Abstract
Co-logic programming is a programming language allowing each predicate to be annotated as either inductive or coinductive. Assuming the stratification restriction, a condition on predicate dependency in co-logic programs (co-LPs), a top-down procedural semantics (co-SLD derivation) as well as an alternating fixpoint semantics has been given. In this paper, we present some extensions of co-LPs, especially focusing on the relationship with the existing alternating tree automata approaches to branching-time model checking. We first consider the local stratification restriction to allow a more general class of co-LPs, so that we can encode the CTL satisfaction relation as a co-LP, which is a direct encoding of the standard alternating automata by Kupferman et al. Next, we consider non-stratified co-LPs based on the Horn \(\mu \)-calculus. We give a proof procedure, co-SLD derivation with the parity acceptance condition, for non-stratified co-LPs, and show that it is sound and complete for a class of non-stratified co-LPs. Its application to a goal-directed top-down proof procedure for normal logic programs is also discussed.
This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 24500171.
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References
Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: J. Minker, (ed.) Foundations of Deductive Databases and Logic Programming, pp. 89–148. Kaufmann (1988)
Charatonik., W., McAllester, D., Niwinski, D., Podelski, A., Walukiewicz, I.: The Horn Mu-calculus. In: Proc. LICS 1998, pp. 58–69 (1998)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press (1999)
Clarke, E.M., Jha, S., Lu, Y., Veit, H.: Tree-Like Counterexamples in Model Checking. In: Proc. LICS 2002, pp. 19–29 (2002)
Colmerauer, A., Prolog and Infinite Trees, Logic Programming, pp. 231–251. Academic Press (1982)
Courcelle, B.: Fundamental Properties of Infinite Trees. Theor. Comput. Sci. 25(2), 95–169 (1983)
Delzanno, G., Podelski, A.: Model Checking in CLP. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 223–239. Springer, Heidelberg (1999)
DeVries, B.W., Gupta, G., Hamlen, K.W., Moore, S., Sridhar, M.: ActionScript bytecode verification with co-logic programming. In: Proc. ACM SIGPLAN PLAS 2009, pp. 9–15 (2009)
Emerson, E.A., Jutla, C.S.: Tree Automata, Mu-Calculus and Determinacy (Extended Abstract). FOCS 1991 91, 368–377 (1991)
Fages, F.: Consistency of Clark’s Completion and Existence of Stable Models. J. Methods of Logic in Comput. Sci. 1(1), 51–60 (1994)
Fitting, M.: A Kripke-Kleene Semantics for Logic Programs. J. Logic Programming 2(4), 295–312 (1985)
Fioravanti, F., Pettorossi, A., Proietti, M.: Verification of Sets of Infinite State Processes Using Program Transformation. In: Pettorossi, A. (ed.) LOPSTR 2001. LNCS, vol. 2372, pp. 111–128. Springer, Heidelberg (2002)
Gastin, P., Oddoux, D.: Fast LTL to Büchi Automata Translation. In: Proc. the 13th Int’l. Conf. on Computer Aided Verification (CAV 2001), pp. 53–65 (2001)
Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: Proc. Joint Int. Conf. and Symp. on Logic Programming, pp. 1070–1080 (1988)
Gottlob, G., Grädel, E., Veith, H.: Datalog LITE: a deductive query language with linear time model checking. ACM Trans. Comput. Logic 3(1), 42–79 (2002)
Gupta, G., Bansal, A., Min, R., Simon, L., Mallya, A.: Coinductive logic programming and its applications. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 27–44. Springer, Heidelberg (2007)
Gupta, G., Saeedloei, N., DeVries, B., Min, R., Marple, K., Kluźniak, F.: Infinite computation, co-induction and computational logic. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 40–54. Springer, Heidelberg (2011)
Jaffar, J., Stuckey, P.: Semantics of infinite tree logic programming. Theoretical Computer Science 46, 141–158 (1986)
Kluźniak, F., Meta-interpreter supporting tabling and coinduction. http://www.utdallas.edu/~gupta/meta.html
Kunen, K.: Signed Data Dependencies in Logic Programs. J. Logic Programming 7, 231–245 (1989)
Kupferman, O., Vardi, M.Y., Wolper, P.: An Automata-Theoretic Approach to Branching-Time Model Checking. J. ACM 47(2), 312–360 (2000)
Leuschel, M., Massart, T.: Infinite State Model Checking by Abstract Interpretation. In: Bossi, A. (ed.) LOPSTR 1999. LNCS, vol. 1817, pp. 62–81. Springer, Heidelberg (2000)
Leuschel, M.: Declarative programming for verification: lessons and outlook. In: Proc. ACM SIGPLAN PPDP 2008, pp. 1–7 (2008)
Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer (1987)
Marek, W., Subrahmanian, V.S.: The relationship between stable, supported, default and autoepistemic semantics for general logic programs. Theoretical Computer Science 103, 365–386 (1992)
Marple, K., Bansal, A., Min, R., Gupta, G.: Goal-directed execution of answer set programs. In: Proc. PPDP 2012 ACM, pp. 35–44 (2012)
Min, R., Gupta, G.: Coinductive Logic Programming with Negation. In: De Schreye, D. (ed.) LOPSTR 2009. LNCS, vol. 6037, pp. 97–112. Springer, Heidelberg (2010)
Min, R., Predicate Answer Set Programming with Coinduction. PhD thesis, University of Texas at Dallas (2010)
Muller, D.E., Saoudi, A., Schupp, P.E.: Alternating automata, the weak monadic theory of the tree, and its complexity, In: Kott, L. (ed.) Automata, Languages and Programming. LNCS, vol. 226, pp. 275–283. Springer, Heidelberg (1986)
Nilsson, U., Lübcke, J.: Constraint Logic Programming for Local and Symbolic Model-Checking. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 384–398. Springer, Heidelberg (2000)
Pettorossi, A., Proietti, M., Senni, V.: Deciding Full Branching Time Logic by Program Transformation. In: De Schreye, D. (ed.) LOPSTR 2009. LNCS, vol. 6037, pp. 5–21. Springer, Heidelberg (2010)
Przymusinski, T.C.: Every Logic Program Has a Natural Stratification and an Iterated Least Fixed Point Model. In: Proc. of the 8th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems (PODS 1989), pp. 11–21 (1989)
Ramakrishna, Y.S., Ramakrishnan, C.R., Ramakrishnan, I.V., Smolka, S.A., Swift, T., Warren, D.S.: Efficient Model Checking Using Tabled Resolution. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 143–145. Springer, Heidelberg (1997)
Seki, H.: Proving Properties of Co-logic Programs with Negation by Program Transformations. In: Albert, E. (ed.) LOPSTR 2012. LNCS, vol. 7844, pp. 213–227. Springer, Heidelberg (2013)
Simon, L., Mallya, A., Bansal, A., Gupta, G.: Coinductive Logic Programming. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 330–345. Springer, Heidelberg (2006)
Simon, L.E., Extending Logic Programming with Coinduction, Ph.D. Dissertation, University of Texas at Dallas (2006)
Talbot, J.-M.: On the Alternation-Free Horn \(\mu\)-Calculus. In: Parigot, M., Voronkov, A. (eds.) LPAR 2000. LNCS (LNAI), vol. 1955, pp. 418–435. Springer, Heidelberg (2000)
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Seki, H. (2014). Extending Co-logic Programs for Branching-Time Model Checking. In: Gupta, G., Peña, R. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2013. Lecture Notes in Computer Science(), vol 8901. Springer, Cham. https://doi.org/10.1007/978-3-319-14125-1_8
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DOI: https://doi.org/10.1007/978-3-319-14125-1_8
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