Temporal logic and annotated constraint logic programming
We introduce a family of logic programming languages for representing and reasoning about time. The family is conceptually simple while covering substantial parts of temporal logic. Given a logic in our framework, there is a systematic way to make it executable as a constraint logic program. Thus we can study and compare various temporal logics and their executable fragments. Our approach allows for different models of time, different temporal operators, and temporal variables for both time points and time periods. Formulas can be labeled with temporal information using annotations. In this way we avoid the proliferation of variables and quantifiers as encountered in first order approaches. Unlike temporal logic, both qualitative and quantitative (metric) temporal reasoning with time points (instants) and periods (temporal intervals) are supported. A Horn clause fragment of our temporal logic can be seen as annotated constraint logic programming language. This class of languages can be implemented by translation into a standard constraint programming language. Thus we can make our temporal logic executable.
This paper is a companion paper to [Fru94c], where an interpreter for annotated languages and their underlying logic is described.
KeywordsLogic Program Temporal Logic Constraint Logic Predicate Symbol Constraint Logic Programming
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- [AbMa89]M. Abadi and Z. Manna, Temporal Logic Programming, J. Symbolic Computation (1989) 8, pp 277–295.Google Scholar
- [A1184]J. F. Allen, Towards a General Theory of Action and Time, Artificial Intelligence, Vol. 23, 1984, pp 123–154.Google Scholar
- [Brz93]C. Brzoska, Temporal Logic Programming with Bounded Universal Goals, 10th ICLP, Budapest, Hungary, MIT Press, 1993.Google Scholar
- [F*92]T. Frühwirth et al., Constraint Logic Programming — An Informal Introduction, Chapter in Logic Programming in Action, Springer LNCS 636, September 1992. Also available by anonymous ftp from ftp.ecrc.de, in pub/ECRC_tech_reports/reports, file ECRC-9305.ps.Z.Google Scholar
- [Fru94a]T. Frühwirth, Temporal Reasoning with Constraint Handling Rules, Technical Report ECRC-9405, ECRC Munich, Germany, January 1994. Available by anonymous ftp from ftp.ecrc.de, in pub/ECRC_tech_reports/reports, file ECRC-9405.ps.Z.Google Scholar
- [Fru94b]T. Fruhwirth, Annotating Formulas with Temporal Information, Workshop on Logic and Change at ECAI 94, Amsterdam, The Netherlands, August 1994.Google Scholar
- [Fru94c]T. Frühwirth, Annotated Constraint Logic Programming Applied to Temporal Reasoning, Programming Language Implementation and Logic Programming (PLILP), Madrid, Spain, Springer LNCS, September 1994. Also available by anonymous ftp from ftp.ecrc.de, in pub/ECRC_tech_reports/reports, file ECRC-94-22.ps.Z.Google Scholar
- [Gal87]A. Galton (ed), Temporal Logics and Their Applications, Academic Press, 1987.Google Scholar
- [Gal90]A. Galton, A Critical Examination of Allen's Theory of Action and Time, Artificial Intelligence, Vol. 42, 1990, pp. 159–188.Google Scholar
- [GaMcB91]D. Gabbay and P. McBrien, Temporal Logic and Historical Databases, 17th Int. Conf. on Very Large Databases, pp 423–430, Barcelona, September 1991.Google Scholar
- [JaMa94]J. Jaffar and M. J. Maher, Constraint Logic Programming: A Survey, Journal of Logic Programming, 1994:19,20:503–581.Google Scholar
- [KiSu89]M. Kifer and V.S. Subrahmanian, On the Expressive Power of Annotated Logic Programs, North American Conf. on Logic Programming, E.L. Lusk and R. A. Overbeek (eds), MIT Press, 1989, pp 1069–1089.Google Scholar
- [KiSu92]M. Kifer and V.S. Subrahmanian, Theory of Generalized Annotated Logic Programming and its Applications, Journal of Logic Programming, April 1992.Google Scholar
- [LeLu94]S. M. Leach and J. J. Lu, Computing Annotated Logic Programs: Theory and Implementation, 11th ICLP, Santa Margherita Ligure, Italy, MIT Press, 1994.Google Scholar
- [McD82]D. McDermot, A Temporal Logic for Reasoning about Processes and Plans, Cognitive Science 6:101–155, 1982.Google Scholar
- [VH91]P. van Hentenryck, Constraint Logic Programming, The Knowledge Engineering Review, Vol 6:3, 1991, pp 151–194.Google Scholar