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Journal articles on the topic 'Modal logics; Temporal logic'

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1

Long, Derek. "A review of temporal logics." Knowledge Engineering Review 4, no. 2 (1989): 141–62. http://dx.doi.org/10.1017/s0269888900004896.

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AbstractA series of temporal reasoning tasks are identified which motivate the consideration and application of temporal logics in artificial intelligence. There follows a discussion of the broad issues involved in modelling time and constructing a temporal logic. The paper then presents a detailed review of the major approaches to temporal logics: first-order logic approaches, modal temporal logics and reified temporal logics. The review considers the most significant exemplars within the various approaches, including logics due to Russell, Hayes and McCarthy, Prior, McDermott, Allen, Kowalsk
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2

NISSAN, EPHRAIM. "Special Issue: Temporal Logic in Engineering." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 13, no. 2 (1999): 65. http://dx.doi.org/10.1017/s0890060499132013.

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Logic-based models are thriving within artificial intelligence. A great number of new logics have been defined, and their theory investigated. Epistemic logics introduce modal operators for knowledge or belief; deontic logics are about norms, and introduce operators of deontic necessity and possibility (i.e., obligation or prohibition). And then we have a much investigated class—temporal logics—to whose application to engineering this special issue is devoted. This kind of formalism deserves increased widespread recognition and application in engineering, a domain where other kinds of temporal
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3

Demri, Stéphane, and Raul Fervari. "The power of modal separation logics." Journal of Logic and Computation 29, no. 8 (2019): 1139–84. http://dx.doi.org/10.1093/logcom/exz019.

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Abstract We introduce a modal separation logic MSL whose models are memory states from separation logic and the logical connectives include modal operators as well as separating conjunction and implication from separation logic. With such a combination of operators, some fragments of MSL can be seen as genuine modal logics whereas some others capture standard separation logics, leading to an original language to speak about memory states. We analyse the decidability status and the computational complexity of several fragments of MSL, obtaining surprising results by design of proof methods that
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4

Маркин, В. И. "What trends in non-classical logic were anticipated by Nikolai Vasiliev?" Logical Investigations 19 (April 9, 2013): 122–35. http://dx.doi.org/10.21146/2074-1472-2013-19-0-122-135.

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In this paper we discuss a question about the trends in non-classical logic that were exactly anticipated by Niko- lai Vasiliev. We show the influence of Vasiliev’s Imaginary logic on paraconsistent logic. Metatheoretical relations between Vasiliev’s logical systems and many-valued predicate logics are established. We also make clear that Vasiliev has developed a sketch of original system of intensional logic and expressed certain ideas of modal and temporal logics.
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5

Baltag, Alexandru, and Johan van Benthem. "A Simple Logic of Functional Dependence." Journal of Philosophical Logic 50, no. 5 (2021): 939–1005. http://dx.doi.org/10.1007/s10992-020-09588-z.

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AbstractThis paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: cont
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6

Kamide, Norihiro. "Logical foundations of hierarchical model checking." Data Technologies and Applications 52, no. 4 (2018): 539–63. http://dx.doi.org/10.1108/dta-01-2018-0002.

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Purpose The purpose of this paper is to develop new simple logics and translations for hierarchical model checking. Hierarchical model checking is a model-checking paradigm that can appropriately verify systems with hierarchical information and structures. Design/methodology/approach In this study, logics and translations for hierarchical model checking are developed based on linear-time temporal logic (LTL), computation-tree logic (CTL) and full computation-tree logic (CTL*). A sequential linear-time temporal logic (sLTL), a sequential computation-tree logic (sCTL), and a sequential full comp
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7

HUET, GÉRARD. "Special issue on ‘Logical frameworks and metalanguages’." Journal of Functional Programming 13, no. 2 (2003): 257–60. http://dx.doi.org/10.1017/s0956796802004549.

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There is both a great unity and a great diversity in presentations of logic. The diversity is staggering indeed – propositional logic, first-order logic, higher-order logic belong to one classification; linear logic, intuitionistic logic, classical logic, modal and temporal logics belong to another one. Logical deduction may be presented as a Hilbert style of combinators, as a natural deduction system, as sequent calculus, as proof nets of one variety or other, etc. Logic, originally a field of philosophy, turned into algebra with Boole, and more generally into meta-mathematics with Frege and
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8

Kuzmin, Egor V. "LTL-Specification of Counter Machines." Modeling and Analysis of Information Systems 28, no. 1 (2021): 104–19. http://dx.doi.org/10.18255/1818-1015-2021-1-104-119.

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The article is written in support of the educational discipline “Non-classical logics”. Within the framework of this discipline, the objects of study are the basic principles and constructive elements, with the help of which the formal construction of various non-classical propositional logics takes place. Despite the abstractness of the theory of non-classical logics, in which the main attention is paid to the strict mathematical formalization of logical reasoning, there are real practical areas of application of theoretical results. In particular, languages of temporal modal logics are widel
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9

PENCZEK, WOJCIECH. "TEMPORAL LOGICS FOR TRACE SYSTEMS: ON AUTOMATED VERIFICATION." International Journal of Foundations of Computer Science 04, no. 01 (1993): 31–67. http://dx.doi.org/10.1142/s0129054193000043.

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We investigate an extension of CTL (Computation Tree Logic) by past modalities, called CTL P, interpreted over Mazurkiewicz’s trace systems. The logic is powerful enough to express most of the partial order properties of distributed systems like serializability of database transactions, snapshots, parallel execution of program segments, or inevitability under concurrency fairness assumption. We show that the model checking problem for the logic is NP-hard, even if past modalities cannot be nested. Then, we give a one exponential time model checking algorithm for the logic without nested past m
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10

Gnatenko, Anton Romanovich, and Vladimir Anatolyevich Zakharov. "On the Model Checking Problem for Some Extension of CTL*." Modeling and Analysis of Information Systems 27, no. 4 (2020): 428–41. http://dx.doi.org/10.18255/1818-1015-2020-4-428-441.

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Sequential reactive systems include programs and devices that work with two streams of data and convert input streams of data into output streams. Such information processing systems include controllers, device drivers, computer interpreters. The result of the operation of such computing systems are infinite sequences of pairs of events of the request-response type, and, therefore, finite transducers are most often used as formal models for them. The behavior of transducers is represented by binary relations on infinite sequences, and so, traditional applied temporal logics (like HML, LTL, CTL
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11

Непейвода, Н. Н. "Formalization as the Immanent Part of Logical Solving." Logical Investigations 24, no. 1 (2018): 129–45. http://dx.doi.org/10.21146/2074-1472-2018-24-1-129-145.

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The work is devoted to the logical analysis of the problem solving by logical means. It starts from general characteristic of the applied logic as a tool: 1. to bound logic with its applications in theory and practice; 2. to import methods and methodologies from other domains into logic; 3. to export methods and methodologies from logic into other domains. The precise solving of a precisely stated logical problem occupies only one third of the whole process of solving real problems by logical means. The formalizing precedes it and the deformalizing follows it. The main topic when considering f
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12

Burrieza, Alfredo, Inmaculada P. de Guzmán, and Emilio Muñoz-Velasco. "Analyzing completeness of axiomatic functional systems for temporal × modal logics." MLQ 56, no. 1 (2010): 89–102. http://dx.doi.org/10.1002/malq.200810038.

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13

Garcez, Artur S. d'Avila, and Luís C. Lamb. "A Connectionist Computational Model for Epistemic and Temporal Reasoning." Neural Computation 18, no. 7 (2006): 1711–38. http://dx.doi.org/10.1162/neco.2006.18.7.1711.

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The importance of the efforts to bridge the gap between the connectionist and symbolic paradigms of artificial intelligence has been widely recognized. The merging of theory (background knowledge) and data learning (learning from examples) into neural-symbolic systems has indicated that such a learning system is more effective than purely symbolic or purely connectionist systems. Until recently, however, neural-symbolic systems were not able to fully represent, reason, and learn expressive languages other than classical propositional and fragments of first-order logic. In this article, we show
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14

Álvarez Domínguez, Daniel. "Hybrid Logic as extension of Modal and Temporal Logic." Revista de Humanidades de Valparaíso, no. 13 (August 18, 2019): 34. http://dx.doi.org/10.22370/rhv2019iss13pp34-67.

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La lógica temporal fue creada por Arthur Prior para representar información temporal en un sistema lógico mediante operadores modales-temporales como P, F, H o G. Intuitivamente tales operadores pueden entenderse respectivamente como “fue alguna vez en el pasado...”, “será alguna vez en el futuro...”, “ha sido siempre en el pasado...” y “será siempre en el futuro...”. La evaluación de las fórmulas construidas a partir de ellos se lleva a cabo en semánticas kripkeanas y, de este modo, la lógica modal y la temporal están relacionadas. Sin embargo, aunque sus mecanismos permiten formalizar la inf
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15

BALTAZAR, P., R. CHADHA, and P. MATEUS. "QUANTUM COMPUTATION TREE LOGIC — MODEL CHECKING AND COMPLETE CALCULUS." International Journal of Quantum Information 06, no. 02 (2008): 219–36. http://dx.doi.org/10.1142/s0219749908003530.

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Logics for reasoning about quantum states and their evolution have been given in the literature. In this paper, we consider quantum computation tree logic (QCTL), which adds temporal modalities to exogenous quantum propositional logic. We give a sound and complete axiomatization of QCTL and combine the standard CTL model-checking algorithm with the dEQPL model-checking algorithm to obtain a model-checking algorithm for QCTL. Finally, we illustrate the use of the logic by reasoning about the BB84 key distribution protocol.
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16

Orgun, Mehmet A. "Temporal and modal logic programming." ACM SIGART Bulletin 5, no. 3 (1994): 52–59. http://dx.doi.org/10.1145/181911.181920.

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17

Sciavicco, Guido. "Reasoning with Time Intervals: A Logical and Computational Perspective." ISRN Artificial Intelligence 2012 (October 14, 2012): 1–19. http://dx.doi.org/10.5402/2012/616087.

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The role of time in artificial intelligence is extremely important. Interval-based temporal reasoning can be seen as a generalization of the classical point-based one, and the first results in this field date back to Hamblin (1972) and Benhtem (1991) from the philosophical point of view, to Allen (1983) from the algebraic and first-order one, and to Halpern and Shoham (1991) from the modal logic one. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in modal and first-order interval temporal reasoning over the past
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18

Kamide, Norihiro, and Daiki Koizumi. "Method for Combining Paraconsistency and Probability in Temporal Reasoning." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 5 (2016): 813–27. http://dx.doi.org/10.20965/jaciii.2016.p0813.

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Computation tree logic (CTL) is known to be one of the most useful temporal logics for verifying concurrent systems by model checking technologies. However, CTL is not sufficient for handling inconsistency-tolerant and probabilistic accounts of concurrent systems. In this paper, a paraconsistent (or inconsistency-tolerant) probabilistic computation tree logic (PpCTL) is derived from an existing probabilistic computation tree logic (pCTL) by adding a paraconsistent negation connective. A theorem for embedding PpCTL into pCTL is proven, thereby indicating that we can reuse existing pCTL-based mo
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19

Phillips, John F. "A Note on the Modal and Temporal Logics for N-Dimensional Spacetime." Notre Dame Journal of Formal Logic 39, no. 4 (1998): 545–53. http://dx.doi.org/10.1305/ndjfl/1039118869.

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20

GORLIN, ANDREY, C. R. RAMAKRISHNAN, and SCOTT A. SMOLKA. "Model checking with probabilistic tabled logic programming." Theory and Practice of Logic Programming 12, no. 4-5 (2012): 681–700. http://dx.doi.org/10.1017/s1471068412000245.

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AbstractWe present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The inference algorithms of existing probabilistic logic-programming systems are well defined only for queries with a finite number of explanations. This restriction prohibits the encoding of probabilistic model checkers, where explanations correspond to executions of the system being model checked.
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21

DEMRI, STÉPHANE, and DAVID NOWAK. "REASONING ABOUT TRANSFINITE SEQUENCES." International Journal of Foundations of Computer Science 18, no. 01 (2007): 87–112. http://dx.doi.org/10.1142/s0129054107004589.

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We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by ordinals replace the standard next-time and until future-time operators. Our aim is to control such systems by designing controllers that safely work on ω-sequences but interact synchronously with the system in order to restrict their behaviors. We show that the satisfiability and model-checking for the logics working on ωk-sequences is EXPSPACE-complete wh
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22

Cleaveland, Rance, S. Purushothaman Iyer, and Murali Narasimha. "Probabilistic temporal logics via the modal mu-calculus." Theoretical Computer Science 342, no. 2-3 (2005): 316–50. http://dx.doi.org/10.1016/j.tcs.2005.03.048.

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23

Burrieza, Alfredo, and Inma P. de Guzm�n. "A functional approach for temporal $\times$ modal logics." Acta Informatica 39, no. 2 (2003): 71–96. http://dx.doi.org/10.1007/s00236-002-0098-z.

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24

Lin, Hai. "Mission Accomplished: An Introduction to Formal Methods in Mobile Robot Motion Planning and Control." Unmanned Systems 02, no. 02 (2014): 201–16. http://dx.doi.org/10.1142/s2301385014300029.

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A new trend in the robotic motion planning literature is to use formal methods, like model checking, reactive synthesis and supervisory control theory, to automatically design controllers that drive a mobile robot to accomplish some high level missions in a guaranteed manner. This is also known as the correct-by-construction method. The high level missions are usually specified as temporal logics, particularly as linear temporal logic formulas, due to their similarity to human natural languages. This paper provides a brief overview of the recent developments in this newly emerged research area
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Marsden, Alan. "Timing in music and modal temporal logic." Journal of Mathematics and Music 1, no. 3 (2007): 173–89. http://dx.doi.org/10.1080/17459730701666887.

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26

Leasure, David E. "TEMPORAL REASONING WITH THE MODAL LOGIC Z." Computational Intelligence 12, no. 3 (1996): 407–22. http://dx.doi.org/10.1111/j.1467-8640.1996.tb00269.x.

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27

Alechina, Natasha, Stéphane Demri, and Brian Logan. "Parameterised Resource-Bounded ATL." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 05 (2020): 7040–46. http://dx.doi.org/10.1609/aaai.v34i05.6189.

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It is often advantageous to be able to extract resource requirements in resource logics of strategic ability, rather than to verify whether a fixed resource requirement is sufficient for achieving a goal. We study Parameterised Resource-Bounded Alternating Time Temporal Logic where parameter extraction is possible. We give a parameter extraction algorithm and prove that the model-checking problem is 2EXPTIME-complete.
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28

Giero, Mariusz. "Propositional Linear Temporal Logic with Initial Validity Semantics." Formalized Mathematics 23, no. 4 (2015): 379–86. http://dx.doi.org/10.1515/forma-2015-0030.

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Summary In the article [10] a formal system for Propositional Linear Temporal Logic (in short LTLB) with normal semantics is introduced. The language of this logic consists of “until” operator in a very strict version. The very strict “until” operator enables to express all other temporal operators. In this article we construct a formal system for LTLB with the initial semantics [12]. Initial semantics means that we define the validity of the formula in a model as satisfaction in the initial state of model while normal semantics means that we define the validity as satisfaction in all states o
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BERNARDO, MARCO, and STEFANIA BOTTA. "A survey of modal logics characterising behavioural equivalences for non-deterministic and stochastic systems." Mathematical Structures in Computer Science 18, no. 1 (2008): 29–55. http://dx.doi.org/10.1017/s0960129507006408.

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Behavioural equivalences are a means of establishing whether computing systems possess the same properties. The specific set of properties that are preserved by a specific behavioural equivalence clearly depends on how the system behaviour is observed and can usually be characterised by means of a modal logic. In this paper we consider three different approaches to the definition of behavioural equivalences – bisimulation, testing and trace – applied to three different classes of systems – non-deterministic, probabilistic and Markovian – and we survey the nine resulting modal logic characteris
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30

Hartonas, Chrysafis. "Modal and temporal extensions of non-distributive propositional logics." Logic Journal of IGPL 24, no. 2 (2015): 156–85. http://dx.doi.org/10.1093/jigpal/jzv051.

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31

Uckelman, Sara L., and Joel Uckelman. "Modal and temporal logics for abstract space–time structures." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38, no. 3 (2007): 673–81. http://dx.doi.org/10.1016/j.shpsb.2007.01.004.

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32

Gorogiannis, Nikos, and Mark Ryan. "Minimal refinements of specifications in modal and temporal logics." Formal Aspects of Computing 19, no. 2 (2007): 273. http://dx.doi.org/10.1007/s00165-007-0038-3.

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33

Gorogiannis, Nikos, and Mark Ryan. "Minimal refinements of specifications in modal and temporal logics." Formal Aspects of Computing 19, no. 4 (2007): 417–44. http://dx.doi.org/10.1007/s00165-007-0040-9.

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34

BAIER, C., E. M. HAHN, B. R. HAVERKORT, H. HERMANNS, and J. P. KATOEN. "Model checking for performability." Mathematical Structures in Computer Science 23, no. 4 (2013): 751–95. http://dx.doi.org/10.1017/s0960129512000254.

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This paper gives a bird's-eye view of the various ingredients that make up a modern, model-checking-based approach to performability evaluation: Markov reward models, temporal logics and continuous stochastic logic, model-checking algorithms, bisimulation and the handling of non-determinism. A short historical account as well as a large case study complete this picture. In this way, we show convincingly that the smart combination of performability evaluation with stochastic model-checking techniques, developed over the last decade, provides a powerful and unified method of performability evalu
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CABALAR, PEDRO, MARTÍN DIÉGUEZ, and CONCEPCIÓN VIDAL. "An infinitary encoding of temporal equilibrium logic." Theory and Practice of Logic Programming 15, no. 4-5 (2015): 666–80. http://dx.doi.org/10.1017/s1471068415000307.

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AbstractThis paper studies the relation between two recent extensions of propositional Equilibrium Logic, a well-known logical characterisation of Answer Set Programming. In particular, we show how Temporal Equilibrium Logic, which introduces modal operators as those typically handled in Linear-Time Temporal Logic (LTL), can be encoded into Infinitary Equilibrium Logic, a recent formalisation that allows the use of infinite conjunctions and disjunctions. We prove the correctness of this encoding and, as an application, we further use it to show that the semantics of the temporal logic programm
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36

Williamson, Timothy. "Modal science." Canadian Journal of Philosophy 46, no. 4-5 (2016): 453–92. http://dx.doi.org/10.1080/00455091.2016.1205851.

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AbstractThis paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. Those assumptions arguably include some necessitist principles.
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AGUADO, FELICIDAD, PEDRO CABALAR, GILBERTO PÉREZ, CONCEPCIÓN VIDAL, and MARTÍN DIÉGUEZ. "Temporal logic programs with variables." Theory and Practice of Logic Programming 17, no. 2 (2016): 226–43. http://dx.doi.org/10.1017/s1471068416000570.

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AbstractIn this note, we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of Temporal Equilibrium Logic that shares the syntax of first-order Linear-time Temporal Logic but has different semantics, selecting some Linear-time Temporal Logic models we call temporal stable models. Then, we consider a subclass of theories (called splittable temporal logic programs) that are close
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38

Mardaev, Sergey. "Definable fixed points in modal and temporal logics : A survey." Journal of Applied Non-Classical Logics 17, no. 3 (2007): 317–46. http://dx.doi.org/10.3166/jancl.17.317-346.

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Gnatenko, Anton, and Vladimir Zakharov. "On the Expressive Power of Some Extensions of Linear Temporal Logic." Modeling and Analysis of Information Systems 25, no. 5 (2018): 506–24. http://dx.doi.org/10.18255/1818-1015-2018-5-506-524.

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One of the most simple models of computation which is suitable for representation of reactive systems behaviour is a finite state transducer which operates over an input alphabet of control signals and an output alphabet of basic actions. The behaviour of such a reactive system displays itself in the correspondence between flows of control signals and compositions of basic actions performed by the system. We believe that the behaviour of this kind requires more suitable and expressive means for formal specifications than the conventionalLT L. In this paper, we define some new (as far as we kno
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40

Lee, J., and R. Palla. "Reformulating the Situation Calculus and the Event Calculus in the General Theory of Stable Models and in Answer Set Programming." Journal of Artificial Intelligence Research 43 (April 24, 2012): 571–620. http://dx.doi.org/10.1613/jair.3489.

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Circumscription and logic programs under the stable model semantics are two well-known nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis of a family of action languages, such as language A and several of its descendants. Based on the discovery that circumscription and the stable model semantics coincide on a class of canonical formulas, we reformulate the situation calculus and the event calculus in the general theory of stable mode
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41

Heinemann, Bernhard. "Temporal aspects of the modal logic of subset spaces." Theoretical Computer Science 224, no. 1-2 (1999): 135–55. http://dx.doi.org/10.1016/s0304-3975(98)00310-7.

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42

Jamroga, Wojciech, Beata Konikowska, Damian Kurpiewski, and Wojciech Penczek. "Multi-valued Verification of Strategic Ability." Fundamenta Informaticae 175, no. 1-4 (2020): 207–51. http://dx.doi.org/10.3233/fi-2020-1955.

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Some multi-agent scenarios call for the possibility of evaluating specifications in a richer domain of truth values. Examples include runtime monitoring of a temporal property over a growing prefix of an infinite path, inconsistency analysis in distributed databases, and verification methods that use incomplete anytime algorithms, such as bounded model checking. In this paper, we present multi-valued alternating-time temporal logic ( mv-ATL → ∗ ), an expressive logic to specify strategic abilities in multi-agent systems. It is well known that, for branchingtime logics, a general method for mod
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43

Olmedo, Francisco M. García, and Antonio J. Rodríguez Salas. "Temporal Algebras, Pretemporal Algebras, and Modal Algebras: A Relation between Time and Necessity." Mathematical Logic Quarterly 41, no. 1 (1995): 24–38. http://dx.doi.org/10.1002/malq.19950410104.

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44

MARCELINO, SÉRGIO, and PEDRO RESENDE. "An algebraic generalization of Kripke structures." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 3 (2008): 549–77. http://dx.doi.org/10.1017/s0305004108001667.

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AbstractThe Kripke semantics of classical propositional normal modal logic is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. This algebraic semantics subsumes the traditional algebraic semantics based on lattices with unary operators, and it suggests natural interpretations of modal logic, of possible interest in the applications, in structures that arise in geometry and analysis, such as foliated manifolds and operator algebras, via topological groupoids and inverse semigroups. We study completeness properties of the quantale
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45

Burrieza, A., I. P. de Guzmán, and E. Muñoz-Velasco. "Functional systems in the context of temporal×modal logics with indexed flows." International Journal of Computer Mathematics 86, no. 10-11 (2009): 1696–706. http://dx.doi.org/10.1080/00207160902795619.

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46

GHILARDI, SILVIO, and SAMUEL J. VAN GOOL. "A MODEL-THEORETIC CHARACTERIZATION OF MONADIC SECOND ORDER LOGIC ON INFINITE WORDS." Journal of Symbolic Logic 82, no. 1 (2017): 62–76. http://dx.doi.org/10.1017/jsl.2016.70.

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AbstractMonadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary predicate symbols.Monadic second order logic over infinite words (S1S) can alternatively be described as a first-order logic interpreted in${\cal P}\left( \omega \right)$, the power set Boolean algebra of the natural numbers, equipped with modal operators for ‘initial’, ‘next’, and ‘future’ states. We prove that the first-order theory of this structure
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47

Rönnedal, Daniel. "The Moral Law and The Good in Temporal Modal Logic with Propositional Quantifiers." Australasian Journal of Logic 17, no. 1 (2020): 22. http://dx.doi.org/10.26686/ajl.v17i1.5674.

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The Moral Law is fulfilled (in a possible world w at a time t) iff (if and only if) everything that ought to be the case is the case (in w at t), and The Good (or The Highest Possible Good) is realised in a possible world w' at a time t' iff w' is deontically accessible from w at t. In this paper, I will introduce a set of temporal alethic deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any propositional quantifiers. Then, I will show how these systems can be ext
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48

Rybakov, V. "Multi-modal and Temporal Logics with Universal Formula--Reduction of Admissibility to Validity and Unification." Journal of Logic and Computation 18, no. 4 (2007): 509–19. http://dx.doi.org/10.1093/logcom/exm078.

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49

Requeno, José Ignacio, and José Manuel Colom. "Analyzing Phylogenetic Trees with Timed and Probabilistic Model Checking: The Lactose Persistence Case Study." Journal of Integrative Bioinformatics 11, no. 3 (2014): 17–31. http://dx.doi.org/10.1515/jib-2014-248.

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Summary Model checking is a generic verification technique that allows the phylogeneticist to focus on models and specifications instead of on implementation issues. Phylogenetic trees are considered as transition systems over which we interrogate phylogenetic questions written as formulas of temporal logic. Nonetheless, standard logics become insufficient for certain practices of phylogenetic analysis since they do not allow the inclusion of explicit time and probabilities. The aim of this paper is to extend the application of model checking techniques beyond qualitative phylogenetic properti
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GAIFMAN, HAIM. "CONTEXTUAL LOGIC WITH MODALITIES FOR TIME AND SPACE." Review of Symbolic Logic 1, no. 4 (2008): 433–58. http://dx.doi.org/10.1017/s1755020308090047.

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We develop a formal apparatus to be used as a tool in analyzing common kinds of context dependence in natural language, and their interaction with temporal and spatial modalities. It is based on context-operators, which act on wffs. The interplay between the various modalities and the context-operators is one of the main targets of the analysis. Statements made by different people at different times in different places, using the same personal temporal and spatial indexicals, can be represented in the system, and can be combined by sentential connectives and be subject to quantification. The u
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