Abstract
There are many different notions of “rule” in the literature. A key feature and main intuition of any such notion is that rules can be “applied” to derive conclusions from certain premises. More formally, a rule is viewed as a function that, when invoked on a set of known facts, can produce new facts. In this paper, we show that this extreme simplification is still sufficient to obtain a number of useful results in concrete cases. We define abstract rules as a certain kind of functions, provide them with a semantics in terms of (abstract) stable models, and explain how concrete normal logic programming rules can be viewed as abstract rules in a variety of ways. We further analyse dependencies between abstract rules to recognise classes of logic programs for which stable models are guaranteed to be unique.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison Wesley (1994)
Baget, J.F.: Improving the forward chaining algorithm for conceptual graphs rules. In: Dubois, D., Welty, C.A., Williams, M.A. (eds.) Proc. 9th Int. Conf. on Principles of Knowledge Representation and Reasoning, KR 2004, pp. 407–414. AAAI Press (2004)
Baget, J.F., Leclère, M., Mugnier, M.L., Salvat, E.: On rules with existential variables: Walking the decidability line. Artificial Intelligence 175(9-10), 1620–1654 (2011)
Deutsch, A., Nash, A., Remmel, J.B.: The chase revisited. In: Lenzerini, M., Lembo, D. (eds.) Proc. 27th Symposium on Principles of Database Systems, PODS 2008, pp. 149–158. ACM (2008)
Eiter, T., Fink, M., Tompits, H., Woltran, S.: On eliminating disjunctions in stable logic programming. In: Dubois, D., Welty, C.A., Williams, M.A. (eds.) Proc. 9th Int. Conf. on Principles of Knowledge Representation and Reasoning, KR 2004, pp. 447–458. AAAI Press (2004)
Eiter, T., Krennwallner, T., Schneider, P., Xiao, G.: Uniform evaluation of nonmonotonic DL-programs. In: Lukasiewicz, T., Sali, A. (eds.) FoIKS 2012. LNCS, vol. 7153, pp. 1–22. Springer, Heidelberg (2012)
Fages, F.: A new fixpoint semantics for general logic programs compared with the well-founded and the stable model semantics. New Generation Comput. 9(3/4), 425–444 (1991)
Fages, F.: Consistency of Clark’s completion and existence of stable models. Meth. of Logic in CS 1(1), 51–60 (1994)
Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: semantics and query answering. Theoretical Computer Science 336(1), 89–124 (2005)
Krötzsch, M., Magka, D., Horrocks, I.: Concrete results on abstract rules. Tech. rep., University of Oxford (2013), http://korrekt.org/page/Publications
Lierler, Y., Lifschitz, V.: One more decidable class of finitely ground programs. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 489–493. Springer, Heidelberg (2009)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Trans. Comput. Logic 2(4), 526–541 (2001)
Lloyd, J.W.: Foundations of Logic Programming. Springer (1988)
Magka, D., Krötzsch, M., Horrocks, I.: Computing stable models for nonmonotonic existential rules. In: Proc. 23rd Int. Joint Conf. on Artificial Intelligence, IJCAI 2013. AAAI Press/IJCAI (to appear, 2013)
Przymusinski, T.C.: On the declarative and procedural semantics of logic programs. J. Autom. Reasoning 5(2), 167–205 (1989)
Turner, H.: Strong equivalence made easy: nested expressions and weight constraints. TPLP 3(4-5), 609–622 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Krötzsch, M., Magka, D., Horrocks, I. (2013). Concrete Results on Abstract Rules. In: Cabalar, P., Son, T.C. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2013. Lecture Notes in Computer Science(), vol 8148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40564-8_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-40564-8_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40563-1
Online ISBN: 978-3-642-40564-8
eBook Packages: Computer ScienceComputer Science (R0)