Some (in)translatability results for normal logic programs and propositional theories

Abstract

ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation functions between the classes. As a result, we obtain a strict ordering among the classes under consideration. Binary programs (n ≤2) are shown to be as expressive as unconstrained programs but strictly more expressive than unary programs (n ≤ 1) which, in turn, are strictly more expressive than atomic programs (n = 0). We also take propositional theories into consideration and prove them to be strictly less expressive than atomic programs. In spite of the gap in expressiveness, we develop a faithful but non-modular translation function from normal programs to propositional theories. We consider this as a breakthrough due to sub-quadratic time complexity (of the order of ||P || × log 2 |Hb(P )|). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems.

Extended ASP Tableaux and Rule Redundancy in Normal Logic Programs

“…Consider the local transformation rule red(Π) := Π \ {r ∈ Π | head(r) ∈ body(Π)}. The rules removed by red are redundant with respect to satisfiability of the program in the sense that red preserves visible equivalence [16]. The visible equivalence relation takes the interfaces of programs into account: atoms(Π) is partitioned into v(Π) and h(Π) determining the visible and the hidden atoms in Π, respectively.…”

Relativized hyperequivalence of logic programs for modular programming

“…7 The class D P consists of all problems expressible as the conjunction of a problem in NP and a problem in coNP. However, this slight increase of complexity compared to Lemma 1 does not influence the subsequent Π P 2 -membership results, since a D P -oracle amounts to an NP-oracle.…”

“…The following lemmas mirror the respective results from the previous section but show some interesting differences. 7 and in the class Pol for normal programs: Given a program P , and sets X, Y , A, and B, decide whether (i)…”

“…Accordingly, there has been much work recently to establish foundations of modular answer-set programming. One line of investigations has focused on the notion of an answer-set program module [6][7][8][9]. This work builds on ideas for compositional semantics of logic programs proposed in [10] and encompasses earlier results on stratification and program splitting [11].…”

Modularity Aspects of Disjunctive Stable Models

“…Consequently, the length of Π in symbols, denoted by Π , gives an upper bound for |At(Π)| which is important when one considers the computational cost of translating programs (Janhunen, 2006). 8.…”