Abstract
In previous work, the so-called Temporal Equilibrium Logic (TEL) was introduced. This formalism provides an extension of the Answer Set semantics for logic programs to arbitrary theories in the syntax of Linear Temporal Logic. It has already been shown that, in the non-temporal case, arbitrary propositional theories can always be reduced to logic program rules (with disjunction and negation in the head) independently on the context. That is, logic programs constitute a normal form for the non-temporal case. In this paper we show that TEL can be similarly reduced to a normal form consisting of a set of implications (embraced by a necessity operator) quite close to logic program rules. This normal form may be useful both for a practical implementation of TEL and a simpler analysis of theoretical problems.
This research was partially supported by Spanish MEC project TIN2009-14562-C05-04 and Xunta de Galicia project INCITE08-PXIB105159PR.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R.A., Bowen, K.A. (eds.) Logic Programming: Proc. of the Fifth International Conference and Symposium, vol. 2, pp. 1070–1080. MIT Press, Cambridge (1988)
Denecker, M., Vennekens, J., Bond, S., Gebser, M., Truszczyński, M.: The second Answer Set Programming competition. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS (LNAI), vol. 5753, pp. 637–654. Springer, Heidelberg (2009)
McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence Journal 4, 463–512 (1969)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1991)
Pearce, D.: A new logical characterisation of stable models and answer sets. In: Dix, J., Przymusinski, T.C., Moniz Pereira, L. (eds.) NMELP 1996. LNCS(LNAI), vol. 1216. Springer, Heidelberg (1997)
Pearce, D.: Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47(1-2), 3–41 (2006)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. Computational Logic 2(4), 526–541 (2001)
Ferraris, P.: Answer sets for propositional theories. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 119–131. Springer, Heidelberg (2005)
Ferraris, P., Lee, J., Lifschitz, V.: A new perspective on stable models. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 372–379 (2007)
Heyting, A.: Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp. 42–56 (1930)
Cabalar, P., Vega, G.P.: Temporal equilibrium logic: a first approach. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds.) EUROCAST 2007. LNCS, vol. 4739, pp. 241–248. Springer, Heidelberg (2007)
Aguado, F., Cabalar, P., Pérez, G., Vidal, C.: Strongly equivalent temporal logic programs. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 8–20. Springer, Heidelberg (2008)
Cabalar, P., Ferraris, P.: Propositional theories are strongly equivalent to logic programs. Theory and Practice of Logic Programming 7(6), 745–759 (2007)
Fisher, M.: A resolution method for temporal logic. In: Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI 1991), pp. 99–104. Morgan Kaufmann Publishers Inc., San Francisco (1991)
Cabalar, P., Valverde, A., Pearce, D.: Reducing propositional theories in equilibrium logic to logic programs. In: Bento, C., Cardoso, A., Dias, G. (eds.) EPIA 2005. LNCS (LNAI), vol. 3808, pp. 4–17. Springer, Heidelberg (2005)
Cabalar, P., Valverde, A., Pearce, D.: Minimal logic programs. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 104–118. Springer, Heidelberg (2007)
Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. In: Artificial Intelligence, pp. 112–117 (2002)
Lifschitz, V., Turner, H.: Splitting a logic program. In: Proceedings of the 11th International Conference on Logic programming (ICLP 1994), pp. 23–37 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cabalar, P. (2010). A Normal Form for Linear Temporal Equilibrium Logic. In: Janhunen, T., Niemelä, I. (eds) Logics in Artificial Intelligence. JELIA 2010. Lecture Notes in Computer Science(), vol 6341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15675-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-15675-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15674-8
Online ISBN: 978-3-642-15675-5
eBook Packages: Computer ScienceComputer Science (R0)