Abstract
We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [2, 3] for positive higher-order programs. In this way we provide an alternative extensional semantics for higher-order logic programs with negation to the one proposed in [6]. As an immediate useful consequence of our developments, we define for the language we consider the notions of stratification and local stratification, which generalize the familiar such notions from classical logic programming. We demonstrate that for stratified and locally stratified higher-order logic programs, the proposed semantics never assigns the unknown truth value.
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Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann (1988)
Bezem, M.: Extensionality of simply typed logic programs. In: Schreye, D.D. (ed.) Logic Programming: The 1999 International Conference, Las Cruces, 29 November–4 December 1999, pp. 395–410. MIT Press (1999)
Bezem, M.: An improved extensionality criterion for higher-order logic programs. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 203–216. Springer, Heidelberg (2001). doi:10.1007/3-540-44802-0_15
Bloom, S.L., Ésik, Z.: Iteration Theories - The Equational Logic of Iterative Processes. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)
Carayol, A., Ésik, Z.: An analysis of the equational properties of the well-founded fixed point. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, Cape Town, 25–29 April 2016, pp. 533–536. AAAI Press (2016)
Charalambidis, A., Ésik, Z., Rondogiannis, P.: Minimum model semantics for extensional higher-order logic programming with negation. TPLP 14(4–5), 725–737 (2014)
Charalambidis, A., Handjopoulos, K., Rondogiannis, P., Wadge, W.W.: Extensional higher-order logic programming. ACM Trans. Comput. Log. 14(3), 21 (2013)
Charalambidis, A., Rondogiannis, P., Symeonidou, I.: Equivalence of two fixed-point semantics for definitional higher-order logic programs. In: Matthes, R., Mio, M. (eds.) Proceedings Tenth International Workshop on Fixed Points in Computer Science, FICS 2015, Berlin, 11–12 September 2015. EPTCS, vol. 191, pp. 18–32 (2015)
Chen, W., Kifer, M., Warren, D.S.: HILOG: a foundation for higher-order logic programming. J. Log. Program. 15(3), 187–230 (1993)
Cholak, P., Blair, H.A.: The complexity of local stratification. Fundam. Inform. 21(4), 333–344 (1994)
Ésik, Z.: Equational properties of stratified least fixed points (extended abstract). In: de Paiva, V., de Queiroz, R., Moss, L.S., Leivant, D., de Oliveira, A. (eds.) WoLLIC 2015. LNCS, vol. 9160, pp. 174–188. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47709-0_13
Gelder, A.V., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)
Kountouriotis, V., Rondogiannis, P., Wadge, W.W.: Extensional higher-order datalog. In: Short Paper Proceedings of the 12th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), pp. 1–5, December 2005
Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)
Miller, D., Nadathur, G.: Programming with Higher-Order Logic, 1st edn. Cambridge University Press, New York (2012)
Rondogiannis, P., Wadge, W.W.: Minimum model semantics for logic programs with negation-as-failure. ACM Trans. Comput. Log. 6(2), 441–467 (2005)
Wadge, W.W.: Higher-order horn logic programming. In: Saraswat, V.A., Ueda, K. (eds.) Proceedings of the 1991 International Symposium on Logic Programming, San Diego, 28 October–1 November 1991, pp. 289–303. MIT Press (1991)
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Rondogiannis, P., Symeonidou, I. (2016). Extensional Semantics for Higher-Order Logic Programs with Negation. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_29
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DOI: https://doi.org/10.1007/978-3-319-48758-8_29
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