented, however none of the systems of modal logic is relevant (...)
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  19. 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 (...)
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  20.  55
    Modal Logic and Universal Algebra I: Modal Axiomatizations of Structures.Valentin Goranko & Dimiter Vakarelov - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 265-292.
    We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for complete axiomatization of the modal logics determined by a large family of classes of structures of any signature.
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  21. 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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  22.  20
    Modal Logic and Universal Algebra I: Modal Axiomatizations of Structures.Valentin Goranko & Dimiter Vakarelov - 2000 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 265-292.
    We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for complete axiomatization of the modal logics determined by a large family of classes of structures of any signature.
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  23.  62
    Algorithmic Correspondence and Completeness in Modal Logic. V. Recursive Extensions of SQEMA.Willem Conradie, Valentin Goranko & Dimitar Vakarelov - 2010 - Journal of Applied Logic 8 (4):319-333.
    The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, (...)
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  24. A Modal Logic for Gödelian Intuition.Hasen Khudairi - manuscript
    This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the axioms of a dynamic provability logic, which augments GL with the modal μ-calculus. Via correspondence results between modal logic and first-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., (...)
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  25. Phonetic Possibility and Modal Logic.Mark Sharlow - 2007
    In this paper I propose a formalization, using modal logic, of the notion of possibility that phoneticians use when they judge speech sounds to be possible or impossible. I argue that the most natural candidate for a modal logic of phonetic possibility is the modal system T.
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  26. Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism.Hasen Khudairi - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer. pp. 65-82.
    This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of Ω-logical validity (...)
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  27.  48
    Algorithmic Correspondence and Completeness in Modal Logic. IV. Semantic Extensions of SQEMA.Willem Conradie & Valentin Goranko - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):175-211.
    In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several (...)
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  28.  75
    An Exposition and Development of Kanger's Early Semantics for Modal Logic.Sten Lindström - 1998 - In J. H. Fetzer & P. Humphreys (eds.), The New Theory of Reference: Kripke, Marcus, and its origins. Kluwer Academic Publishers.
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  29. Ruzsa on Quine’s Argument Against Modal Logic.Zsófia Zvolenszky - 2010 - Hungarian Philosophical Review (Magyar Filozófiai Szemle) (4):40-48.
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  30.  54
    Weakly Aggregative Modal Logic: Characterization and Interpolation.Jixin Liu, Yanjing Wang & Yifeng Ding - 2019 - In Patrick Blackburn, Emiliano Lorini & Meiyun Guo (eds.), Logic, Rationality, and Interaction 7th International Workshop, LORI 2019, Chongqing, China, October 18–21, 2019, Proceedings. pp. 153-167.
    Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation.
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  31. Natural Deduction for Modal Logic with a Backtracking Operator.Jonathan Payne - 2015 - Journal of Philosophical Logic 44 (3):237-258.
    Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to (...)
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  32. Intuitionism and the Modal Logic of Vagueness.Susanne Bobzien & Ian Rumfitt - 2020 - Journal of Philosophical Logic 49 (2):221-248.
    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 advantages (...)
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  33. Boxes and Diamonds. An Open Introduction to Modal Logic.Richard Zach - 2019
    A textbook for modal and other intensional logics based on the Open Logic Project. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals.
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  34. Modal Science.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):453-492.
    This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal (...)
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  35.  24
    Making Theorem-Proving in Modal Logic Easy.Paul Needham - 2009 - In Lars-Göran Johansson, Jan Österberg & Rysiek Śliwiński (eds.), Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel. Uppsala, Sverige: pp. 187-202.
    A system for the modal logic K furnishes a simple mechanical process for proving theorems.
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  36. The Possibility of Unicorns and Modal Logic.Lee Walters - 2014 - Analytic Philosophy 55 (2):295-305.
    Michael Dummett argues, against Saul Kripke, that there could have been unicorns. He then claims that this possibility shows that the logic of metaphysical modality is not S5, and, in particular, that the B axiom is false. Dummett’s argument against B, however, is invalid. I show that although there are number of ways to repair Dummett’s argument against B, each requires a controversial metaphysical or semantic commitment, and that, regardless of this, the case against B is undermotivated. Dummett’s case (...)
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  37.  64
    Remark on Al-Fārābī's Missing Modal Logic and its Effect on Ibn Sīnā.Wilfrid Hodges - 2019 - Eshare: An Iranian Journal of Philosophy 1 (3):39-73.
    We reconstruct as much as we can the part of al-Fārābī's treatment of modal logic that is missing from the surviving pages of his Long Commentary on the Prior Analytics. We use as a basis the quotations from this work in Ibn Sīnā, Ibn Rushd and Maimonides, together with relevant material from al-Fārābī's other writings. We present a case that al-Fārābī's treatment of the dictum de omni had a decisive effect on the development and presentation of Ibn Sīnā's (...)
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  38. Two-Sided Trees for Sentential Logic, Predicate Logic, and Sentential Modal Logic.Jesse Fitts & David Beisecker - 2019 - Teaching Philosophy 42 (1):41-56.
    This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.
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  39. Dispositionalism and the Modal Operators.David Yates - 2015 - Philosophy and Phenomenological Research 91 (2):411-424.
    Actualists of a certain stripe—dispositionalists—hold that metaphysical modality is grounded in the powers of actual things. Roughly: p is possible iff something has, or some things have, the power to bring it about that p. Extant critiques of dispositionalism focus on its material adequacy, and question whether there are enough powers to account for all the possibilities we intuitively want to countenance. For instance, it seems possible that none of the actual contingent particulars ever existed, but it is impossible to (...)
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  40. The Logic(s) of Modal Knowledge.Daniel Cohnitz - 2012 - In Greg Restall & Gillian Russell (eds.), New Waves in Philosophical Logic. MacMillan.
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  41. A Perspective on Modal Sequent Logic.Stephen Blamey & Lloyd Humberstone - 1991 - Publications of the Research Institute for Mathematical Sciences 27 (5):763-782.
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  42. Modal Skepticism and Counterfactual Knowledge.Juhani Yli-Vakkuri - 2013 - Philosophical Studies 162 (3):605-623.
    Abstract Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic ( Reducibility ). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference ( counterfactual development , or CD ) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays any essential role in (...)
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  43. Hegel’s Modal Argument Against Spinozism. An Interpretation of the Chapter ‘Actuality’ in the Science of Logic.Franz Knappik - 2015 - Hegel Bulletin 36 (1):53-79.
    I propose a new reading of Hegel’s discussion of modality in the ‘Actuality’ chapter of the Science of Logic. On this reading, the main purpose of the chapter is a critical engagement with Spinoza’s modal metaphysics. Hegel first reconstructs a rationalist line of thought — corresponding to the cosmological argument for the existence of God — that ultimately leads to Spinozist necessitarianism. He then presents a reductio argument against necessitarianism, contending that as a consequence of necessitarianism, no adequate (...)
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  44. Debunking Arguments: Mathematics, Logic, and Modal Security.Justin Clarke-Doane - forthcoming - In Robert Richards and Michael Ruse (ed.), The Cambridge Handbook of Evolutionary Ethics. Cambridge University Press.
    I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...)
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  45.  94
    Modal Fragmentalism.Samuele Iaquinto - 2020 - The Philosophical Quarterly 70 (280):570-587.
    In this paper I will argue that there is a version of possibilism—inspired by the modal analogue of Kit Fine’s fragmentalism—that can be combined with a weakening of actualism. The reasons for analysing this view, which I call Modal Fragmentalism, are twofold. Firstly, it can enrich our understanding of the actualism/possibilism divide, by showing that, at least in principle, the adoption of possibilia does not correspond to an outright rejection of the actualist intuitions. Secondly, and more specifically, it (...)
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  46.  56
    Modal Definability in Enriched Languages.Valentin Goranko - 1989 - Notre Dame Journal of Formal Logic 31 (1):81-105.
    The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So, a notion of "polymodal base" arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper's main paradigm. The modal definability (in the spirit of van Benthem's correspondence theory) of arbitrary and ~-elementary classes of frames in this base and (...)
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  47. Modal Ontology and Generalized Quantifiers.Peter Fritz - 2013 - Journal of Philosophical Logic 42 (4):643-678.
    Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with (...)
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  48. Post Completeness in Congruential Modal Logics.Peter Fritz - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. College Publications. pp. 288-301.
    Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in (...)
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  49. A Semantic Constraint on the Logic of Modal Conditionals.Zsófia Zvolenszky - 2006 - Proceedings of the Ninth Symposium on Logic and Language (LoLa 9).
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  50. Modal Set Theory.Christopher Menzel - forthcoming - In Otávio Bueno & Scott Shalkowski (eds.), The Routledge Handbook of Modality. London and New York: Routledge.
    This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.
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