Abstract
We define the class of head-cycle free nested logic programs, and its proper subclass of acyclic nested programs, generalising similar classes originally defined for disjunctive logic programs. We then extend several results known for acyclic and head-cycle free disjunctive programs under the stable-model semantics to the nested case. Most notably, we provide a propositional semantics for the program classes under consideration. This generalises different extensions of Fages’ theorem, including a recent result by Erdem and Lifschitz for tight logic programs. We further show that, based on a shifting method, head-cycle free nested programs can be rewritten into normal programs in polynomial time and space, extending a similar technique for head-cycle free disjunctive programs. All this shows that head-cycle free nested programs constitute a subclass of nested programs possessing a lower computational complexity than arbitrary nested programs, providing the polynomial hierarchy does not collapse.
This work was partially supported by the Austrian Science Fund (FWF) under projects Z29-N04 and P15068-INF, by the German Science Foundation (DFG) under grants FOR 375/1 and SCHA 550/6, TP C, as well as by the European Commission under projects FET-2001-37004 WASP and IST-2001-33570 INFOMIX.
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Linke, T., Tompits, H., Woltran, S. (2004). On Acyclic and Head-Cycle Free Nested Logic Programs. In: Demoen, B., Lifschitz, V. (eds) Logic Programming. ICLP 2004. Lecture Notes in Computer Science, vol 3132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27775-0_16
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