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  1. Mohammed Abouzahr (2013). Future Contingents, Freedom, and Foreknowledge. Dissertation, Wayne State University
    This essay is a contribution to the new trend and old tradition of analyzing theological fatalism in light of its relationship to logical fatalism. All results pertain to branching temporal systems that use the A-theory and assume presentism. The project focuses on two kinds of views about branching time. One position is true futurism, which designates what will occur regardless of contingency. The opposing view is open futurism, by which no possible course of events is privileged over others; that is, (...)
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  2. Thomas Ågotnes (2006). Action and Knowledge in Alternating-Time Temporal Logic. Synthese 149 (2):375 - 407.
    Alternating-time temporal logic (ATL) is a branching time temporal logic in which statements about what coalitions of agents can achieve by strategic cooperation can be expressed. Alternating-time temporal epistemic logic (ATEL) extends ATL by adding knowledge modalities, with the usual possible worlds interpretation. This paper investigates how properties of agents’ actions can be expressed in ATL in general, and how properties of the interaction between action and knowledge can be expressed in ATEL in particular. One commonly discussed property is that (...)
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  3. Mai Ajspur & Valentin Goranko (2013). Tableaux-Based Decision Method for Single-Agent Linear Time Synchronous Temporal Epistemic Logics with Interacting Time and Knowledge. In Kamal Lodaya (ed.), Logic and its Applications. Springer 80--96.
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  4. Seiki Akama, Yasunori Nagata & Chikatoshi Yamada (2008). Three-Valued Temporal Logic Q T and Future Contingents. Studia Logica 88 (2):215 - 231.
    Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of future contingents.
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  5. Krzysztof R. Apt & Robert van Rooij (eds.) (2008). New Perspectives on Games and Interactions. Amsterdam University Press.
    This volume is a collection of papers presented at the colloquium, and it testifies to the growing importance of game theory as a tool that can capture concepts ...
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  6. L. Åqvist (1991). Discrete Tense Logic with Beginning and Ending Time: An Infinite Hierarchy of Complete Axiomatic Systems. Logique Et Analyse 34:359-401.
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  7. 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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  8. 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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  9. Lennart Åqvist (1999). The Logic of Historical Necessity as Founded on Two-Dimensional Modal Tense Logic. Journal of Philosophical Logic 28 (4):329-369.
    We consider a version of so called T x W logic for historical necessity in the sense of R.H. Thomason (1984), which is somewhat special in three respects: (i) it is explicitly based on two-dimensional modal logic in the sense of Segerberg (1973); (ii) for reasons of applicability to interesting fields of philosophical logic, it conceives of time as being discrete and finite in the sense of having a beginning and an end; and (iii) it utilizes the technique of systematic (...)
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  10. 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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  11. Lennart Åqvist (1979). A Conjectured Axiomatization of Two-Dimensional Reichenbachian Tense Logic. Journal of Philosophical Logic 8 (1):1 - 45.
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  12. C. Areces, P. Blackburn & M. Marx (2000). The Computational Complexity of Hybrid Temporal Logics. Logic Journal of the Igpl 8 (5):653-679.
    In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics.In this paper we analyze the complexity of the satisfiability problem of (...)
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  13. Miloš Arsenijević (2002). Determinism, Indeterminism and the Flow of Time. Erkenntnis 56 (2):123 - 150.
    A set of axioms implicitly defining the standard, though not instant-based but interval-based, time topology is used as a basis to build a temporal modal logic of events. The whole apparatus contains neither past, present, and future operators nor indexicals, but only B-series relations and modal operators interpreted in the standard way. Determinism and indeterminism are then introduced into the logic of events via corresponding axioms. It is shown that, if determinism and indeterminism are understood in accordance with their core (...)
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  14. S. Artemov, Dynamic Topological Logic.
    Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system be (...)
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  15. Zdzisław Augustynek (1976). Past, Present and Future in Relativity. Studia Logica 35 (1):45 - 53.
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  16. Sergey Babenyshev & Vladimir Rybakov (2011). Unification in Linear Temporal Logic LTL. Annals of Pure and Applied Logic 162 (12):991-1000.
    We prove that a propositional Linear Temporal Logic with Until and Next has unitary unification. Moreover, for every unifiable in LTL formula A there is a most general projective unifier, corresponding to some projective formula B, such that A is derivable from B in LTL. On the other hand, it can be shown that not every open and unifiable in LTL formula is projective. We also present an algorithm for constructing a most general unifier.
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  17. Philippe Balbiani, Andreas Herzig & Nicolas Troquard (2008). Alternative Axiomatics and Complexity of Deliberative Stit Theories. Journal of Philosophical Logic 37 (4):387 - 406.
    We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...)
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  18. Roberta Ballarin (2007). Prior on the Logic and the Metaphysics of Time. Logique Et Analyse 199:317-334.
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  19. Robert F. Barnes (1981). Interval Temporal Logic: A Note. [REVIEW] Journal of Philosophical Logic 10 (4):395 - 397.
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  20. Howard Barringer (1996). The Imperative Future Principles of Executable Temporal Logic.
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  21. Rainer Bäuerle (1979). Tense Logics and Natural Language. Synthese 40 (2):225 - 230.
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  22. Donald L. M. Baxter (2000). A Humean Temporal Logic. The Proceedings of the Twentieth World Congress of Philosophy 2000 (Analytic Philosophy and Logic):209-216.
    Hume argues that the idea of duration is just the idea of the manner in which several things in succession are arrayed. In other words, the idea of duration is the idea of successiveness. He concludes that all and only successions have duration. Hume also argues that there is such a thing as a steadfast object—something which co-exists with many things in succession, but which is not itself a succession. Thus, it seems that Hume has committed himself to a contradiction: (...)
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  23. Jc Beall (2012). Future Contradictions. Australasian Journal of Philosophy 90 (3):547-557.
    A common and much-explored thought is ?ukasiewicz's idea that the future is ?indeterminate??i.e., ?gappy? with respect to some claims?and that such indeterminacy bleeds back into the present in the form of gappy ?future contingent? claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future?one which is ?glutty? with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...)
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  24. 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 modal theorems, and to make (...)
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  25. Giacomo Bonanno (2008). Belief Revision in a Temporal Framework. In Krzysztof Apt & Robert van Rooij (eds.), New Perspectives on Games and Interaction. Amsterdam University Press
    The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update (see [6]). The former deals with situations where the objective facts describing the world do not change (so that only the beliefs of the agent change over time), while the letter allows for situations where both the facts and the doxastic state of the agent change over time. We focus on (...)
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  26. Giacomo Bonanno (2007). Axiomatic Characterization of the AGM Theory of Belief Revision in a Temporal Logic. Artificial Intelligence 171 (2-3):144-160.
    Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the (...)
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  27. Craig Bourne (2004). Future Contingents, Non-Contradiction, and the Law of Excluded Middle Muddle. Analysis 64 (2):122–128.
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  28. David Bresolin, Joanna Golinska-Pilarek & Ewa Orlowska (2006). Relational Dual Tableaux for Interval Temporal Logics. Journal of Applied Non-Classical Logics 16 (3-4):251–277.
    Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems enable us to verify validity and entailment of these temporal logics. We show how to incorporate in the systems various relations between intervals and/or (...)
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  29. Leonard Earl Brewster (1971). Time, Logic, and What There Is. Dissertation, Southern Illinois University at Carbondale
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  30. Rachael Briggs & Graeme A. Forbes (2012). The Real Truth About the Unreal Future. In Karen Bennett & Dean Zimmerman (eds.), Oxford Studies in Metaphysics, volume 7.
    Growing-Block theorists hold that past and present things are real, while future things do not yet exist. This generates a puzzle: how can Growing-Block theorists explain the fact that some sentences about the future appear to be true? Briggs and Forbes develop a modal ersatzist framework, on which the concrete actual world is associated with a branching-time structure of ersatz possible worlds. They then show how this branching structure might be used to determine the truth values of future contingents. They (...)
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  31. Eric M. Brown, Logic II: The Theory of Propositions.
    This is part two of a complete exposition of Logic, in which there is a radically new synthesis of Aristotelian-Scholastic Logic with modern Logic. Part II is the presentation of the theory of propositions. Simple, composite, atomic, compound, modal, and tensed propositions are all examined. Valid consequences and propositional logical identities are rigorously proven. Modal logic is rigorously defined and proven. This is the first work of Logic known to unite Aristotelian logic and modern logic using scholastic logic as the (...)
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  32. Mark Brown & Valentin Goranko (1999). An Extended Branching-Time Ockhamist Temporal Logic. Journal of Logic, Language and Information 8 (2):143-166.
    For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated restricted variables called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.We construct an axiomatic system for this (...)
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  33. Robert S. Brumbaugh (1965). Logic and Time. Review of Metaphysics 18 (4):647 - 656.
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  34. R. A. Bull (1970). An Approach to Tense Logic. Theoria 36 (3):282-300.
    The author's motivation for constructing the calculi of this paper\nis so that time and tense can be "discussed together in the same\nlanguage" (p. 282). Two types of enriched propositional caluli for\ntense logic are considered, both containing ordinary propositional\nvariables for which any proposition may be substituted. One type\nalso contains "clock-propositional" variables, a,b,c, etc., for\nwhich only clock-propositional variables may be substituted and that\ncorrespond to instants or moments in the semantics. The other type\nalso contains "history-propositional" variables, u,v,w, etc., for\nwhich only history-propositional variables may (...)
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  35. John P. Burgess (1984). Review: Beyond Tense Logic. [REVIEW] Journal of Philosophical Logic 13 (3):235 - 248.
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  36. John P. Burgess & Yuri Gurevich (1985). The Decision Problem for Linear Temporal Logic. Notre Dame Journal of Formal Logic 26 (2):115-128.
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  37. Richard N. Burnor (2000). Modal Models of Time. Southern Journal of Philosophy 38 (1):19-37.
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  38. J. Butterfield (1987). Predicate modifiers in tense logic. Logique Et Analyse 30 (17):31.
    We explain two ways of revising a tense logic like kripke's (1963) modal logic by adding predicate modifiers. first we show that modifiers allow us to render valid some mixing formulas--conditionals reversing the order of a quantifier and an operator--within a complete bivalent system. then we show how modifiers enable a tense logic to give analyses close to the surface form for sentences with temporal qualifications of singular terms, e.g., 'toby was fatter then than william is today'.
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  39. Jeremy Butterfield (1984). The Logic of Time. Philosophical Books 25 (1):53-55.
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  40. F. K. C. (1977). Tense Logic. Review of Metaphysics 31 (2):327-329.
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  41. Carlos Caleiro, Luca Viganò & Marco Volpe (2013). On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators. [REVIEW] Logica Universalis 7 (1):33-69.
    We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness (...)
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  42. Hector-Neri Castañeda (1977). Ought, Time, and the Deontic Paradoxes. Journal of Philosophy 74 (12):775-791.
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  43. Roberto Ciuni & Carlo Proietti (2013). The Abundance of the Future. A Paraconsistent Approach to Future Contingents. Logic and Logical Philosophy 22 (1):21-43.
    Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this “abundance of the future” is a non-adjunctive paraconsistent formalism based on subvaluations, (...)
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  44. M. J. Cresswell (2013). Predicate Metric Tense Logic for 'Now' and 'Then'. Journal of Philosophical Logic 42 (1):1-24.
    In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices as (...)
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  45. M. J. Cresswell (2010). The Modal Predicate Logic of Real Time. Logique Et Analyse 209:3-7.
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  46. M. J. Cresswell (2006). Now is the Time. Australasian Journal of Philosophy 84 (3):311 – 332.
    The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only 'real' time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the (...)
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  47. Max Cresswell (2013). Axiomatising the Prior Future in Predicate Logic. Logica Universalis 7 (1):87-101.
    Prior investigated a tense logic with an operator for ‘historical necessity’, where a proposition is necessary at a time iff it is true at that time in all worlds ‘accessible’ from that time. Axiomatisations of this logic all seem to require non-standard axioms or rules. The present paper presents an axiomatisation of a first-order version of Prior’s logic by using a predicate which enables any time to be picked out by an individual in the domain of interpretation.
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  48. Newton da Costa & Steven French (1989). A Note on Temporal Logic. Bulletin of the Section of Logic 18 (2):51-55.
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  49. Anatoli Degtyarev, Michael Fisher & Alexei Lisitsa (2002). Equality and Monodic First-Order Temporal Logic. Studia Logica 72 (2):147-156.
    It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e., the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.
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  50. L. Farinas del Cerro (forthcoming). L. Farinas and E. ORLOWSKA, Preface 115 P. WOLPER, The Tableau Method for Temporal Logic: An Over-View 119 M. MICHEL, Computation of Temporal Operators 137. [REVIEW] Logique Et Analyse.
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