Element contents
Series: Elements in Philosophy and Logic
Temporal Logics
Published online by Cambridge University Press: 08 September 2023
Summary
Temporal Logics are a rich variety of logical systems designed for formalising reasoning about time, and about events and changes in the world over time. These systems differ by the ontological assumptions made about the nature of time in the associated models, by the logical languages involving various operators for composing temporalized expressions, and by the formal logical semantics adopted for capturing the precise intended meaning of these temporal operators. Temporal logics have found a wide range of applications as formal frameworks for temporal knowledge representation and reasoning in artificial intelligence, and as tools for formal specification, analysis, and verification of properties of computer programs and systems. This Element aims at providing both a panoramic view on the landscape of the variety of temporal logics and closer looks at some of their most interesting and important landmarks.
Information
- Type
- Element
- Information
- Series: Elements in Philosophy and LogicOnline ISBN: 9781009170093Publisher: Cambridge University PressPrint publication: 05 October 2023
References
Allen, J. (1983). Maintaining knowledge about Temporal Intervals. Communications of the ACM, 26(11), 832–43.CrossRefGoogle Scholar
Allen, J. (1984). Towards a general theory of action and time. Artificial Intelligence, 23(2), 123–54.CrossRefGoogle Scholar
Allen, J., & Ferguson, G. (1994). Actions and events in interval temporal logic. Journal of Logic and Computation, 4(5), 531–79.Google Scholar
Alur, R., & Henzinger, T. A. (1992). Logics and models of real time: A survey. In de Bakker, J. W., Huizing, C., de Roever, W. P., & Rozenberg, G. (Eds.), Real-time: Theory in practice (pp. 74–106). Springer.Google Scholar
Alur, R., & Henzinger, T. (1993). Real-time logics: Complexity and expressiveness. Information and Computation, 104(1), 35–77.CrossRefGoogle Scholar
Alur, R., & Henzinger, T. A. (1994). A really temporal logic. Journal of the ACM, 41(1), 181–203.CrossRefGoogle Scholar
Alur, R., Henzinger, T. A., & Kupferman, O. (2002). Alternating-time temporal logic. Journal of the ACM, 49(5), 672–713.CrossRefGoogle Scholar
Andréka, H., Madarász, J. X., & Németi, I. (2007). Logic of space-time and relativity theory. In Aiello, M., Pratt-Hartmann, I., & Van Benthem, J. (Eds.), Handbook of Spatial Logics (pp. 607–711). Springer.CrossRefGoogle Scholar
Areces, C., & ten Cate, B. (2006). Hybrid logics. In Handbook of modal logic. Elsevier.Google Scholar
, Aristotle. (1984/350 BC). Organon II. On Interpretation. In Complete Works of Aristotle, ed. Jonathan Barnes, . Princeton University Press.Google Scholar
Artale, A., & Franconi, E. (2000). A survey of temporal extensions of description logics. Annals of Mathematics and Artificial Intelligence, 30, 171–210.CrossRefGoogle Scholar
Barcan, R. C. (1946). A functional calculus of first order based on strict implication. The Journal of Symbolic Logic, 11(1), 1–16.Google Scholar
Belnap, N., & Green, M. (1994). Indeterminism and the Thin Red Line. Philosophical Perspectives, 8, 365–88.CrossRefGoogle Scholar
Belnap, N., & Müller, T. (2014a). CIFOL: Case-intensional first order logic. Journal of Philosophical Logic (I) Toward a Theory of Sorts., 43(2–3), 393–437.CrossRefGoogle ScholarPubMed
Belnap, N., & Müller, T. (2014b). BH-CIFOL: Case-intensional first order logic. Journal of Philosophical Logic (II) Branching Histories., 43(5), 835–66.Google Scholar
Belnap, N., Müller, T., & Placek, T. (2022). Branching space-times. Theory and applications. Oxford University Press.Google Scholar
Belnap, N., & Perloff, M. (1988). Seeing to it that: A canonical form for agentives. Theoria, 54, 175–99.Google Scholar
Belnap, N., Perloff, M., & Xu, M. (2001). Facing the future: Agents and choices in our indeterminist world. Oxford University Press.CrossRefGoogle Scholar
Ben-Ari, M., Pnueli, A., & Manna, Z. (1983). The temporal logic of branching time. Acta Informatica, 20, 207–26.Google Scholar
Blackburn, P. (2006). Arthur Prior and hybrid logic. Synthese, 150(3), 329–72.CrossRefGoogle Scholar
Blackburn, P., Hasle, P., & Øhrstrøm, P. (Eds.),. (2019). Logic and philosophy of time: Further themes from Prior, volume 2. Aalborg University Press.Google Scholar
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. Cambridge University Press.CrossRefGoogle Scholar
Bolc, L., & Szałas, A. (Eds.),. (1995). Time and logic: A computational approach. University College London.Google Scholar
Braüner, T., Øhrstrøm, P., & Hasle, P. (2000). Determinism and the origins of temporal logic. In Advances in temporal logic (pp. 185–206). Springer.Google Scholar
Braüner, T. (2022). Hybrid logic. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Spring 2022 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Bresolin, D., Della Monica, D., Goranko, V., Montanari, A., & Sciavicco, G. (2013). Metric propositional neighborhood logics on natural numbers. Software & Systems Modeling, 12(2), 245–64.CrossRefGoogle Scholar
Broersen, J. (2011). Deontic epistemic stit logic distinguishing modes of mens rea. Journal of Applied Logic, 9(2), 137–52.Google Scholar
Brown, M. A. (2014). Worlds enough, and time: Musings on foundations. In Müller, T. (Ed.), Nuel Belnap on indeterminism and free action, (pp. 99–121). Springer.CrossRefGoogle Scholar
Burgess, J. (1980). Decidability for branching time. Studia logica, 39(2–3), 203–18.CrossRefGoogle Scholar
Burgess, J. (1982a). Axioms for tense logic: II. Time periods. Notre Dame Journal of Formal Logic, 23(4), 375–83.Google Scholar
Burgess, J. (1982b). Axioms for tense logic: I. “‘Since” and “Until”’. Notre Dame Journal of Formal Logic, 23(4), 367–74.CrossRefGoogle Scholar
Burgess, J. (1984). Basic tense logic. In Handbook of philosophical logic (pp. 89–133). Springer.CrossRefGoogle Scholar
Burgess, J. (2002). Basic tense logic. In Gabbay, D. & Guenthner, F. (Eds.), Handbook of philosophical logic (Vol. 7, pp. 1–43). Springer.Google Scholar
Burgess, J., & Gurevich, Y. (1985). The decision problem for linear temporal logic. Notre Dame Journal of Formal Logic, 26(2), 115–28.CrossRefGoogle Scholar
Carnielli, W., & Coniglio, M. E. (2020). Combining logics. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Fall 2020 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Cocchiarella, N. B. (2002). Philosophical perspectives on quantification in tense and modal logic. In Gabbay, D. & Guenthner, F. (Eds.), Handbook of philosophical logic (Vol 7, pp. 672–713). Springer.Google Scholar
Conradie, W., Marais, C., & Goranko, V. (2023). Axiomatisations of some classes of trees in the Priorean temporal language. In preparation.Google Scholar
Copeland, B. J. (2022). Arthur Prior. In, E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Summer 2022 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Correia, F., & Iacona, A. (Eds.). (2013). Around the tree: Semantic and metaphysical issues concerning branching and the open future (Vol. 361). Springer.Google Scholar
Dean, T. L., & McDermott, D. V. (1987). Temporal database management. Artificial Intelligence, 32(1), 1–55.Google Scholar
Della Monica, D., Goranko, V., Montanari, A., & Sciavicco, G. (2011). Interval temporal logics: A journey. Bulletin of EATCS, 3(105), 73–99.Google Scholar
Demri, S., Goranko, V., & Lange, M. (2016). Temporal logics in computer science. Cambridge University Press.Google Scholar
Dyke, H., & Bardon, A. (Eds.). (2013). A companion to the philosophy of time (Vol. 154). John Wiley & Sons.Google Scholar
Emerson, E. (1990). Temporal and modal logics. In van Leeuwen, J. (Ed.), Handbook of theoretical computer science (Vol. B, pp. 995–1072). MIT Press.Google Scholar
Emerson, E. A., & Clarke, E. M. (1982). Using branching time temporal logic to synthesize synchronization skeletons. Science of Computer Programming, 2(3), 241–66.CrossRefGoogle Scholar
Emerson, E. A., & Halpern, J. Y. (1985). Decision procedures and expressiveness in the temporal logic of branching time. Journal of computer and system sciences, 30, 1–24.Google Scholar
Emerson, E., & Sistla, A. (1984). Deciding full branching time logic. Information and Control, 61, 175–201.Google Scholar
Emery, N., Markosian, N., & Sullivan, M. (2020). Time. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Winter 2020 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Euzenat, J., & Montanari, A. (2005). Time granularity. In Handbook of temporal reasoning in artificial intelligence (pp. 59–118). Elsevier.Google Scholar
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about knowledge. MIT Press.Google Scholar
Finger, M., & Gabbay, D. (1992). Adding a temporal dimension to a logic system. Journal of Logic, Language and Information, 1, 203–33.CrossRefGoogle Scholar
Finger, M., & Gabbay, D. (1996, Spring). Combining temporal logic systems. Notre Dame Journal of Formal Logic, 37(2), 204–32.Google Scholar
Finger, M., Gabbay, D., & Reynolds, M. (2002). Advanced tense logic. In Gabbay, D. & Guenthner, F. (Eds.), Handbook of philosophical logic (Vol. 7, pp. 43–204). Springer.Google Scholar
Fisher, M. (2008). Temporal representation and reasoning. In van Harmelen, F., Lifschitz, V., & Porter, B. (Eds.), Handbook of knowledge representation (pp. 513–50). Elsevier.Google Scholar
Fisher, M. (2011). An introduction to practical formal methods using temporal logic. Wiley.CrossRefGoogle Scholar
Fisher, M., Gabbay, D., & Vila, L. (Eds.). (2005). Handbook of temporal reasoning in artificial intelligence. Elsevier.Google Scholar
Fitting, M. (2022). Intensional logic. In Zalta, E. N. & Nodelman, U. (Eds.), The Stanford encyclopedia of philosophy (Winter 2022 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Fitting, M., & Mendelsohn, R. L. (1998). First order modal logic. Kluwer Academic Publishers.Google Scholar
Florio, C. D., & Frigerio, A. (2020). The thin red line, Molinism, and the flow of time. Journal of Logic, Language and Information, 29(3), 307–29. DOI: http://10.1007/s10849-019-09304-4.Google Scholar
Gabbay, D. (1973). A survey of decidability results for modal, tense and intermediate logics. In Heyting, A., Keisler, J., Moskowski, A., Robinson, A. & Suppes, P. (Eds.), Proceedings of the fourth international congress on logic, methodology and philosophy of science (pp. 29–43). North-Holland.Google Scholar
Gabbay, D. (1975). Decidability results in non-classical logics. Annals of Mathematical Logic, 8, 237–95.Google Scholar
Gabbay, D. (1981). An irreflexivity lemma with applications to axiomatizations of conditions on linear frames. In Mönnich, U. (Ed.), Aspects of philosophical logic (pp. 67–89). Reidel.Google Scholar
Gabbay, D. M. (1987). The declarative past and imperative future: Executable temporal logic for interactive systems. In Banieqbal, B., Barringer, H., & Pnueli, A. (Eds.), Temporal logic in specification, Altrincham, UK, April 8–10, 1987, Proceedings (Vol. 398, pp. 409–48). Springer.Google Scholar
Gabbay, D., & Guenthner, F. (Eds.). (2002). Handbook of philosophical logic, (2nd ed., Vol. 7). Springer.Google Scholar
Gabbay, D., Hodkinson, I., & Reynolds, M. (1994). Temporal logic, vol. 1: Mathematical foundations and computational aspects. Clarendon Press.Google Scholar
Gabbay, D., Pnueli, A., Shelah, S., & Stavi, J. (1980). On the temporal analysis of fairness. In Proceedings of POPL ’80 (Proceedings of the Seventh Annual ACM Symposium on Principles of Programming) Languages (pp. 163–73). ACM Press.Google Scholar
Gabbay, D., Reynolds, M., & Finger, M. (2000). Temporal Logic, Vol. 2: Mathematical foundations and computational aspects, vol. 2 Clarendon Press.Google Scholar
Gabelaia, D., Kontchakov, R., Kurucz, A., Wolter, F., & Zakharyaschev, M. (2005). Combining spatial and temporal logics: Expressiveness vs. complexity. Journal of Artificial Intelligence Research, 23, 167–243.Google Scholar
Gallois, A. (2016). Identity over time. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Winter 2016 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Galton, A. (1987). Temporal logic and computer science: An overview. In Galton, A. (Ed.), Temporal logics and their applications (pp. 1–52). Academic Press.Google Scholar
Galton, A. (1995). Time and change for AI. In Gabbay, D. M., Hogger, C. J., Robinson, J. A., & Antony, A. Galton (Eds.), Handbook of logic in artificial intelligence and logic programming, vol. 4: Epistemic and temporal reasoning (pp. 175–240). Oxford University Press.Google Scholar
Galton, A. (1996). Time and continuity in philosophy, mathematics, and artificial intelligence. Kodikas/Code, 19(1–2), 101–19.Google Scholar
Garson, J. W. (1984). Quantification in modal logic. In Gabbay, D. & Guenthner, F. (Eds.), Handbook of philosophical logic, volume II: Extensions of classical logic (Vol. 165, pp. 249–307). Reidel.Google Scholar
Goranko, V. (1996). Hierarchies of modal and temporal logics with references pointers. Journal of Logic, Language and Information, 5, 1–24.Google Scholar
Goranko, V., Montanari, A., & Sciavicco, G. (2003). Propositional interval neighborhood temporal logics. Journal of Universal Computer Science, 9(9), 1137–67.Google Scholar
Goranko, V., Montanari, A., & Sciavicco, G. (2004). A road map of interval temporal logics and duration calculi. Journal of Applied Non-Classical Logics, 14(1–2) 9–54.Google Scholar
Goranko, V., & Rumberg, A. (2020). Temporal logic. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Spring 2020 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Goranko, V., & Shkatov, D. (2010). Tableau-based decision procedures for logics of strategic ability in multiagent systems. ACM Transactions on Computational Logic, 11(1), 3–51.Google Scholar
Goranko, V., & van Drimmelen, G. (2006). Complete axiomatization and decidablity of Alternating-time temporal logic. Theoretical Computer Science, 353, 93–117.Google Scholar
Goré, R. (1999). Tableau methods for modal and temporal logics. In D’Agostino, M., Gabbay, D., Hähnle, R., & Posega, J. (Eds.), Handbook of tableau methods (pp. 297–396). Kluwer.CrossRefGoogle Scholar
Grädel, E., & Otto, M. (1999). On logics with two variables. Theoretical Computer Science 224(1–2), 73–113.Google Scholar
Gurevich, Y., & Shelah, S. (1985). The decision problem for branching time logic. The Journal of Symbolic Logic, 50, 668–81.Google Scholar
Halpern, J., & Shoham, Y. (1991). A propositional modal logic of time intervals. Journal of the ACM, 38(4), 935–62.Google Scholar
Halpern, J., & Vardi, M. (1989). The complexity of reasoning about knowledge and time I: Lower bounds. Journal of Computer and System Sciences, 38(1), 195–237.Google Scholar
Hamblin, C. (1972). Instants and intervals. In Fraser, J., Haber, F., & Mueller, G. (Eds.), The study of time (volume 1) (pp. 324–31). Springer.Google Scholar
Hamm, F., & Bott, O. (2021). Tense and aspect. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Fall 2021 ed.). Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Hansen, M., & Chaochen, Z. (1997). Duration calculus: Logical foundations. Formal Aspects of Computing, 9, 283–330.Google Scholar
Hasle, P., Blackburn, P. R., & Øhrstrøm, P. (2017). Logic and philosophy of time: Themes from Prior, volume 1. Aalborg University Press.Google Scholar
Hodges, W. (2001). Logic – an introduction to elementary logic, 2nd edition. Penguin Books.Google Scholar
Hodges, W., & Johnston, S. (2017). Medieval modalities and modern methods: Avicenna and Buridan. IfCoLog Journal of Logics and Their Applications, 4(4), 1029–73.Google Scholar
Hodkinson, I., & Reynolds, M. (2007). Temporal logic. In Blackburn, P., Van Benthem, J., & Wolter, F. (Eds.), Handbook of modal logic (Vol. 3, pp. 655–720). Elsevier.Google Scholar
Hodkinson, I., Wolter, F., & Zakharyaschev, M. (2000). Decidable fragment of first-order temporal logics. Annals of Pure and Applied Logic, 106(1–3) 85–134.Google Scholar
Hodkinson, I., Wolter, F., & Zakharyaschev, M. (2001). Monodic fragments of first-order temporal logics: 2000–2001 A.D. In Nieuwenhuis, R. & Voronkov, A. (Eds.), Logic for programming, artificial intelligence, and reasoning (pp. 1–23). Springer.Google Scholar
Hodkinson, I. M., Wolter, F., & Zakharyaschev, M. (2002). Decidable and undecidable fragments of first-order branching temporal logics. In 17th IEEE symposium on Logic in Computer Science (LICS 2002), 22–25 July 2002, Copenhagen, Denmark, Proceedings (pp. 393–402). IEEE Computer Society.Google Scholar
Humberstone, I. L. (1979). Interval semantics for tense logic: Some remarks. Journal of Philosophical Logic, 8, 171–196.Google Scholar
Humberstone, L. (2016). Philosophical applications of modal logic. College Publications.Google Scholar
Ju, F., Grilletti, G., & Goranko, V. (2018). A logic for temporal conditionals and a solution to the sea battle puzzle. In Bezhanishvili, G., D’Agostino, G., Metcalfe, G., & Studer, T. (Eds.), Proceedings of the 12th International Conference on Advances in Modal Logic (AiML’ 2018) (pp. 407–426). College Publications.Google Scholar
Kamp, H. (1979). Events, Instants and Temporal Reference. In Bäuerle, R., Egli, U., & Schwarze, C. (Eds.), Semantics from different points of view (pp. 376–417). De Gruyter.Google Scholar
Kamp, H., & Reyle, U. (1993). From discourse to logic: Introduction to modeltheoretic semantics of natural language, formal logic and discourse representation theory. Kluwer Academic Publishers.Google Scholar
Kamp, J. (1968). Tense logic and the theory of linear order (Doctoral dissertation UCLA). UCLA ProQuest Dissertations Publishing.Google Scholar
Kesten, Y., & Pnueli, A. (2002). Complete proof system for QPTL. Journal of Logic and Computation, 12(5), 701–45.Google Scholar
Kontchakov, R., Kurucz, A., Wolter, F., & Zakharyaschev, M. (2007). Spatial logic + temporal logic=? In Aiello, M., Van Benthem, J., & Pratt-Hartmann, I. (Eds.), Handbook of spatial logics (pp. 497–564). Springer.Google Scholar
Kontchakov, R., Lutz, C., Wolter, F., & Zakharyaschev, M. (2004). Temporalising tableaux. Studia Logica, 76(1), 91–134.Google Scholar
Kowalski, R., & Sergot, M. (1986). A logic-based calculus of events. New Generation Computing, 4(1), 67–95.Google Scholar
Koymans, R. (1990). Specifying real-time properties with metric temporal logic. Real Time Systems, 2(4), 255–299.Google Scholar
Kuhn, S. T., & Portner, P. (2002). Tense and time. In Gabbay, D. & Guenthner, F. (Eds.), Handbook of philosophical logic (pp. 277–346). Springer.Google Scholar
Kurucz, A., Wolter, F., Zakharyaschev, M., & Gabbay, D. (2003). Multidimentional modal logics: Theory and applications. Elsevier.Google Scholar
Ladkin, P. (1987). The logic of time representation (Unpublished doctoral dissertation). University of California, Berkeley.Google Scholar
Lamport, L. (1994, March). The temporal logic of actions. ACM Transactions on Programming Languages and Systems, 16(3), 872–923.Google Scholar
Lindström, S., & Segerberg, K. (2007). Modal logic and philosophy. In Blackburn, P., van Benthem, J., & Wolter, F. (Eds.), Handbook of modal logic (Vol. 3, pp. 1149–1214). North-Holland.Google Scholar
Linsky, B., & Zalta, E. N. (1994). In defense of the simplest quantified modal logic. Philosophical Perspectives, 8, 431–458.Google Scholar
Lorini, E. (2013). Temporal logic and its application to normative reasoning. Journal of Applied Non-Classical Logics, 23(4), 372–399.Google Scholar
Ludlow, P. (2021). Descriptions. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Fall 2021 ed.). Metaphysics Research Lab, Stanford University.Google Scholar
Lutz, C., Wolter, F., & Zakharyaschev, M. (2008). Temporal description logics: A survey. In Demri, S.P. & Jensen, C. S. (Eds.), 2008 15th International Symposium on Representation and Reasoning (pp. 3–14). IEEE Computer Society.Google Scholar
Manna, Z., & Pnueli, A. (1992). The temporal logic of reactive and concurrent systems: Specifications. Springer.Google Scholar
Marx, M., & Reynolds, M. (1999). Undecidability of compass logic. Journal of Logic and Computation, 9(6), 897–914.Google Scholar
McArthur, R. P. (1976). Tense logic (1st ed., Vol. 111). D. Reidel Publishing Company.Google Scholar
McCall, S. (1994). A model of the universe: Space-time, probability, and decision. Oxford University Press.Google Scholar
McCarthy, J., & Hayes, P. J. (1969). Some philosophical problems from the standpoint of artificial intelligence. In Meltzer, B. & Michie, D. (Eds.), Machine intelligence 4 (pp. 463–502). Edinburgh University Press.Google Scholar
McDermott, D. (1982). A temporal logic for reasoning about processes and plans. Cognitive Science, 6(2), April, 101–55.Google Scholar
Merz, S. (1992). Decidability and incompleteness results for first-order temporal logics of linear time. Journal of Applied Non-Classical Logics, 2(2), 139–56.Google Scholar
Montanari, A. (1996). Metric and layered temporal logic for time granularity (Doctoral dissertation, ILLC, University of Amsterdam). ILLC Dissertation Series, 1996-02.Google Scholar
Montanari, A., & Policriti, A. (1996). Decidability results for metric and layered temporal logics. Notre Dame Journal of Formal Logic, 37(2), 260—82.Google Scholar
Moszkowski, B. (1983). Reasoning about digital circuits (Doctoral dissertation, Department of Computer Science, Stanford University, Stanford, CA). Technical Report STAN-CS-83-970.Google Scholar
Müller, T. (Ed.). (2014). Nuel Belnap on indeterminism and free action (Vol. 2). Springer.Google Scholar
Nishimura, H. (1979). Is the semantics of branching structures adequate for chronological modal logics? Journal of Philosophical Logic, 8(4), 469–75.Google Scholar
Ohrstrom, P. (2014). What William of Ockham and Luis de Molina would have said to Nuel Belnap: A discussion of some arguments against ‘the Thin Red Line’. In Müller, T. (Ed.), Nuel Belnap on indeterminism and free action (Vol. 2, pp. 175–190). Springer.Google Scholar
Ohrstrom, P. (2019). A critical discussion of Prior’s philosophical and tense-logical analysis of the ideas of indeterminism and human freedom. Synthese, 196(1), 69–85.Google Scholar
Ohrstrom, P., & Hasle, P. (2006). Modern temporal logic: The philosophical background. In Handbook of the history of logic (Vol. 7, pp. 447–98). Elsevier.Google Scholar
Ohrstrom, P., & Hasle, P. (2020). Future Contingents. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Summer 2020 ed.). Metaphysics Research Lab, Stanford University.Google Scholar
Ohrstrom, P., & Hasle, P. F. V. (1995). Temporal logic: From ancient ideas to artificial intelligence. Springer.Google Scholar
Pani, A., & Bhattacharjee, G. (2001). Temporal representation and reasoning in artificial Intelligence: A review. Mathematical and Computer Modelling, 34(1–2), 55–80.Google Scholar
Pinto, J., & Reiter, R. (1995). Reasoning about time in the situation calculus. Annals of Mathematics and Artificial Intelligence, 14(2), 251–68.Google Scholar
Ploug, T., & Øhrstrøm, P. (2012). Branching time, indeterminism and tense logic. Synthese, 188(3), 367–79.Google Scholar
Pnueli, A. (1977). The temporal logic of programs. In Proceedings of the Eighteenth IEEE Symposium on the Foundations of Computer Science (pp. 46–57). IEEE Computer Society.Google Scholar
Prior, A. N. (1962). Tense logic and the continuity of time. Studia Logica, 13, 133–48.Google Scholar
Reynolds, M. (1994). Axiomatizing U and S over integer time. In Gabbay, D. & Ohlbach, H. J. (Eds.), Proceedings of the first International conference on temporal logic (pp. 117–32). Springer-Verlag.Google Scholar
Reynolds, M. (1996). Axiomatising first-order temporal logic: Until and Since over linear time. Studia Logica, 57(2/3), 279–302.Google Scholar
Reynolds, M. (2001). An axiomatization of full computation tree logic. The Journal of Symbolic Logic, 66(3), 1011–57.Google Scholar
Reynolds, M. (2002). Axioms for Branching Time. Journal of Logic and Computation, 12(4), 679–97.Google Scholar
Reynolds, M. (2003). An Axiomatization of Prior’s Ockhamist logic of historical necessity. In Balbiani, P., Suzuki, N. Y., Wolter, F., & Zakharyaschev, M. (Eds.), Proceedings of AiML 2002 (pp. 355–70).Google Scholar
Reynolds, M. (2005). An axiomatization of PCTL*. Information and Computation, 201(1), 72–119.Google Scholar
Reynolds, M. (2007). A tableau for bundled CTL*. Journal of Logic and Computation, 17(1), 117–32.Google Scholar
Reynolds, M. (2010). The complexity of temporal logic over the reals. Annals of Pure and Applied Logic, 161(8), 1063–96.Google Scholar
Reynolds, M. (2011). A tableau-based decision procedure for CTL*. Formal Aspects of Computing, 23(6), 739–79.Google Scholar
Reynolds, M. (2014). A Tableau for temporal logic over the reals. In Goré, R., Kooi, B., & Kurucz, A. (Eds.), Advances in modal logic (vol. 10, pp. 439–58). CSLI Publications.Google Scholar
Reynolds, M., & French, T. (2003). A sound and complete proof system for QPTL. In Balbiani, P., Suzuki, N. Y., Wolter, F., & Zakharyaschev, M. (Eds.), Advances In modal logic (pp. 127–48). King’s College Publications.Google Scholar
Rumberg, A. (2016). Transition semantics for branching time. Journal of Logic, Language and Information, 25(1), 77–108.Google Scholar
Segerberg, K. (1970). Modal logics with linear alternative relations. Theoria, 36(3), 301–22.Google Scholar
Sistla, A., & Clarke, E. M. (1985). The complexity of propositional linear temporal logics. Journal of the ACM, 32(3), 733–49.Google Scholar
Steedman, M. (1997). Temporality. In van Benthem, J. & ter Meulen, A. (Eds.), Handbook of logic and language (pp. 895–938). Elsevier.Google Scholar
Stirling, C. (1992). Modal and temporal logics. In Handbook of logic in computer science (Vol. 2, Background: Computational Structures), pp. 477–563. Clarendon Press.Google Scholar
ter Meulen, A. (2005). Temporal reasoning in natural language. In Fisher, M. & Gabbay, D. (Eds.), Handbook of temporal logic In artificial intelligence, vol. 1 (pp. 559–86). Elsevier.Google Scholar
Thomason, R. (1984). Combinations of tense and modality. In Gabbay, D. & Guenthner, F. (Eds.), Handbook of philosophical logic, volume II: Extensions of classical logic (pp. 135–166). Reidel.Google Scholar
Uckelman, S. L., & Uckelman, J. (2007). 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(3), 673–81.Google Scholar
van Benthem, J. (1983). The logic of time – a model-theoretic investigation into the varieties of temporal ontology and temporal discourse (Vol. 156). Springer.Google Scholar
van Benthem, J. (1995). Temporal logic. In Gabbay, D., Hogger, C. J., & Robinson, J. A. (Eds.), Handbook of logic in artificial intelligence and logic programming (pp. 241–350). Oxford: Clarendon Press.Google Scholar
van Benthem, J., & Pacuit, E. (2006). The tree of knowledge in action: Towards a common perspective. In Governatori, G., Hodkinson, I. M., & Venema, Y. (Eds.), Proceedings of Advances in Modal Logic, 2006 (pp. 87–106). College Publications.Google Scholar
Vardi, M. Y. (2007). Automata-theoretic techniques for temporal reasoning. In Blackburn, P., Van Benthem, J., & Wolter, F. (Eds.), Handbook of modal logic (Vol. 3, pp. 971–89). Elsevier.Google Scholar
Venema, Y. (1990). Expressiveness and completeness of an interval tense logic. Notre Dame Journal of Formal Logic, 31(4), 529–47.Google Scholar
Venema, Y. (1991). A modal logic for chopping intervals. Journal of Logic and Computation, 1(4), 453–76.Google Scholar
Venema, Y. (1993). Completeness via Completeness: Since and Until. In de Rijke, M. (Ed.), Diamonds and defaults (pp. 279–86). Kluwer.Google Scholar
Venema, Y. (2001). Temporal logic. In Goble, L. (Ed.), The Blackwell Guide to Philosophical Logic (pp. 259–81). Wiley-Blackwell.Google Scholar
Vila, L. (1994). A survey on temporal reasoning in artificial intelligence. AI Communications, 7(1), 4–28.Google Scholar
Wałȩga, P. (2019). Hybrid fragments of Halpern-Shoham logic and their expressive power. Theoretical Computer Science, 797, 102–28.Google Scholar
Wölfl, S. (1999). Combinations of tense and modality for predicate logic. Journal of Philosophical Logic, 28(4), 371–98.Google Scholar
Wolper, P. (1985). The tableau method for temporal logic: An overview. Logique et Analyse, 110–111, 119–36.Google Scholar
Wolter, F., & Zakharyaschev, M. (2000). Temporalizing description logics. In Gabbay, D. & de Rijke, M. (Eds.), Frontiers of combining systems 2 (Vol. 2, pp. 379–402). Research Studies Press.Google Scholar
Wolter, F., & Zakharyaschev, M. (2002). Axiomatizing the monodic fragment of first-order temporal logic. Annals of Pure and Applied Logic, 118(1–2) 133–45.Google Scholar
Zanardo, A. (1985). A finite axiomatization of the set of strongly valid Ockamist formulas. Journal of Philosophical Logic, 14, 447–68.Google Scholar
Zanardo, A. (1990). Axiomatization of ‘Peircean’ branching-time logic. Studia Logica, 49(2), 183–95.Google Scholar
Zanardo, A. (1991). A complete deductive system for since-until branching time logic. Journal of Philosophical Logic, 20, 131–48.Google Scholar
Zanardo, A. (1996). Branching-time logic with quantification over branches: The point of view of modal logic. Journal of Symbolic Logic, 61(1), 1–39.Google Scholar
Zanardo, A. (1998). Undivided and indistinguishable histories in branching time logics. Journal of Logic, Language and Information, 7, 297–315.Google Scholar
Zanardo, A., Barcellan, B., & Reynolds, M. (1999). Non-definability of the class of complete bundled trees. Logic Journal of the IGPL, 7(1), 125–36.Google Scholar
Ohrstrom, P., & Hasle, P. (2020). Future contingents. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy (Summer 2020 ed.). Metaphysics Research Lab, Stanford University.Google Scholar
Accessibility standard: Unknown
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
Accessibility compliance for the HTML of this element is currently unknown
and may be updated in the future.
- 23
- Cited by