Search results for 'modal relations' (try it on Scholar)

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  1.  10
    Natasha Alechina, Philippe Balbiani & Dmitry Shkatov (2012). Modal Logics for Reasoning About Infinite Unions and Intersections of Binary Relations. Journal of Applied Non-Classical Logics 22 (4):275 - 294.
    (2012). Modal logics for reasoning about infinite unions and intersections of binary relations. Journal of Applied Non-Classical Logics: Vol. 22, No. 4, pp. 275-294. doi: 10.1080/11663081.2012.705960.
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  2. Bruno Teheux (forthcoming). Modal Definability Based on Łukasiewicz Validity Relations. Studia Logica:1-21.
    We study two notions of definability for classes of relational structures based on modal extensions of Łukasiewicz finitely-valued logics. The main results of the paper are the equivalent of the Goldblatt-Thomason theorem for these notions of definability.
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  3.  1
    Philippe Balbiani & Ewa Orlowska (1999). A Hierarchy of Modal Logics with Relative Accessibility Relations. Journal of Applied Non-Classical Logics 9 (2-3):303-328.
    ABSTRACT In this paper we introduce and investigate various classes of multimodal logics based on frames with relative accessibility relations. We discuss their applicability to representation and analysis of incomplete information. We provide axiom systems for these logics and we prove their completeness.
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  4.  17
    Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part I. Studia Logica 65 (3):323-353.
    This work is divided in two papers (Part I and Part II). In Part I, we study a class of polymodal logics (herein called the class of "Rare-logics") for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability are established by faithfully translating (...)
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  5.  10
    Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II. Studia Logica 66 (3):349-384.
    This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal (...)
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  6.  32
    Robin Hirsch & Ian Hodkinson (1999). Mosaics and Step-by-Step| Remarks onA Modal Logic of Relations' by Venema & Marx. In E. Orłowska (ed.), Logic at Work. Heidelberg
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  7.  11
    Krister Segerberg (1970). Modal Logics with Linear Alternative Relations. Theoria 36 (3):301-322.
  8.  3
    Krister Segerberg (1986). Modal Logics with Functional Alternative Relations. Notre Dame Journal of Formal Logic 27 (4):504-522.
  9.  14
    Frederic B. Fitch (1973). A Correlation Between Modal Reduction Principles and Properties of Relations. Journal of Philosophical Logic 2 (1):97 - 101.
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  10.  4
    Mary-Anne Williams, Thomas Meyer, Basic Infobase Change, David Billington & Andrew Rock (2001). Witold A. Pogorzelski, Piotr Wojtylak/Cn-Defini-Tions of Propositional Connectives 1 Su Gao, Peter Gerdes/Computably Enumerable Equiva-Lence Relations 27 Yoshihito Tanaka/Model Existence in Non-Compact Modal. [REVIEW] Studia Logica 67:439-440.
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  11. Gebhard Fuhrken (1959). Review: Chandler Davis, Modal Operators, Equivalence Relations, and Projective Algebras. [REVIEW] Journal of Symbolic Logic 24 (3):253-253.
     
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  12. Robin Hirsch, Ian Hodkinson, Maarten Marx, Szabolsc Mikulás & Mark Reynolds (1999). Mosaics and Step-by-Step. Remarks on “A Modal Logic of Relations”. In E. Orłowska (ed.), Logic at Work. Heidelberg
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  13. Moshe Kroy (1976). Mentalism and Modal Logic: A Study in the Relations Between Logical and Metaphysical Systems. Athenaion.
     
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  14. Dimiter Vakarelov (2008). A Modal Approach to Dynamic Ontology: Modal Mereotopology. Logic and Logical Philosophy 17 (1-2):163-183.
    In this paper we show how modal logic can be applied in the axiomatizations of some dynamic ontologies. As an example we consider the case of mereotopology, which is an extension of mereology with some relations of topological nature like contact relation. We show that in the modal extension of mereotopology we may define some new mereological and mereotopological relations with dynamic nature like stable part-of and stable contact. In some sense such “stable” relations can (...)
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  15.  38
    Hans Smessaert (2009). On the 3d Visualisation of Logical Relations. Logica Universalis 3 (2):303-332.
    The central aim of this paper is to present a Boolean algebraic approach to the classical Aristotelian Relations of Opposition, namely Contradiction and (Sub)contrariety, and to provide a 3D visualisation of those relations based on the geometrical properties of Platonic and Archimedean solids. In the first part we start from the standard Generalized Quantifier analysis of expressions for comparative quantification to build the Comparative Quantifier Algebra CQA. The underlying scalar structure allows us to define the Aristotelian (...)
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  16.  19
    Jesse Hughes, Albert Esterline & Bahram Kimiaghalam (2006). Means-End Relations and a Measure of Efficacy. Journal of Logic, Language and Information 15 (1-2):83-108.
    Propositional dynamic logic (PDL) provides a natural setting for semantics of means-end relations involving non-determinism, but such models do not include probabilistic features common to much practical reasoning involving means and ends. We alter the semantics for PDL by adding probabilities to the transition systems and interpreting dynamic formulas 〈α〉 ϕ as fuzzy predicates about the reliability of α as a means to ϕ. This gives our semantics a measure of efficacy for means-end relations.
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  17.  50
    Peter Fritz (forthcoming). First-Order Modal Logic in the Necessary Framework of Objects. Canadian Journal of Philosophy.
    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 that (...)
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  18.  16
    Lloyd Humberstone (2007). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 36 (5):435 - 487.
    We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and (...)
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  19.  15
    Lloyd Humberstone (2006). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 35 (5):435 - 487.
    We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and (...)
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  20.  62
    Jan Heylen (2013). Modal-Epistemic Arithmetic and the Problem of Quantifying In. Synthese 190 (1):89-111.
    The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of (...)
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  21. Susanne Bobzien (1993). Chrysippus' Modal Logic and Its Relation to Philo and Diodorus. In K. Doering & Th Ebert (eds.), Dialektiker und Stoiker. Franz Steiner 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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  22.  78
    Sam Cowling (2012). Haecceitism for Modal Realists. Erkenntnis 77 (3):399-417.
    In this paper, I examine the putative incompatibility of three theses: (1) Haecceitism, according to which some maximal possibilities differ solely in terms of the non-qualitative or de re possibilities they include; (2) Modal correspondence, according to which each maximal possibility is identical with a unique possible world; (3) Counterpart theory, according to which de re modality is analyzed in terms of counterpart relations between individuals. After showing how the modal realism defended by David Lewis resolves this (...)
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  23.  37
    Xavier Caicedo & Ricardo O. Rodriguez (2010). Standard Gödel Modal Logics. Studia Logica 94 (2):189 - 214.
    We prove strong completeness of the □-version and the ◊-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations (...)
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  24. Norman M. Swartz, Foreknowledge and Free Will. Internet Encyclopedia of Philosophy.
    Suppose it were known, by someone else, what you are going to choose to do tomorrow. Wouldn't that entail that tomorrow you must do what it was known in advance that you would do? In spite of your deliberating and planning, in the end, all is futile: you must choose exactly as it was earlier known that you would. The supposed exercise of your free will is ultimately an illusion. Historically, the tension between foreknowledge and the exercise of free will (...)
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  25.  26
    Susanne Bobzien (1986). Die stoische Modallogik (Stoic Modal Logic). Königshausen & Neumann.
    ABSTRACT: Part 1 discusses the Stoic notion of propositions (assertibles, axiomata): their definition; their truth-criteria; the relation between sentence and proposition; propositions that perish; propositions that change their truth-value; the temporal dependency of propositions; the temporal dependency of the Stoic notion of truth; pseudo-dates in propositions. Part 2 discusses Stoic modal logic: the Stoic definitions of their modal notions (possibility, impossibility, necessity, non-necessity); the logical relations between the modalities; modalities as properties of propositions; contingent propositions; the relation (...)
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  26.  22
    Edward N. Zalta, The Theory of Relations, Complex Terms, and a Connection Between Λ and Ε Calculi.
    This paper introduces a new method of interpreting complex relation terms in a second-order quantified modal language. We develop a completely general second-order modal language with two kinds of complex terms: one kind for denoting individuals and one kind for denoting n-place relations. Several issues arise in connection with previous, algebraic methods for interpreting the relation terms. The new method of interpreting these terms described here addresses those issues while establishing an interesting connection between λ and ε (...)
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  27.  30
    Gilbert T. Null (2007). The Ontology of Intentionality II: Dependence Ontology as Prolegomenon to Noetic Modal Semantics. [REVIEW] Husserl Studies 23 (2):119-159.
    This is the second in a sequence of three essays which axiomatize and apply Edmund Husserl's dependence ontology of parts and wholes as a non-Diodorean, non-Kantian temporal semantics for first-order predicate modal languages. The Ontology of Intentionality I introduced enough of Husserl's dependence-ontology of parts and wholes to formulate his account of order as effected by relating moments of unity, and The Ontology of Intentionality II extends that axiomatic dependence-ontology far enough to enable its semantic application. Formalizing the compatibility (...)
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  28.  25
    Arnon Avron, Furio Honsell, Marino Miculan & Cristian Paravano (1998). Encoding Modal Logics in Logical Frameworks. Studia Logica 60 (1):161-208.
    We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbert- and Natural Deduction-style proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed -calculus metalanguage of the Logical Frameworks. These formalizations yield readily proof-editors for Modal Logics when implemented in Proof Development Environments, such as Coq (...)
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  29.  18
    Ernst Zimmermann (2003). Elementary Definability and Completeness in General and Positive Modal Logic. Journal of Logic, Language and Information 12 (1):99-117.
    The paper generalises Goldblatt's completeness proof for Lemmon–Scott formulas to various modal propositional logics without classical negation and without ex falso, up to positive modal logic, where conjunction and disjunction, andwhere necessity and possibility are respectively independent.Further the paper proves definability theorems for Lemmon–Scottformulas, which hold even in modal propositional languages without negation and without falsum. Both, the completeness theorem and the definability theoremmake use only of special constructions of relations,like relation products. No second order logic, (...)
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  30.  14
    Tim Fernando (1999). A Modal Logic for Non-Deterministic Discourse Processing. Journal of Logic, Language and Information 8 (4):445-468.
    A modal logic for translating a sequence of English sentences to a sequence of logical forms is presented, characterized by Kripke models with points formed from input/output sequences, and valuations determined by entailment relations. Previous approaches based (to one degree or another) on Quantified Dynamic Logic are embeddable within it. Applications to presupposition and ambiguity are described, and decision procedures and axiomatizations supplied.
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  31.  7
    Jonas De Vuyst (2013). Dynamic Tableaux for Dynamic Modal Logics. Dissertation, Vrije Universiteit Brussel
    In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- (...)
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  32.  10
    Gunnar Björnsson (2004). A Naturalist's Approach to Modal Intuitions. In Erik Weber Tim De Mey (ed.), Modal Epistemology.
    Modal inquiry is plagued by methodological problems. The best-developed views on modal semantics and modal ontology take modalstatements to be true in virtue of relations between possible worlds. Unfortunately, such views turn modal epistemology into a mystery, and this paper is about ways to avoid that problem. It looks at different remedies suggested by Quine, Blackburn and Peacocke and finds them all wanting. But although Peacocke’s version of the popular conceptualist approach fails to give a (...)
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  33. Christopher Menzel (2015). Logic, Essence, and Modality Bob Hale. Necessary Beings: An Essay on Ontology, Modality, & the Relations Between Them. Oxford University Press, 2013. ISBN: 978-0-19-966262-3 ; 978-0-19-874803-8 ; 978-0-19-164834-2 . Pp. Ix + 298. [REVIEW] Philosophia Mathematica 23 (3):407-428.
    Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonably thorough (if (...)
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  34.  78
    Allen Hazen (1976). Expressive Completeness in Modal Language. Journal of Philosophical Logic 5 (1):25--46.
    The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, (...)
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  35.  50
    Melvin Fitting, Many-Valued Modal Logics II.
    Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common (...) language, and on what sentences will they agree? This problem can be reformulated as one about many-valued Kripke models, allowing many-valued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the many-valued version and the multiple expert one will be formally established. Finally we will axiomatize many-valued modal logics, and sketch a proof of completeness. (shrink)
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  36.  27
    Jennifer Wang, Modal Primitivism.
    Modal primitivism is the view that there are modal features of the world which cannot be reduced to the non-modal. Theories which embrace primitive modality are often rejected for reasons of ideological simplicity: the fewer primitive notions a theory invokes, the better. Furthermore, modal primitivism is often associated with the view that all modal features of the world are irreducibly modal, which appears unsystematic and unexplanatory. As a result, many prefer modal reductionism. This (...)
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  37.  2
    Hans Smessaert (2012). The Classical Aristotelian Hexagon Versus the Modern Duality Hexagon. Logica Universalis 6 (1-2):171-199.
    Peters and Westerståhl (Quantifiers in Language and Logic, 2006), and Westerståhl (New Perspectives on the Square of Opposition, 2011) draw a crucial distinction between the “classical” Aristotelian squares of opposition and the “modern” Duality squares of opposition. The classical square involves four opposition relations, whereas the modern one only involves three of them: the two horizontal connections are fundamentally distinct in the Aristotelian case (contrariety, CR vs. subcontrariety, SCR) but express the same Duality relation of internal negation (SNEG). Furthermore, (...)
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  38. George Bealer (1979). Theories of Properties, Relations, and Propositions. Journal of Philosophy 76 (11):634-648.
    This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the (...)
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  39.  24
    Marko Malink (2006). A Reconstruction of Aristotle's Modal Syllogistic. History and Philosophy of Logic 27 (2):95-141.
    Ever since ?ukasiewicz, it has been opinio communis that Aristotle's modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle's syllogistic is a pure term logic that does not recognize an extra syntactic category of individual symbols besides syllogistic terms and, (...)
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  40.  10
    Pavel Hrubeš (2007). Lower Bounds for Modal Logics. Journal of Symbolic Logic 72 (3):941 - 958.
    We give an exponential lower bound on number of proof-lines in the proof system K of modal logic, i.e., we give an example of K-tautologies ψ₁, ψ₂,... s.t. every K-proof of ψi must have a number of proof-lines exponential in terms of the size of ψi. The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel—Löb's logic, S and S4. We also determine some speed-up relations between different systems of modal logic on formulas (...)
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  41.  17
    Vaughan R. Pratt (1980). Application of Modal Logic to Programming. Studia Logica 39 (2-3):257 - 274.
    The modal logician's notion of possible world and the computer scientist's notion of state of a machine provide a point of commonality which can form the foundation of a logic of action. Extending ordinary modal logic with the calculus of binary relations leads to a very natural logic for describing the behavior of computer programs.
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  42.  57
    Jaap van der Does, Willem Groeneveld & Frank Veltman (1997). An Update on “Might”. Journal of Logic, Language and Information 6 (4):361-380.
    This paper is on the update semantics for might of Veltman (1996). Threeconsequence relations are introduced and studied in an abstract setting.Next we present sequent-style systems for each of the consequence relations.We show the logics to be complete and decidable. The paper ends with asyntactic cut elimination result.
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  43.  38
    Milan Božić & Kosta Došen (1984). Models for Normal Intuitionistic Modal Logics. Studia Logica 43 (3):217 - 245.
    Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given for analogues of the modal systemK based on Heyting's prepositional logic. It is shown that these two relations can combine with each other in various ways. Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both. Embeddings in modal systems with several modal operators, based on classical propositional logic, are also considered. (...)
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  44.  18
    Melvin Fitting (1995). Tableaus for Many-Valued Modal Logic. Studia Logica 55 (1):63 - 87.
    We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cut-free tableau formulation is presented, and its completeness is proved.
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  45.  17
    Bengt Hansson (1968). Fundamental Axioms for Preference Relations. Synthese 18 (4):423 - 442.
    The basic theory of preference relations contains a trivial part reflected by axioms A1 and A2, which say that preference relations are preorders. The next step is to find other axims which carry the theory beyond the level of the trivial. This paper is to a great part a critical survey of such suggested axioms. The results are much in the negative — many proposed axioms imply too strange theorems to be acceptable as axioms in a general theory (...)
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  46.  96
    Edward N. Zalta (1997). The Modal Object Calculus and its Interpretation. In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer 249--279.
    The modal object calculus is the system of logic which houses the (proper) axiomatic theory of abstract objects. The calculus has some rather interesting features in and of itself, independent of the proper theory. The most sophisticated, type-theoretic incarnation of the calculus can be used to analyze the intensional contexts of natural language and so constitutes an intensional logic. However, the simpler second-order version of the calculus couches a theory of fine-grained properties, relations and propositions and serves as (...)
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  47.  18
    Kosta Došen (1985). Models for Stronger Normal Intuitionistic Modal Logics. Studia Logica 44 (1):39 - 70.
    This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown (...)
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  48.  6
    Alberto Gatto (forthcoming). Axiomatization of a Branching Time Logic with Indistinguishability Relations. Journal of Philosophical Logic:1-28.
    Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.
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  49.  49
    Tim Fernando, Towards a Many-Dimensional Modal Logic for Semantic Processing.
    Notions of context for natural language interpretation are factored in terms of three processes: translation, entailment and attunement. The processes are linked by accessibility relations of the kind studied in many-dimensional modal logic, modulo complications from constraints between translation and entailment (violations in which may trigger re-attunement) and from refinement and underspecification.
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  50.  65
    David Hunter (2007). Common Ground and Modal Disagreement. In H. V. Hanson (ed.), Dissensus and the Search for Common Ground. 134-143.
    The common ground in an inquiry consists of what the participants agree on, at least for the sake of the inquiry. The relations between the factual and linguistic components of common ground are notoriously difficult to trace. I clarify them by exploring how modal disagreements – disagreements about how things might be – interact with the linguistic and the factual common ground. I argue that modal agreement is essential to common ground of any kind.
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