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  1. Ernest W. Adams (1977). A Note on Comparing Probabilistic and Modal Logics of Conditionals. Theoria 43 (3):186-194.
  2. J. W. Addison (ed.) (1965). The Theory of Models. Amsterdam, North-Holland Pub. Co..
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  3. Thomas Ågotnes, Wiebe van der Hoek & Michael Wooldridge (2008). Quantified Coalition Logic. Synthese 165 (2):269 - 294.
    We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is (...)
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  4. Juan C. Agudelo & Walter Carnielli (2011). Polynomial Ring Calculus for Modal Logics: A New Semantics and Proof Method for Modalities. Review of Symbolic Logic 4 (1):150-170.
    A new (sound and complete) proof style adequate for modal logics is defined from the polynomial ring calculus (PRC). The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra–Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S5, and can be easily extended (...)
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  5. Luca Alberucci & Alessandro Facchini (2009). The Modal Μ-Calculus Hierarchy Over Restricted Classes of Transition Systems. Journal of Symbolic Logic 74 (4):1367 - 1400.
    We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternationfree fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for (...)
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  6. Jean-Pascal Alcantara (2012). Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as a Procrustean Bed for His Modal Metaphysics. In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. 53--71.
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  7. Gerard Allwein, Hilmi Demir & Lee Pike (2004). Logics for Classes of Boolean Monoids. Journal of Logic, Language and Information 13 (3):241-266.
    This paper presents the algebraic and Kripke modelsoundness and completeness ofa logic over Boolean monoids. An additional axiom added to thelogic will cause the resulting monoid models to be representable as monoidsof relations. A star operator, interpreted as reflexive, transitiveclosure, is conservatively added to the logic. The star operator isa relative modal operator, i.e., one that is defined in terms ofanother modal operator. A further example, relative possibility,of this type of operator is given. A separate axiom,antilogism, added to the logic (...)
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  8. J. E. J. Altham (1969). An Introduction to Modal Logic. Philosophical Books 10 (3):10-12.
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  9. José Tomás Alvarado Marambio (2013). Fórmulas Barcan de segundo orden Y universales trascendentes. Ideas Y Valores 62 (152):111-131.
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  10. José Tomás Alvarado Marambio (2013). Second-Order Barcan Formulas and Transcendent Universals. Ideas Y Valores 62 (152):111-131.
    RESUMEN Se ha destacado que la Fórmula de Barcan -FB- y la Conversa de la Fórmula de Barcan -CFB- para lógica modal cuantificacional de orden superior parecen válidas. Si se interpreta que los cuantificadores tienen como rango propiedades, la validez de FB y CFB parece implicar la existencia de universales trascendentes, que no requieren estar instanciados para existir en un mundo posible. Se discute esta argumentación, porque la semántica, en la que los resultados de validez se siguen, no requiere que (...)
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  11. Logique A. Analyse (1999). Combination Semantics for Intensional Logics Part I Makings and Their Use in Making Combination Semantics Jerzy Perzanowski. Logique Et Analyse 42:181.
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  12. Alan Ross Anderson (1958). A Reduction of Deontic Logic to Alethic Modal Logic. Mind 67 (265):100-103.
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  13. C. Anthony Anderson (1989). Russellian Intensional Logic. In John Perry, J. Almog & Howard K. Wettstein (eds.), Themes From Kaplan. Oxford University Press. 67--103.
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  14. Hajnal Andréka, István Németi & Johan van Benthem (1998). Modal Languages and Bounded Fragments of Predicate Logic. Journal of Philosophical Logic 27 (3):217 - 274.
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  15. G. Aldo Antonelli & Richmond H. Thomason (2002). Representability in Second-Order Propositional Poly-Modal Logic. Journal of Symbolic Logic 67 (3):1039-1054.
    A propositional system of modal logic is second-order if it contains quantifiers ∀p and ∃p, which, in the standard interpretation, are construed as ranging over sets of possible worlds (propositions). Most second-order systems of modal logic are highly intractable; for instance, when augmented with propositional quantifiers, K, B, T, K4 and S4 all become effectively equivalent to full second-order logic. An exception is S5, which, being interpretable in monadic second-order logic, is decidable.
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  16. Takahito Aoto & Hiroyuki Shirasu (1999). On the Finite Model Property of Intuitionistic Modal Logics Over MIPC. Mathematical Logic Quarterly 45 (4):435-448.
    MIPC is a well-known intuitionistic modal logic of Prior and Bull . It is shown that every normal intuitionistic modal logic L over MIPC has the finite model property whenever L is Kripke-complete and universal.
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  17. Peter Apostoli (1997). On the Completeness of First Degree Weakly Aggregative Modal Logics. Journal of Philosophical Logic 26 (2):169-180.
    This paper extends David Lewis' result that all first degree modal logics are complete to weakly aggregative modal logic by providing a filtration-theoretic version of the canonical model construction of Apostoli and Brown. The completeness and decidability of all first-degree weakly aggregative modal logics is obtained, with Lewis's result for Kripkean logics recovered in the case k = 1.
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  18. Peter Apostoli & Bryson Brown (1995). A Solution to the Completeness Problem for Weakly Aggregative Modal Logic. Journal of Symbolic Logic 60 (3):832-842.
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  19. Lennart Åqvist (2010). Grades of Probability Modality in the Law of Evidence. Studia Logica 94 (3):307 - 330.
    The paper presents an infinite hierarchy PR m [ m = 1, 2, . . . ] of sound and complete axiomatic systems for modal logic with graded probabilistic modalities , which are to reflect what I have elsewhere called the Bolding-Ekelöf degrees of evidential strength as applied to the establishment of matters of fact in law-courts. Our present approach is seen to differ from earlier work by the author in that it treats the logic of these graded modalities not (...)
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  20. Lennart Åqvist (2002). Old Foundations for the Logic of Agency and Action. Studia Logica 72 (3):313-338.
    The paper presents an infinite hierarchy of sound and complete axiomatic systems for Two-Dimensional Modal Tense Logic with Historical Necessity, Agents and Acts. A main novelty of these logics is their capacity to represent formally (i) basic action-sentences asserting that such and such an act is performed/omitted by an agent, as well as (ii) causative action-sentences asserting that by performing/omitting a certain act, an agent causes that such and such a state-of-affairs is realized (e.g. comes about/ceases/remains/remains absent). We illustrate how (...)
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  21. Lennart Åqvist (1996). Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization. [REVIEW] Journal of Philosophical Logic 25 (1):45 - 100.
    The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with (...)
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  22. Lennart Åqvist (1971). The Completeness of Some Modal Logics with Circumstantials, Subjunctive Conditionals, Transworld Identity and Dispositional Predicates. [Uppsala,Uppsala Universitet].
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  23. Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano (2013). Completeness in Hybrid Type Theory. Journal of Philosophical Logic (2-3):1-30.
    We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and first-order hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that (...)
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  24. H. Arlo-Costa (forthcoming). First-Order Modal Logic', to Appear in V. Hendricks & SA Pedersen, Eds.,'40 Years of Possible Worlds', Special Issue Of. Studia Logica.
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  25. Sergei Artemov & Giorgie Dzhaparidze (1990). Finite Kripke Models and Predicate Logics of Provability. Journal of Symbolic Logic 55 (3):1090-1098.
    The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic: If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that $PA \nvdash fR$ . This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding "the predicate part" as a specific (...)
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  26. Francesco Arzillo (2011). Il Fondamento Del Giudizio: Una Proposta Teoretica a Partire Dalla Filosofia Del Senso Comune di Antonio Livi. Casa Editrice Leonardo da Vinci.
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  27. 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 or LEGO.
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  28. Steve Awodey, Lars Birkedal & Dana Scott, Local Realizability Toposes and a Modal Logic for Computability.
    This work is a step toward the development of a logic for types and computation that includes not only the usual spaces of mathematics and constructions, but also spaces from logic and domain theory. Using realizability, we investigate a configuration of three toposes that we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we first study axiomatically, and then by deriving a modal calculus as its internal logic. The resulting (...)
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  29. Franz Baader & Silvio Ghilardi (2007). Connecting Many-Sorted Theories. Journal of Symbolic Logic 72 (2):535 - 583.
    Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the so-called E-connection approach for combining modal logics to an (...)
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  30. John Bacon (1988). Four Modal Modelings. Journal of Philosophical Logic 17 (2):91 - 114.
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  31. Patrice Bailhache (1997). Modal Logic: Acompleteness Met Up Again. Logica Trianguli 1:3-14.
    There are two approaches to logic, semantic and axiomatic. In 1910's, when C.I. Lewis wrote his first papers on modal logic, he adopted the axiomatic approach, the sole one apparently available. The situation remained identical during about forty years, until Kanger, Kripke, and Hintikka discovered the so-called possible worlds semantics. A new flourishing “paradigmatic” period began, and it became possible to define soundness and completeness in modal logic. Unfortunately , however, this period did not go on for more than twenty (...)
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  32. John Robert Baker (1978). Essentialism and the Modal Semantics of J. Hintikka. Notre Dame Journal of Formal Logic 19 (1):81-91.
  33. John Robert Baker (1978). Some Remarks on Quine's Arguments Against Modal Logic. Notre Dame Journal of Formal Logic 19 (4):663-673.
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  34. Roberta Ballarin (2005). Validity and Necessity. Journal of Philosophical Logic 34 (3):275 - 303.
    In this paper I argue against the commonly received view that Kripke's formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke's three main innovations vis-à-vis Carnap's PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: (...)
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  35. Alexandru Baltag & Lawrence S. Moss (2004). Logics for Epistemic Programs. Synthese 139 (2):165 - 224.
    We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of (...)
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  36. Juan Barba Escriba (1991). A Multidimensional Modal Translation for a Formal System Motivated by Situation Semantics. Notre Dame Journal of Formal Logic 32 (4):598-608.
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  37. Juan Barba Escriba (1991). Two Formal Systems for Situation Semantics. Notre Dame Journal of Formal Logic 33 (1):70-88.
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  38. Juan Barba Escriba (1991). A Multidimensional Modal Translation for a Formal System Motivated by Situation Semantics. Notre Dame Journal of Formal Logic 32 (4):598-608.
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  39. Juan Barba Escriba (1991). Two Formal Systems for Situation Semantics. Notre Dame Journal of Formal Logic 33 (1):70-88.
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  40. Richard L. Barber (1954). Two Logics of Modality. Tulane Studies in Philosophy 3:41-54.
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  41. Ruth Barcan Marcus (2011). C. I. Lewis on Intensional Predicate Logic: A Letter Dated May 11, 1960. History and Philosophy of Logic 32 (2):103 - 106.
    History and Philosophy of Logic, Volume 32, Issue 2, Page 103-106, May 2011.
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  42. Stephen Francis Barker (2006). Lewis on Implication. Transactions of the Charles S. Peirce Society 42 (1):10-16.
  43. Jon Barwise & Lawrence S. Moss (1998). Modal Correspondence for Models. Journal of Philosophical Logic 27 (3):275-294.
    This paper considers the correspondence theory from modal logic and obtains correspondence results for models as opposed to frames. The key ideas are to consider infinitary modal logic, to phrase correspondence results in terms of substitution instances of a given modal formula, and to identify bisimilar model-world pairs.
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  44. Patrick K. Bastable (1972). An Introduction to Modal Logic. Philosophical Studies 21:278-278.
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  45. Arnould Bayart (1959). Quasi-Adéquation de la Logique Modale du Second Ordre S5 Et Adéquation de la Logique Modale du Premier Ordre S5 [Quasi-Completeness of Second-Order S5 Modal Logic and Completeness of First-Order S5 Modal Logic]. [REVIEW] Logique Et Analyse 2 (6):99-121.
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  46. J. C. Beall (2003). Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic. Oxford University Press.
    Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.
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  47. Jc Beall (2007). Review of J. W. Garson, Modal Logic for Philosophers. [REVIEW] Notre Dame Philosophical Reviews 2007 (6).
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  48. Jc Beall (2003). Algebraic Methods in Philosophical Logic. Australasian Journal of Philosophy 81 (3):442 – 444.
    Book Information Algebraic Methods in Philosophical Logic. By J. Michael Dunn and Gary Hardegree. Clarendon Press. Oxford. 2001. Pp. xv + 470. 60.50.
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  49. Lev D. Beklemishev (2010). Kripke Semantics for Provability Logic GLP. Annals of Pure and Applied Logic 161 (6):756-774.
    A well-known polymodal provability logic inlMMLBox due to Japaridze is complete w.r.t. the arithmetical semantics where modalities correspond to reflection principles of restricted logical complexity in arithmetic. This system plays an important role in some recent applications of provability algebras in proof theory. However, an obstacle in the study of inlMMLBox is that it is incomplete w.r.t. any class of Kripke frames. In this paper we provide a complete Kripke semantics for inlMMLBox . First, we isolate a certain subsystem inlMMLBox (...)
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  50. Fabio Bellissima & Saverio Cittadini (1999). Minimal P-Morphic Images, Axiomatizations and Coverings in the Modal Logic K. Studia Logica 62 (3):371-398.
    We define the concepts of minimal p-morphic image and basic p-morphism for transitive Kripke frames. These concepts are used to determine effectively the least number of variables necessary to axiomatize a tabular extension of K4, and to describe the covers and co-covers of such a logic in the lattice of the extensions of K4.
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