Temporal reasoning over linear discrete time
In this work we present a new Automated Theorem Prover, called TAS-FNext, applied to temporal logic. This is part of a broader project developed by our research group GIMAC. It is an extension of works ,  and  concerns classical logic and  Minimal Temporal Logic.
TAS-FNext is strongly based on formula structures and, specifically, on the structure of the syntactic tree of each formula. It works by making transformations on these syntactic trees (TAS stands for Transformaciones de Árboles Sintácticos, Spanish rendering of Syntactic Tree Transformations).
The power of TAS-FNext is mainly based on its capacity to extract efficiently any potentially useful information contained in the syntactic trees with two aims: to detect and classify any subformulas found, whether or not they are valid, unsatisfiable, equivalent or equal, and to transform the formula in question into a simultaneous unsatisfiable, but with less size, formula.
TAS-FNext is sound and complete, and, moreover, it generates counter-models in a natural way .
Keywordstemporal logics automated theorem proving
Unable to display preview. Download preview PDF.
- 1.A. Artosi and G. Governatori. Labeled model modal logic. In CADE12 Workshop on Automated Model Building. Springer-Verlag. LNAI, 1994. 838Google Scholar
- 2.M. Abadi and Z. Manna. Modal theorem proving. In Springer-Verlag, editor, 8th Int. Conf. on Automated Deduction. Lecture Notes in Computer Science, 1986.Google Scholar
- 4.G. Aguilera, I.P. de Guzmán and M. Ojeda. Automated model building via syntactic trees transformations. In Proceedings of CADE-12 Workshop on Automated Model Building, pages 4–10, Nancy, France. June 1994.Google Scholar
- 5.G. Aguilera, I.P. de Guzmán and M. Ojeda. TAS-D++ syntactic trees transformations for automated theorem proving. Lectures Notes in Artifial Intelligence n. 838, pages 198–216. Sept 1994.Google Scholar
- 6.G. Aguilera, I.P. de Guzmán and M. Ojeda. Increasing the efficiency of automated theorem proving. Journal of Applied non-Classical logics 5 (1):9–29. 1995.Google Scholar
- 7.C. Dixon, M. Fisher, and R. Johnson. Parallel temporal resolution. In International Workshop on Temporal Representation and Reasoning TIME'95, Melbourne. Florida. EEUU, 1995.Google Scholar
- 8.M. Enciso. Demostración Automática de Teoremas: Eficiencia y Paralelismo. PhD thesis, Universidad de Málaga. España, 1995.Google Scholar
- 9.M. Enciso and I.P. de Guzmán. A new and complete Theorem Prover for Temporal Logic. In In Proceedings of IJCAI-95 Workshop on Executable Temporal Logics. Montreal, Canada. Aug. 1995.Google Scholar
- 10.M. Fitting. Destructive modal resolution. Journal of Logic and Computation, 1(1), 1990.Google Scholar
- 11.A. Galton, editor. Temporal Logic and Their Applications. Academic Press, 1987.Google Scholar
- 12.L. Fariñas del Cerro and A. Herzig. Modal Deduction with applications in Epistemic and Temporal Logics. Springer Verlag, 1991.Google Scholar
- 13.M. Fisher. A resolution method for temporal logic. In 12th International Joint Conference on Artificial Intelligence (IJCAI), Sydney. Australia, 1991.Google Scholar
- 14.G. Governatori. Labeled tableaux for multimodal logics. In 4th Workshop on Theorem Proving, Analytic Tableaux and Related Methods, Berlin. German, 1995. Springer-Verlag. LNAI. 918Google Scholar
- 15.R. Hahnle. Automated Deduction in Multiple-valued Logics. Oxford University Press, 1993.Google Scholar
- 16.R. Hahnle and O. Ibens. Improving temporal logic tableaux using integer constraints. In 1st International Conference on Temporal Logic. Springer-Verlag. LNAI., Munich. German, 1994. Vol. 827Google Scholar
- 17.R. Johnson. A blackboard approach to parallel temporal tableaux. In Artificial Intelligence Methodologies, Systems and Applications (AIMSA). World Scientific, 1994.Google Scholar
- 18.A. Massini. A Proof Theory of Modalities for Computer Science. PhD thesis, Universita di Pisa-Genova-Udine, Italy, 1993.Google Scholar
- 19.A. Ramsay. Formal Methods in Artificial Intelligence. Cambridge University Press, 1988.Google Scholar
- 20.F. Sanz. Hacia una alternativa a resolución. PhD thesis, Universidad de Málaga, Spain, 1992.Google Scholar
- 21.L. A. Wallen. Automated proof search in non-classical logics: efficient matrix proof methods for modal and intuitionistic logics. The MIT Press, Cambridge, Massachusetts, 1990.Google Scholar