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  1. Implication, Modality and Intension in Symbolic Logic.Leo Abraham - 1933 - The Monist 43 (1):119-153.
  2. A Note on Comparing Probabilistic and Modal Logics of Conditionals.Ernest W. Adams - 1977 - Theoria 43 (3):186-194.
  3. The Theory of Models.J. W. Addison (ed.) - 1965 - Amsterdam: North-Holland Pub. Co..
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  4. Quantified Coalition Logic.Ågotnes Thomas, Hoek Wiebe van der & Wooldridge Michael - 2008 - 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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  5. A Logic for Reasoning About Knowledge of Unawareness.Thomas Ågotnes & Natasha Alechina - 2014 - Journal of Logic, Language and Information 23 (2):197-217.
    In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of”—without using a stronger statement such as “Ann knows that Bill is aware of \(p\) and Ann is not aware of \(p\) ”, for some particular \(p\) . In Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b) Halpern and Rêgo introduced a logic (...)
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  6. Multi-Modal CTL: Completeness, Complexity, and an Application. [REVIEW]Thomas Ågotnes, Wiebe Van der Hoek, Juan A. Rodríguez-Aguilar, Carles Sierra & Michael Wooldridge - 2009 - Studia Logica 92 (1):1-26.
    We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that (...)
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  7. The Modal Μ-Calculus Hierarchy Over Restricted Classes of Transition Systems.Luca Alberucci & Alessandro Facchini - 2009 - 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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  8. Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as a Procrustean Bed for His Modal Metaphysics.Jean-Pascal Alcantara - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 53--71.
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  9. A General Method for Proving Decidability of Intuitionistic Modal Logics.Natasha Alechina & Dmitry Shkatov - 2006 - Journal of Applied Logic 4 (3):219-230.
  10. Logics for Classes of Boolean Monoids.Gerard Allwein, Hilmi Demir & Lee Pike - 2004 - 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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  11. Simulation Logic.Gerard Allwein, William L. Harrison & David Andrews - 2013 - Logic and Logical Philosophy.
    Simulation relations have been discovered in many areas: Computer Science, philosophical and modal logic, and set theory. However, the simulation condition is strictly a first-order logic statement. We extend modal logic with modalities and axioms, the latter’s modeling conditions are the simulation conditions. The modalities are normal, i.e., commute with either conjunctions or disjunctions and preserve either Truth or Falsity (respectively). The simulations are considered arrows in a category where the objects are descriptive, general frames. One can augment the simulation (...)
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  12. Logic and the World.Joseph Almog - 1989 - Journal of Philosophical Logic 18 (2):197 - 220.
  13. An Introduction to Modal Logic.J. E. J. Altham - 1969 - Philosophical Books 10 (3):10-12.
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  14. Fórmulas Barcan de segundo orden Y universales trascendentes.Alvarado Marambio José Tomás - 2013 - Ideas Y Valores 62 (152):111-131.
    Se ha destacado recientemente que la Fórmula de Barcan y la Conversa de la Fórmula de Barcan para lógica modal cuantificacional de orden superior parecen válidas. Si se interpreta que los cuantificadores tienen como rango propiedades, la validez de y de orden superior parece implicar la existencia de universales trascendentes, esto es, universales que no requieren estar instanciados para existir en un mundo posible. Este trabajo discute esta línea de argumentación. En primer lugar, se sostiene que la semántica en la (...)
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  15. Second-Order Barcan Formulas and Transcendent Universals.José Tomás Alvarado Marambio - 2013 - 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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  16. A Structural Property On Modal Frames Characterizing Default Logic.Gianni Amati, Luigia Aiello, Dov Gabbay & Fiora Pirri - 1996 - Logic Journal of the IGPL 4 (1):7-22.
    We show that modal logics characterized by a class of frames satisfying the insertion property are suitable for Reiter's default logic. We refine the canonical fix point construction defined by Marek, Schwarz and Truszczyński for Reiter's default logic and thus we addrress a new paradigm for nonmonotonic logic. In fact, differently from the construction defined by these authors. we show that suitable modal logics for such a construction must indeed contain K D4. When reflexivity is added to the modal logic (...)
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  17. Combination Semantics for Intensional Logics Part I Makings and Their Use in Making Combination Semantics Jerzy Perzanowski.Logique A. Analyse - 1999 - Logique Et Analyse 42:181.
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  18. A Reduction of Deontic Logic to Alethic Modal Logic.Alan Ross Anderson - 1958 - Mind 67 (265):100-103.
  19. Review: Naoto Yonemitsu, A Note on Modal Systems (II). [REVIEW]Alan Ross Anderson - 1958 - Journal of Symbolic Logic 23 (1):64-64.
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  20. Review: Naoto Yonemitsu, A Note on Modal Systems, von Wright's M and Lewis's SI. [REVIEW]Alan Ross Anderson - 1956 - Journal of Symbolic Logic 21 (4):379-379.
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  21. Yonemitsu Naoto. A Note on Modal Systems, von Wright's M and Lewis's SI. Memoirs of the Osaka University of the Liberal Arts and Education, B. Natural Science, No. 4 , P. 45. [REVIEW]Alan Ross Anderson - 1956 - Journal of Symbolic Logic 21 (4):379.
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  22. Review: Takeo Sugihara, Strict Implication Free From Implicational Paradoxes. [REVIEW]Alan Ross Anderson - 1955 - Journal of Symbolic Logic 20 (3):303-303.
  23. Review: G. H. Von Wright, Interpretations of Modal Logic. [REVIEW]Alan Ross Anderson - 1953 - Journal of Symbolic Logic 18 (2):176-177.
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  24. Review: Georg H. V. Wright, An Essay in Modal Logic. [REVIEW]Alan Ross Anderson - 1953 - Journal of Symbolic Logic 18 (2):174-176.
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  25. Von Wright G. H.. Interpretations of Modal Logic. Mind, N.S. Vol. 61 , Pp. 165–177.Alan Ross Anderson - 1953 - Journal of Symbolic Logic 18 (2):176-177.
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  26. Russellian Intensional Logic.C. Anthony Anderson - 1989 - In John Perry, J. Almog & Howard K. Wettstein (eds.), Themes From Kaplan. Oxford University Press. pp. 67--103.
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  27. Modal Languages and Bounded Fragments of Predicate Logic.Andréka Hajnal, Németi István & Benthem Johan van - 1998 - Journal of Philosophical Logic 27 (3):217 - 274.
    What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...)
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  28. Back and Forth Between Modal Logic and Classical Logic.Hajnal Andreka, Johan van Benthem & Istvan Nemeti - 1995 - Logic Journal of the IGPL 3 (5):685-720.
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  29. Representability in Second-Order Propositional Poly-Modal Logic.G. Aldo Antonelli & Richmond H. Thomason - 2002 - 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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  30. On the Finite Model Property of Intuitionistic Modal Logics Over MIPC.Takahito Aoto & Hiroyuki Shirasu - 1999 - 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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  31. On the Completeness of First Degree Weakly Aggregative Modal Logics.Peter Apostoli - 1997 - 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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  32. Modal Aggregation and the Theory of Paraconsistent Filters.Peter Apostoli - 1996 - Mathematical Logic Quarterly 42 (1):175-190.
    This paper articulates the structure of a two species of weakly aggregative necessity in a common idiom, neighbourhood semantics, using the notion of a k-filter of propositions. A k-filter on a non-empty set I is a collection of subsets of I which contains I, is closed under supersets on I, and contains ∪{Xi ≤ Xj : 0 ≤ i < j ≤ k} whenever it contains the subsets X0,…, Xk. The mathematical content of the proof that weakly aggregative modal logic (...)
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  33. An Essay in Natural Modal Logic.Peter Apostoli - 1991 - Dissertation, The University of British Columbia (Canada)
    A generalized inclusion frame consists of a set of points W and an assignment of a binary relation $R\sb{w}$ on W to each point w in W. Generalized inclusion frames whose $R\sb{w}$ are partial orders are called comparison frames. Conditional logics of various comparative notions, for example, Lewis's V-logic of comparative possibility and utilitarian accounts of conditional obligation, model the dyadic modal operator $>$ on comparison frames according to the following truth condition: $\alpha > \beta$ "holds at w" iff every (...)
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  34. A Solution to the Completeness Problem for Weakly Aggregative Modal Logic.Peter Apostoli & Bryson Brown - 1995 - Journal of Symbolic Logic 60 (3):832-842.
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  35. Grades of Probability Modality in the Law of Evidence.Lennart Åqvist - 2010 - 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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  36. Combinations of Tense and Deontic Modality: On the R T Approach to Temporal Logic with Historical Necessity and Conditional Obligation.Lennart Åqvist - 2005 - Journal of Applied Logic 3 (3-4):421-460.
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  37. Old Foundations for the Logic of Agency and Action.Lennart Åqvist - 2002 - 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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  38. Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization. [REVIEW]Lennart Åqvist - 1996 - 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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  39. The Completeness of Some Modal Logics with Circumstantials, Subjunctive Conditionals, Transworld Identity and Dispositional Predicates.Lennart Åqvist - 1971 - [Uppsala, Uppsala Universitet].
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  40. The Completeness of Some Modal Logics with Circumstantials, Subjunctive Conditionals, Transworld Identity and Dispositional Predicates a Study in the Prolegomena to the Logic of Science.Lennart Åqvist - 1971 - Uppsala Universitet].
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  41. On Some Completeness Theorems in Modal Logic.Lennart Aqvist & D. Makinson - 1970 - Journal of Symbolic Logic 35 (1):135.
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  42. On Some Questions of L. Åqvist.Mohammed Ardeshir & Fateme Nabavi - 2006 - Logic Journal of the IGPL 14 (1):1-13.
    We give answers to some questions raised by L. Åqvist in [6] and [7]. The question raised in [7] which we will answer positively is about the representability of Åqvist's system G in a hierarchy of alethic modal logics Hm, m = 1, 2, …. On the other hand, the questions raised in [6] are about the completeness of some monadic alethic denotic logics with respect to their Kripke semantics.
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  43. Methods for Modalities 3.Carlos Areces - 2006 - Journal of Applied Logic 4 (3):215-217.
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  44. Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2013 - 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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  45. Hybrid Type Theory: A Quartet in Four Movements.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2012 - Principia 15 (2):225.
    Este artigo canta uma canção — uma canção criada ao unir o trabalho de quatro grandes nomes na história da lógica: Hans Reichenbach, Arthur Prior, Richard Montague, e Leon Henkin. Embora a obra dos primeiros três desses autores tenha sido previamente combinada, acrescentar as ideias de Leon Henkin é o acréscimo requerido para fazer com que essa combinação funcione no nível lógico. Mas o presente trabalho não se concentra nas tecnicalidades subjacentes (que podem ser encontradas em Areces, Blackburn, Huertas, e (...)
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  46. 'First-Order Modal Logic', to Appear in V. Hendricks & SA Pedersen, Eds.,'40 Years of Possible Worlds', Special Issue Of.H. Arlo-Costa - forthcoming - Studia Logica.
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  47. Language, Propositional Logic, and Real World Applications: A Comment on Ascription.Bruce A. Arrigo - 1998 - International Journal for the Semiotics of Law - Revue Internationale de Sémiotique Juridique 11 (1):73-77.
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  48. Finite Kripke Models and Predicate Logics of Provability.Sergei Artemov & Giorgie Dzhaparidze - 1990 - 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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  49. Data Storage Interpretation of Labeled Modal Logic.Sergei Artëmov & Vladimir Krupski - 1996 - Annals of Pure and Applied Logic 78 (1-3):57-71.
    We introduce reference structures — a basic mathematical model of a data organization capable of storing and utilizing information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for modal language gives a method of building and optimizing reference structures satisfying a given formula. Corresponding labeled modal logics are presented, supplied with cut free axiomatizations, completeness and decidability theorems are proved. Initialization of typed variables in some programming (...)
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  50. Il Fondamento Del Giudizio: Una Proposta Teoretica a Partire Dalla Filosofia Del Senso Comune di Antonio Livi.Francesco Arzillo - 2011 - Casa Editrice Leonardo da Vinci.
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