Continuous Temporal Models

We develop notation for describing a temporal structure over the real numbers flow of time. This forms a basis for various reasoning tasks including synthesizing a model from a given temporal or first-order specification. We announce an efficient procedure for finding a manageable description of such a model. There are applications in reasoning about multi-agent systems, understanding natural language, analogue devices, robotics and artificial reasoning.

[1]  Johan Anthory Willem Kamp,et al.  Tense logic and the theory of linear order , 1968 .

[2]  Thomas A. Henzinger,et al.  Real-time logics: complexity and expressiveness , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[3]  Yde Venema Completeness through Flatness in Two-Dimensional Temporal Logic , 1994, ICTL.

[4]  Jim Cunningham,et al.  Modelling Linguistic Events , 2000 .

[5]  Maarten Marx,et al.  The Mosaic Method for Temporal Logics , 2000, TABLEAUX.

[6]  Ben C. Moszkowski,et al.  Executing temporal logic programs , 1986, Seminar on Concurrency.

[7]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

[8]  Mark Reynolds,et al.  An axiomatization for until and since over the reals without the IRR rule , 1992, Stud Logica.

[9]  José Luiz Fiadeiro,et al.  Sometimes "Tomorrow" is "Sometime" - Action Refinement in a Temporal Logic of Objects , 1994, ICTL.

[10]  Howard Bowman,et al.  A Tableau Method for Interval Temporal Logic with Projection , 1998, TABLEAUX.

[11]  Mark Reynolds,et al.  A Decidable Temporal Logic of Parallelism , 1997, Notre Dame J. Formal Log..

[12]  Dov M. Gabbay,et al.  Temporal Logic: Mathematical Foundations and Computational Aspects: Volume 2 , 1994 .

[13]  Howard Bowman,et al.  Specification and Prototyping of Structured Multimedia Documents using Interval Temporal Logic , 2000 .

[14]  J. van Benthem,et al.  Temporal logic , 1995 .

[15]  Dov M. Gabbay,et al.  Temporal logic (vol. 1): mathematical foundations and computational aspects , 1994 .

[16]  Zohar Manna,et al.  Temporal Verification of Simulation and Refinement , 1993, REX School/Symposium.

[17]  Vaughan R. Pratt,et al.  Models of program logics , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[18]  O. Stock Spatial and Temporal Reasoning , 1899 .

[19]  Hava T. Siegelmann,et al.  Verifying Properties of Neural Networks , 2001, IWANN.

[20]  James F. Allen Towards a General Theory of Action and Time , 1984, Artif. Intell..

[21]  Alexander Moshe Rabinovich,et al.  On the Decidability of Continuous Time Specification Formalisms , 1998, J. Log. Comput..

[22]  Amir Pnueli,et al.  On the Synthesis of an Asynchronous Reactive Module , 1989, ICALP.

[23]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (Vol. 4): epistemic and temporal reasoning , 1995 .

[24]  D. Gabbay,et al.  Temporal expressive completeness in the presence of gaps , 1993 .

[25]  A. Prasad Sistla,et al.  Reasoning in a Restricted Temporal Logic , 1993, Inf. Comput..

[26]  Yoav Shoham,et al.  A propositional modal logic of time intervals , 1991, JACM.

[27]  Jonathan S. Ostroff,et al.  Composition and refinement of discrete real-time systems , 1999, TSEM.

[28]  John P. Burgess,et al.  The decision problem for linear temporal logic , 1985, Notre Dame J. Formal Log..

[29]  Bernhard Nebel,et al.  On the Computational Complexity of Temporal Projection, Planning, and Plan Validation , 1994, Artif. Intell..

[30]  Amir Pnueli,et al.  A really abstract concurrent model and its temporal logic , 1986, POPL '86.

[31]  Amir Pnueli,et al.  The temporal logic of programs , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[32]  Henry A. Kautz,et al.  Reasoning about plans , 1991, Morgan Kaufmann series in representation and reasoning.

[33]  Mark Steedman,et al.  Temporal Ontology and Temporal Reference , 1988, CL.

[34]  Thomas A. Henzinger,et al.  Real-Time Logics: Complexity and Expressiveness , 1993, Inf. Comput..

[35]  Dov M. Gabbay,et al.  An Axiomitization of the Temporal Logic with Until and Since over the Real Numbers , 1990, J. Log. Comput..