Results for 'S4'

18 found
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  1. If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 Axiom.Susanne Bobzien - 2012 - In B. Morison K. Ierodiakonou (ed.), Episteme, etc.: Essays in honour of Jonathan Barnes. OUP UK.
    The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context (...)
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  2. 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 (...)
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  3. Peacockes Principle-Based Account of Modality: “Flexibility of OriginsPlus S4.Sonia Roca-Royes - 2006 - Erkenntnis 65 (3):405-426.
    Due to the influence of Nathan Salmons views, endorsement of theflexibility of originsthesis is often thought to carry a commitment to the denial of (...)S4. This paper rejects the existence of this commitment and examines how Peacockes theory of the modal may accommodate flexibility of origins without denying S4. One of the essential features of Peacockes account is the identification of the Principles of Possibility, which include the Modal Extension Principle (MEP), and a set of Constitutive Principles. Regarding their modal status, Peacocke argues for the necessity of MEP, but leaves open the possibility that some of the Constitutive Principles be only contingently true. Here, I show that the contingency of the Constitutive Principles is inconsistent with the recursivity of MEP, and this makes the account validate S4. It is also shown that, compatibly with the necessity of the Constitutive Principles, the account can still accommodate intuitions about flexibility of origins. However, the account we end up with once those intuitions are consistently accommodated may not be satisfactory, and this opens up the debate about whether or not artefacts allow for some variation in their origins. (shrink)
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  4. McKinsey Algebras and Topological Models of S4.1.Thomas Mormann - manuscript
    The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The (...)construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can be used to prove a completeness theorem for S4.1. Further, it is shown that the McKinsey algebra MKX of a space X endoewed with an alpha-topologiy satisfies Esakia's GRZ axiom. (shrink)
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  5. 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; but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. -/- This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the likethereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewiss S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The authors apologize for the now obsolete terminology. For example, these papers speak ofa proof of a sentence from a set of premiseswhere todaya deduction of a sentence from a set of premiseswould be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 15377. J P R -/- 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 37084. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 37078. MR0351765 (50 #4253). (shrink)
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  6. Essence and Necessity.Andreas Ditter - forthcoming - Journal of Philosophical Logic:1-38.
    What is the relation between metaphysical necessity and essence? This paper defends the view that the relation is one of identity: metaphysical necessity is a special case (...)
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  7. Contingent Existence and the Reduction of Modality to Essence.Trevor Teitel - 2019 - Mind 128 (509):39-68.
    This paper first argues that we can bring out a tension between the following three popular doctrines: (i) the canonical reduction of metaphysical modality to essence, due (...)
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  8. The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
    In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it (...)
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  9. The Reduction of Necessity to Essence.Andreas Ditter - 2020 - Mind 129 (514):351-380.
    In `Essence and Modality', Kit Fine proposes that for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of (...)
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  10. 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 (...)
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  11. IColumnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness.Susanne Bobzien - 2015 - Aristotelian Society Supplementary Volume 89 (1):61-87.
    Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, (...)the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system QS4M+BF+FIN. It corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlinenessone associated with genuine higher-order vagueness, the other employed to sort objects into categoriesand that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)
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  12. Topological Models of Columnar Vagueness.Thomas Mormann - 2020 - Erkenntnis:1-24.
    This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology (...). First, we provide atranslationof Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitts recent topological reconstruction of Sainsburys theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobziens account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenforsconceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamsonslogic of clarityis explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamsons logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of aslim boundaryare (stably) columnar. Thus, Williamsons logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)
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  13.  52
    A Henkin-Style Completeness Proof for the Modal Logic S5.Bruno Bentzen - 2021 - In Pietro Baroni, Christoph Benzmüller & Yì N. Wáng (eds.), Logic and Argumentation: Fourth International Conference, CLAR 2021, Hangzhou, China, October 20–22. Springer. pp. 459-467.
    This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is (...)close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive logical connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2. (shrink)
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  14. Essentialism Vis-À-Vis Possibilia, Modal Logic, and Necessitism.Sonia Roca-Royes - 2011 - Philosophy Compass 6 (1):54-64.
    Pace Necessitismroughly, the view that existence is not contingentessential 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 will briefly see the challenge that arises against S4 from flexible essential properties; as well as the moves available to block it. After this, the emphasis is put on the Barcan Formula (BF), and on why it is problematic for essentialists. As we will see, Necessitism can accommodate both (BF) and essential properties. What necessitists cannot do at the same time is to continue to understanding essential properties as providing necessary conditions for the existence of individuals; against what might be for some a truism. (shrink)
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  15. 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 (...)
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  16. An Imaginative Persons Guide to Objective Modality.Derek Lam - forthcoming - In Amy Kind & Christopher Badura (eds.), Epistemic Uses of Imagination. Routledge.
    Imagination is a source of evidence for objective modality. It is through this epistemic connection that the idea of modality first gains traction in our intellectual life. (...)
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  17.  44
    Computational Capacity of Pyramidal Neurons in the Cerebral Cortex.Danko D. Georgiev, Stefan K. Kolev, Eliahu Cohen & James F. Glazebrook - 2020 - Brain Research 1748:147069.
    The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their (...)length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper assessment of the computational capacity of pyramidal neurons, we have analyzed an extensive dataset of three-dimensional digital reconstructions from the NeuroMorphoOrg database, and quantified basic dendritic or axonal morphometric measures in different regions and layers of the mouse, rat or human cerebral cortex. Physical estimates of the total number and type of ions involved in neuronal electric spiking based on the obtained morphometric data, combined with energetics of neurotransmitter release and signaling fueled by glucose consumed by the active brain, support highly efficient cerebral computation performed at the thermodynamically allowed Landauer limit for implementation of irreversible logical operations. Individual proton tunneling events in voltage-sensing S4 protein alpha-helices of Na+, K+ or Ca2+ ion channels are ideally suited to serve as single Landauer elementary logical operations that are then amplified by selective ionic currents traversing the open channel pores. This miniaturization of computational gating allows the execution of over 1.2 zetta logical operations per second in the human cerebral cortex without combusting the brain by the released heat. (shrink)
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  18. Business Development Strategy Analysis PT. X Using the SWOT Method.Novi Shobi Hendri, Ahmadi, Okol S. Suharyo & Arica Dwi Susanto - 2019 - International Journal of Academic and Applied Research (IJAAR) 3 (4):15-20.
    Abstract: With the many businesses in Indonesia, the competition for change and uncertainty becomes more stringent, so that this situation creates sharp competition between companies. The aim (...)
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