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A review of temporal logics

Published online by Cambridge University Press:  07 July 2009

Derek Long
Derek Long
Affiliation:
Department of Computer Science, University College London, Gower Street, London, UK
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Abstract

A 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, Kowalski and Sergot. The logics are compared and contrasted, particularly in their treatments of change and action, the roles they seek to fulfil and the underlying models of time on which they rest. The paper concludes with a brief consideration of the problem of granularity—a problem of considerable significance in temporal reasoning, which has yet to be satisfactorily treated in a temporal logic.

Type
Research Article
Information
The Knowledge Engineering Review , Volume 4 , Issue 2 , June 1989 , pp. 141 - 162
Copyright
Copyright © Cambridge University Press 1989

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References

References and Bibliography

van Benthem, JFAK, 1983. The logic of time, Dordrecht: D. ReidelGoogle Scholar
Galton, AP, 1987. “Temporal logic and computer science: An overview, Temporal logics and their applications, Galton, AP ed, pp 1–50, New York: Academic PressGoogle Scholar
McArthur, RP, 1976. Tense logic, Dorcrecht: D. RiegelGoogle Scholar
Prior, AN, 1967. Past, present and future, Oxford: Clarendon PressCrossRefGoogle Scholar
Rescher, N and Urquhart, A, 1971. Temporal logic, New York: Springer-VerlagCrossRefGoogle Scholar
Turner, R, 1984. Logics for artificial intelligence, Chichester: Ellis-HorwoodGoogle Scholar
Allen, JF, 1984. “Towards a general theory of action and time”, Artificial Intelligence 23, 123–154CrossRefGoogle Scholar
Barringer, H, Kuiper, R and Pnueli, A, 1984. “Now you may compose temporal logic specifications” Proc. 16th ACM Symp. on Theory of Computing, pp 51–63Google Scholar
Davidson, D, 1967. “The logical form of action sentences” The logic of decision and action, Recher, N, ed, pp 81–95, Pittsburgh: University of Pittsburgh PressGoogle Scholar
Dean, TL and McDermott, D, 1987. “Temporal dala base management” Artificial Intelligence 32 pp 1–55Google Scholar
Eshgi, K, 1988. “Abductive planning wilh event calculus”, Tech. Report, Dept. of Comp. Sci., Imperial College, LondonGoogle Scholar
Gabbay, D, 1986. “Executable temporal logic for interactive systems, Technical Report, Imperial College, LondonGoogle Scholar
Gabbay, D, 1987. “Modal and temporal logic programming” Temporal logics and their applications, Galton, A, ed, pp 197–239, New York: Academic PressGoogle Scholar
Galton, AP, 1984. The logic of aspect, Oxford: Oxford Clarendon PressGoogle Scholar
Galton, AP, 1986. “A critical examinalion of J. F. Allen's theory of time and action”, Report 6.86, Centre for Theoretical Comp. Sci., Univ. of Leeds, EnglandGoogle Scholar
Galton, AP, 1987. “The logic of occurrence” Temporal logics and their applications, Galton, AP, ed, pp 169–175, New York: Academic PressGoogle Scholar
Hale, R, 1987. “Temporal logic programming” Temporal logics and their applications, Galton, AP, ed, pp 91–119, New York: Academic PressGoogle Scholar
Hobbs, J, 1985. “Granularity” IJCAI 9Google Scholar
Kenny, A, 1963. Action, emotion and will, London: Routledge and Kegan PaulGoogle Scholar
Kowalski, RA and Sergot, MJ, 1986. “A logic-based calculus of events” New Generation Computing 4 67–95CrossRefGoogle Scholar
Kripke, S, 1963. “Semantical considerations on modal logic” Acta Philosophica Fennica 16 83–94Google Scholar
Lee, RM, Coelho, H and Cotta, JC, 1985. “Temporal inferencing on administrative databases” Information Systems 10 197–206Google Scholar
Lewis, D, 1973. “Causation” J. of Philosophy 70 556–567CrossRefGoogle Scholar
Mackey, JL, 1974. The cement of the universe: A study of causation, Oxford: Oxford University PressGoogle Scholar
McCarthy, J and Hayes, PJ, 1969. “Some philosophical problems form the standpoint of artificial intelligence” Machine intelligence, Meltzer, B and Michie, D, eds, Vol. 4, Edinburgh: Edinburgh University PressGoogle Scholar
McDermott, DV, 1978. “Tarskian semantics or, no notation without denotation” Cog. Sci. 2(3)Google Scholar
McDermott, DV, 1982. “A temporal logic for reasoning about processes and plans” Cog. Sci. 6 101–155Google Scholar
Moszkowski, B, 1986. Executing temporal logic programs, Cambridge: Cambridge University PressGoogle Scholar
Newton-Smith, WH, 1980. The structure of time, London: Routledge and Kegan PaulGoogle Scholar
Prior, AN, 1955. “Diodoran modalities” Philosophical Quarterly 5 205–213Google Scholar
Quine, WV, 1965. Elementary logic, New York: Harper and RowGoogle Scholar
Reichenbach, H, 1947. Elements of symbolic logic, New York: MacmillanGoogle Scholar
Russell, B, 1903. Principles of mathematics, London: George and UnwinGoogle Scholar
Russell, B, 1913. “On the notion of cause” Proc. of the Aristotelian Society 13 1–26Google Scholar
Shanahan, M, 1988. “A single logical framework for prediction problems”, Tech. Report, Dept. of Comp., Imperial College, LondonGoogle Scholar
Shoham, Y, 1985. “Ten requirements for a theory of change” New Generating Computing 3 467–77CrossRefGoogle Scholar
Shoham, Y, 1988. Reasoning about change, Massachusetts: MIT PressGoogle Scholar
Suppes, P, 1970. A probabilistic theory of causation, Amsterdam: North HollandGoogle Scholar
von Wright, GH, 1965. “And next” Acta Philosophica Fennica 18 293–304Google Scholar
von Wright, GH, 1966. “And then” Commentationes Physico-Mathematicae of the Finnish Society of Sciences 32(7)Google Scholar
Allen, JF, 1981. “An interval based representation of temporal knowledge” Proc. IJCAI 7 221–226Google Scholar
Allen, JF, 1983. “Maintaining knowledge about temporal intervals” CACM 26(11) 832–843Google Scholar
Allen, JF and Koomen, JA, 1983. “Planning using a temporal world model” Proc. IJCAI 8 741–747Google Scholar
Allen, JF and Hayes, PJ, 1985. “A common sense theory of time” Proc. IJCAI 9 528–531Google Scholar
Aoyagi, T, Fujita, M and Mota-Oka, T, 1985. “Temporal logic programming language Tokio: programming in Tokio” Logic Programming '85, vol. 221, pp 128–137, LNCS, New York: Springer-VerlagGoogle Scholar
Ben-Ari, M, Pnueli, A and Manna, Z, 1981. “The temporal logic of branching time” Proc. 8th ACM Symp. on Principles of Progrmming Languages, pp 164–176Google Scholar
Bruce, BC, 1972. “A model for temporal references and its application in a question answering program” Artificial Intelligence 3 1–25Google Scholar
Burgess, JP, 1982. “Axioms for tense logic ii: time periods”, Notre Dame J. of Formal Logic, 23(4) 375–383CrossRefGoogle Scholar
Clarke, EM, Emerson, EA and Sistla, AP, 1986. “Automatic verification of finite-state concurrent systems using temporal logic specifications” ACM Trans. on Programming Languages and Systems 8 244–263Google Scholar
Cresswell, MJ, 1977. “Interval semantics and logical words” On the logical analysis of tense and aspect, Rohrer, C, ed., Tubingen: Gunter NarrGoogle Scholar
Dean, TL, 1986. “Temporal imagery: An approach to reasoning about time for planning and problem solving” PhD Thesis, Yale UniversityGoogle Scholar
Doyle, J, 1979. “A truth maintenance system”, Artificial Intelligence 12 231–272CrossRefGoogle Scholar
Emerson, EA and Halpern, JY, 1983. “‘Sometimes’ and ‘not never’ revisited: on branching vs. linear time” Proc. 10th ACM Symp. on Principles of Programming Languages, pp 127–140Google Scholar
Farinas del Cerro, L, 1985. “Resolution modal logics” Logics and Models of Concurrent Programs, Apt, K, ed., pp. 27–56, New York: Springer-VerlagCrossRefGoogle Scholar
Findlay, JN, 1941. “Time: a treatment of some puzzles” Austalasian J. of Philosophy 19 216–235Google Scholar
Fujita, M et al. , 1986. “Tokio: logic programming language based on temporal logic and its compilation to Prolog” Proc. 3rd Int. Conf. on Logic Prog. Vol. 225, pp 695–709, LNCS, New York: Springer-VerlagGoogle Scholar
Gabbay, D et al. , 1980. “On the temporal analysis of fairness” Proc. 7th ACM Symp on Principles of Programming Languages, pp 163–173Google Scholar
Ginsberg, ML, 1986. “Counterfactuals” Artificial Intelligence 30(1) 35–81Google Scholar
Ginsberg, ML and Smith, DE, 1986. “Reasoning about action I: A possible worlds approach”, Tech. Report KSL-86–37, Stanford Knowledge Systems LabGoogle Scholar
Hanks, S and McDermott, D, 1985. “Temporal reasoning and default logics”, CS Research Report, Vol. 430, Yale UniversityGoogle Scholar
Hanks, S and McDermott, D, 1986. “Default reasoning, nonmonotonic logics and the frame problem” Proc. 5th Nat. Conf. on AI, AAAI, Vol. 1, pp 328–333Google Scholar
Hamblin, CL, 1971. “Instants and intervals” 24 127–134Google Scholar
Halpern, J, Manna, Z and Moszkowski, B, 1983. “A high level semantics based on interval logics” Proc. ICALP 278–291Google Scholar
Halpern, J and Shoham, Y, 1986. “A proposition modal logic of time intervals” Proc. Symp. on Logic in CS, Boston, Massachusetts: IEEEGoogle Scholar
Hayes, P, 1978. “The naive physics manifesto” Expert systems in the microelectronic age, Michie, D, ed., Edinburgh: Edinburgh University PressGoogle Scholar
Humberstone, IL, 1979. “Interval semantics for tense logic” J. Philosophical Logic 8 171–196Google Scholar
Kahn, K and Gorry, GA, 1977. “Mechanizing temporal knowledge” Artificial Intelligence 9 87–108CrossRefGoogle Scholar
Kamp, JAW, 1968. “Tense logic and the theory of linear order”, PhD Thesis, University of CaliforniaGoogle Scholar
Kim, J, 1971. “Causes and events: Mackey on causation” J. of Philosophy 68 426–441CrossRefGoogle Scholar
Kowalski, RA, 1986. “Database updates in the event calculus” DoC, 86/12, Dept. of Comp., Imperial College, LondonGoogle Scholar
Lamport, L, 1980. “‘Sometimes’ is sometimes ‘not never”: on the temporal logic of programs” Proc. 7th ACM Symp. on Principles of Programming Languages, pp 174–185Google Scholar
Massey, G, 1969. “Tense logic! Why bother?” Nous 3 17–32Google Scholar
Moens, M and Steedman, M, 1987. “Temporal ontology in natural languages” Proceedings of the 25th ACL, pp 1–7Google Scholar
Moens, M and Steedman, M, 1989. “Temporal ontology and temporal reference” Computational Linguistics 14Google Scholar
Moszkowski, B, 1983. “Reasoning about digital circuits” PhD thesis, Stanford UniversityGoogle Scholar
Moszkowski, B, 1985. “A temporal logic for multi-level reasoning about hardware” Computer 18 10–19CrossRefGoogle Scholar
Piaget, J and Garcia, R, 1974. “Understanding causality” W. W. MortonGoogle Scholar
Pnueli, A, 1977. “The temporal logic of programs” Proc. 18th IEEE Symp. on Foundations of Comp. Sci. pp. 46–67CrossRefGoogle Scholar
Reichgelt, H, 1987. “Semantics for reified temporal logic”, Hallam, J and Mellish, C, eds, Advances in artificial intelligence, Proceedings of the 1987 AISB Conference, pp 49–61, Chichester: Wiley and SonsGoogle Scholar
Richards, B, 1982. “Tense, aspect and adverbials” Linguistics and Philosophy 5 59–107CrossRefGoogle Scholar
Robinson, JA, 1965. “A machine-oriented logic based on the resolution principle” J. of ACM 12 23–41Google Scholar
Roper, P, 1980. “Intervals and tenses” J. of Philosophical Logic 9Google Scholar
Sadri, F, 1987. “Three recent approaches to temporal reasoning” Temporal logics and their applications, Galton, A, ed., pp 121–167, New York: Academic PressGoogle Scholar
Schwartz, RL, Melliar-Smith, PM and Vogt, FH, 1983. “An interval logic for higher-level temporal reasoning”, SRI Int., CS Lab.CrossRefGoogle Scholar
Shoham, Y, 1986. “Chronological ignorance: Time, nonmonotonocity and necessity” Proc. AAAI, Philadelphia, PAGoogle Scholar
Shoham, Y, 1987. “Temporal logics in AI: Semantical and ontological considerations” Artificial Intelligence 33 89–104CrossRefGoogle Scholar
Taylor, B, 1985. Modes of occurrence, Oxford: Basil BlackwellGoogle Scholar
Tichy, P, 1985. “Do we need interval semantics?” Linguistics and Philosophy 8 263–282Google Scholar
Williams, BC, 1986. “Doing time: Putting qualitative reasoning on firmer ground” Proc. AAAIGoogle Scholar
Wolper, P, 1981. ‘Temporal logics can be more expressive’ Proc. 22nd IEEE Symp. on Foundations of Comp. Sci., pp 340–348Google Scholar