Search results for 'temporal logic' (try it on Scholar)

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  1. Temporal Logic (forthcoming). Temporal Logic. Stanford Encyclopedia of Philosophy.score: 570.0
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  2. Mark Brown & Valentin Goranko (1999). An Extended Branching-Time Ockhamist Temporal Logic. Journal of Logic, Language and Information 8 (2):143-166.score: 93.0
    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 (...)
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  3. Natasha Kurtonina & Maarten de Rijke (1997). Bisimulations for Temporal Logic. Journal of Logic, Language and Information 6 (4):403-425.score: 93.0
    We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief discussion of the wider applicability of our ideas.
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  4. Joeri Engelfriet & Jan Treur (2002). Linear, Branching Time and Joint Closure Semantics for Temporal Logic. Journal of Logic, Language and Information 11 (4):389-425.score: 93.0
    Temporal logic can be used to describe processes: their behaviour ischaracterized by a set of temporal models axiomatized by a temporaltheory. Two types of models are most often used for this purpose: linearand branching time models. In this paper a third approach, based onsocalled joint closure models, is studied using models which incorporateall possible behaviour in one model. Relations between this approach andthe other two are studied. In order to define constructions needed torelate branching time models, appropriate (...)
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  5. D. M. Gabbay & G. Malod (2002). Naming Worlds in Modal and Temporal Logic. Journal of Logic, Language and Information 11 (1):29-65.score: 93.0
    In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y)which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a (...)
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  6. Marta Cialdea Mayer, Carla Limongelli, Andrea Orlandini & Valentina Poggioni (2007). Linear Temporal Logic as an Executable Semantics for Planning Languages. Journal of Logic, Language and Information 16 (1):63-89.score: 93.0
    This paper presents an approach to artificial intelligence planning based on linear temporal logic (LTL). A simple and easy-to-use planning language is described, Planning Domain Description Language with control Knowledge (PDDL-K), which allows one to specify a planning problem together with heuristic information that can be of help for both pruning the search space and finding better quality plans. The semantics of the language is given in terms of a translation into a set of LTL formulae. Planning is (...)
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  7. Heinrich Wansing & Norihiro Kamide (2011). Synchronized Linear-Time Temporal Logic. Studia Logica 99 (1-3):365-388.score: 90.0
    A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n -Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus δ SLTL is defined.
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  8. Marcelo Finger & Dov M. Gabbay (1992). Adding a Temporal Dimension to a Logic System. Journal of Logic, Language and Information 1 (3):203-233.score: 84.0
    We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) (...)
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  9. Joeri Engelfriet, Catholijn M. Jonker & Jan Treur (2002). Compositional Verification of Multi-Agent Systems in Temporal Multi-Epistemic Logic. Journal of Logic, Language and Information 11 (2):195-225.score: 84.0
    Compositional verification aims at managing the complexity of theverification process by exploiting compositionality of the systemarchitecture. In this paper we explore the use of a temporal epistemiclogic to formalize the process of verification of compositionalmulti-agent systems. The specification of a system, its properties andtheir proofs are of a compositional nature, and are formalized within acompositional temporal logic: Temporal Multi-Epistemic Logic. It isshown that compositional proofs are valid under certain conditions.Moreover, the possibility of incorporating default persistence (...)
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  10. Tomohiro Hoshi & Audrey Yap (2009). Dynamic Epistemic Logic with Branching Temporal Structures. Synthese 169 (2):259 - 281.score: 81.0
    van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic ( ETL : Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic ( DEL : Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged (...)
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  11. Joeri Engelfriet & Jan Treur (1998). An Interpretation of Default Logic in Minimal Temporal Epistemic Logic. Journal of Logic, Language and Information 7 (3):369-388.score: 81.0
    When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this (...)
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  12. S. Baratella (2004). An Infinitary Variant of Metric Temporal Logic Over Dense Time Domains. Mathematical Logic Quarterly 50 (3):249.score: 78.0
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  13. Stefano Baratella & Andrea Masini (2006). A Note on Unbounded Metric Temporal Logic Over Dense Time Domains. Mathematical Logic Quarterly 52 (5):450-456.score: 78.0
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  14. Norihiro Kamide (2009). Temporal Non-Commutative Logic: Expressing Time, Resource, Order and Hierarchy. Logic and Logical Philosophy 18 (2):97-126.score: 78.0
    A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and (...)
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  15. F. Montagna, G. M. Pinna & E. B. Tiezzi (2000). A Cut-Free Proof System for Bounded Metric Temporal Logic Over a Dense Time Domain. Mathematical Logic Quarterly 46 (2):171-182.score: 78.0
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  16. Franco Montagna, G. Michele Pinna & B. P. Tiezzi (2002). Investigations on Fragments of First Order Branching Temporal Logic. Mathematical Logic Quarterly 48 (1):51-62.score: 78.0
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  17. Sara L. Uckelman (2013). A Quantified Temporal Logic for Ampliation and Restriction. Vivarium 51 (1-4):485-510.score: 75.0
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  18. Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra (2009). A Temporal Semantics for Basic Logic. Studia Logica 92 (2):147 - 162.score: 74.0
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show (...)
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  19. V. Rybakov (2008). Discrete Linear Temporal Logic with Current Time Point Clusters, Deciding Algorithms. Logic and Logical Philosophy 17 (1-2):143-161.score: 74.0
    The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules (...)
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  20. Swarup Mohalik & R. Ramanujam (2010). Automata for Epistemic Temporal Logic with Synchronous Communication. Journal of Logic, Language and Information 19 (4):451-484.score: 69.0
    We suggest that developing automata theoretic foundations is relevant for knowledge theory, so that we study not only what is known by agents, but also the mechanisms by which such knowledge is arrived at. We define a class of epistemic automata, in which agents’ local states are annotated with abstract knowledge assertions about others. These are finite state agents who communicate synchronously with each other and information exchange is ‘perfect’. We show that the class of recognizable languages has good closure (...)
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  21. Mark Reynolds (1997). A Decidable Temporal Logic of Parallelism. Notre Dame Journal of Formal Logic 38 (3):419-436.score: 63.0
    In this paper we shall introduce a simple temporal logic suitable for reasoning about the temporal aspects of parallel universes, parallel processes, distributed systems, or multiple agents. We will use a variant of the mosaic method to prove decidability of this logic. We also show that the logic does not have the finite model property. This shows that the mosaic method is sometimes a stronger way of establishing decidability.
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  22. V. V. Rybakov (2005). Logical Consecutions in Discrete Linear Temporal Logic. Journal of Symbolic Logic 70 (4):1137 - 1149.score: 63.0
    We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the (...)
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  23. Alfredo Burrieza & Inma P. De Guzmán (1992). A New Algebraic Semantic Approach and Some Adequate Connectives for Computation with Temporal Logic Over Discrete Time. Journal of Applied Non-Classical Logics 2 (2):181-200.score: 61.0
    ABSTRACT In this paper we present a new semantic approach for propositional linear temporal logic with discrete time, strongly based in the well-order of IN (the set of natural numbers). We consider temporal connectives which express precedence, posteriority and simultaneity, and they provide a family of expressively complete temporal logics. The selection of the new semantics and connectives used in this work was principally to obtain a suitable executable temporal logic, which can be used (...)
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  24. Marcelo Finger (1992). Handling Database Updates in Two-Dimensional Temporal Logic. Journal of Applied Non-Classical Logics 2 (2):201-224.score: 61.0
    ABSTRACT We introduce a two-dimensional temporal logic as a formalism which enables the description of both the history of a world and the evolution of an observer's views about the history. We apply such formalism to the description of certain problems that occur in historical database systems due to updates. The historical dimension describes the history of a world according to an observer's view at a certain moment in time. The transaction dimension describes the evolution of an observer's (...)
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  25. Osamu Morikawa (2001). Extended Gentzen-Type Formulations of Two Temporal Logics Based on Incomplete Knowledge Systems. Notre Dame Journal of Formal Logic 42 (1):55-64.score: 61.0
    Nakamura proposed two three-valued temporal logics. We present two extended Gentzen-type formulations of these logics. Then we prove the soundness as well as the completeness theorem.
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  26. Regimantas Pliuskevicius (1998). Replacement of Induction by Similarity Saturation in a First Order Linear Temporal Logic. Journal of Applied Non-Classical Logics 8 (1-2):141-169.score: 61.0
    ABSTRACT A new type of calculi is proposed for a first order linear temporal logic. Instead of induction-type postulates the introduced calculi contain a similarity saturation principle, indicating some form of regularity in the derivations of the logic. In a finitary case we obtained the finite set of saturated sequents, showing that ?nothing new? can be obtained continuing the derivation process. Instead of the ?-type rule of inference, an infinitary saturated calculus has an infinite set of saturated (...)
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  27. Bernd-Holger Schlingloff (1992). Expressive Completeness of Temporal Logic of Trees. Journal of Applied Non-Classical Logics 2 (2):157-180.score: 61.0
    ABSTRACT Many temporal and modal logic languages can be regarded as subsets of first order logic, i.e. the semantics of a temporal logic formula is given as a first order condition on points of the underlying models (Kripke structures). Often the set of possible models is restricted to models which are trees. A temporal logic language is (first order) expressively complete, if for every first order condition for a node of a tree there (...)
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  28. Thomas Ågotnes (2006). Action and Knowledge in Alternating-Time Temporal Logic. Synthese 149 (2):375 - 407.score: 60.0
    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. (...)
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  29. Seiki Akama, Yasunori Nagata & Chikatoshi Yamada (2008). Three-Valued Temporal Logic Q T and Future Contingents. Studia Logica 88 (2):215 - 231.score: 60.0
    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 (...)
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  30. Giacomo Bonanno (2007). Axiomatic Characterization of the AGM Theory of Belief Revision in a Temporal Logic. Artificial Intelligence 171 (2-3):144-160.score: 60.0
    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 (...)
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  31. Mark Reynolds (1996). Axiomatising First-Order Temporal Logic: Until and Since Over Linear Time. Studia Logica 57 (2-3):279 - 302.score: 60.0
    We present an axiomatisation for the first-order temporal logic with connectives Until and Since over the class of all linear flows of time. Completeness of the axiom system is proved.We also add a few axioms to find a sound and complete axiomatisation for the first order temporal logic of Until and Since over rational numbers time.
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  32. Walter Hussak (2008). Decidable Cases of First-Order Temporal Logic with Functions. Studia Logica 88 (2):247 - 261.score: 60.0
    We consider the decision problem for cases of first-order temporal logic with function symbols and without equality. The monadic monodic fragment with flexible functions can be decided with EXPSPACE-complete complexity. A single rigid function is sufficient to make the logic not recursively enumerable. However, the monadic monodic fragment with rigid functions, where no two distinct terms have variables bound by the same quantifier, is decidable and EXPSPACE-complete.
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  33. Anatoli Degtyarev, Michael Fisher & Alexei Lisitsa (2002). Equality and Monodic First-Order Temporal Logic. Studia Logica 72 (2):147-156.score: 60.0
    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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  34. Andrzej Indrzejczak (2003). A Labelled Natural Deduction System for Linear Temporal Logic. Studia Logica 75 (3):345 - 376.score: 60.0
    The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity (...)
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  35. 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.score: 60.0
    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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  36. 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.score: 59.0
    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 (...)
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  37. Sara L. Uckelman (2010). Logic and the Condemnations of 1277. Journal of Philosophical Logic 39 (2):201 - 227.score: 57.0
    The struggle to delineate the relationship between theology and logic flourished in the thirteenth century and culminated in two condemnations in early 1277, one in Paris and the other in Oxford. To see how much and what kind of effect ecclesiastical actions such as condemnations and prohibitions to teach had on the development of logic in the Middle Ages, we investigate the events leading up to the 1277 actions, the condemned propositions, and the parts of these condemnations connected (...)
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  38. Thomas Ågotnes & Dirk Walther (2009). A Logic of Strategic Ability Under Bounded Memory. Journal of Logic, Language and Information 18 (1):55-77.score: 57.0
    We study the logic of strategic ability of coalitions of agents with bounded memory by introducing Alternating-time Temporal Logic with Bounded Memory (ATLBM), a variant of Alternating-time Temporal Logic (ATL). ATLBM accounts for two main consequences of the assumption that agents have bounded memory. First, an agent can only remember a strategy that specifies actions in a bounded number of different circumstances. While the ATL-formula means that coalition C has a joint strategy which will make (...)
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  39. Joshua Sack (2008). Temporal Languages for Epistemic Programs. Journal of Logic, Language and Information 17 (2):183-216.score: 57.0
    This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision (...)
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  40. Jean-Pierre Desclés, Anca Christine Pascu & Hee-Jin Ro (forthcoming). Aspecto-Temporal Meanings Analysed by Combinatory Logic. Journal of Logic, Language and Information:1-22.score: 57.0
    What is the meaning of language expressions and how to compute or calculate it? In this paper, we give an answer to this question by analysing the meanings of aspects and tenses in natural languages inside the formal model of an grammar of applicative, cognitive and enunciative operations (GRACE) (Desclés and Ro in Math Sci Hum 194:39–70, 2011), using the applicative formalism, functional types of categorial grammars and combinatory logic (CL) (Curry and Feys in Combinatory Logic. North-Holland Publishing, (...)
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  41. Boudewijn de Bruin (2008). Epistemic Logic and Epistemology. In Vincent F. Hendricks & Duncan Pritchard (eds.), New Waves in Epistemology. Palgrave Macmillan.score: 54.0
    This paper contributes to an increasing literature strengthening the connection between epistemic logic and epistemology (Van Benthem, Hendricks). I give a survey of the most important applications of epistemic logic in epistemology. I show how it is used in the history of philosophy (Steiner's reconstruction of Descartes' sceptical argument), in solutions to Moore's paradox (Hintikka), in discussions about the relation between knowledge and belief (Lenzen) and in an alleged refutation of verificationism (Fitch) and I examine an early argument (...)
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  42. Avi Sion (1990). Future Logic: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional, and Logical Modalities. Lulu.com.score: 54.0
    Future Logic is an original and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. This is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision. This is the first work ever to develop a formal logic of the natural, temporal and extensional types (...)
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  43. David Fernández-Duque (2011). Dynamic Topological Logic Interpreted Over Minimal Systems. Journal of Philosophical Logic 40 (6):767-804.score: 54.0
    Dynamic Topological Logic ( ) is a modal logic which combines spatial and temporal modalities for reasoning about dynamic topological systems , which are pairs consisting of a topological space X and a continuous function f : X → X . The function f is seen as a change in one unit of time; within one can model the long-term behavior of such systems as f is iterated. One class of dynamic topological systems where the long-term behavior (...)
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  44. Philip Kremer (2010). The Modal Logic of Continuous Functions on the Rational Numbers. Archive for Mathematical Logic 49 (4):519-527.score: 54.0
    Let ${{\mathcal L}^{\square\circ}}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality □ and a temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language ${{\mathcal L}^{\square\circ}}$ by interpreting ${{\mathcal L}^{\square\circ}}$ in dynamic topological systems, i.e., ordered pairs 〈X, f〉, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and (...)
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  45. M. J. Cresswell (2013). Predicate Metric Tense Logic for 'Now' and 'Then'. Journal of Philosophical Logic 42 (1):1-24.score: 54.0
    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 (...)
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  46. Sara L. Uckelman (2012). Arthur Prior and Medieval Logic. Synthese 188 (3):349-366.score: 54.0
    Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his ground-breaking innovations in the 1950s and 1960s. Because of the important rôle played by Prior's research in ancient and medieval logic in his development of temporal and hybrid logic, any student of (...)
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  47. Joeri Engelfriet (1996). Minimal Temporal Epistemic Logic. Notre Dame Journal of Formal Logic 37 (2):233-259.score: 54.0
    In the study of nonmonotonic reasoning the main emphasis has been on static (declarative) aspects. Only recently has there been interest in the dynamic aspects of reasoning processes, particularly in artificial intelligence. We study the dynamics of reasoning processes by using a temporal logic to specify them and to reason about their properties, just as is common in theoretical computer science. This logic is composed of a base temporal epistemic logic with a preference relation on (...)
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  48. Sándor Vályi (2013). On the Axiomatizability of Some First-Order Spatio-Temporal Theories. Synthese:1-17.score: 54.0
    Spatio-temporal logic is a variant of branching temporal logic where one of the so-called causal relations on spacetime plays the role of a time flow. Allowing only rational numbers as space and time co-ordinates, we prove that a first-order spatio-temporal theory over this flow is recursively enumerable if and only if the dimension of spacetime does not exceed 2. The situation is somewhat different compared to the case of real co-ordinates, because we establish that even (...)
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  49. Felicidad Aguado, Pedro Cabalar, Martín Diéguez, Gilberto Pérez & Concepción Vidal (2013). Temporal Equilibrium Logic: A Survey. Journal of Applied Non-Classical Logics 23 (1-2):2-24.score: 52.0
    This paper contains a survey of the main definitions and results obtained to date related to Temporal Equilibrium Logic, a nonmonotonic hybrid approach that combines Equilibrium Logic (the best-known logical characterisation for the stable models semantics of logic programs) with Linear-Time Temporal Logic.
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  50. Wiebe van der Hoek & Michael Wooldridge (2003). Cooperation, Knowledge, and Time: Alternating-Time Temporal Epistemic Logic and its Applications. Studia Logica 75 (1):125-157.score: 51.0
    Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal (...) (ATL). The key insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems. (shrink)
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