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A polynomial translation of logic programs with nested expressions into disjunctive logic programs
(2002)

In this paper, we show how an approach to belief revision and belief contraction can be axiomatized by means of quantified Boolean formulas. Specifically, we consider the approach of belief change scenarios, a general framework that has been introduced for expressing different forms of belief change. The essential idea is that for a belief change scenario (K, R, C), the set of formulas K, representing the knowledge base, is modified so that the sets of formulas R and C are respectively true in, and consistent with the result. By restricting the form of a belief change scenario, one obtains specific belief change operators including belief revision, contraction, update, and merging. For both the general approach and for specific operators, we give a quantified Boolean formula such that satisfying truth assignments to the free variables correspond to belief change extensions in the original approach. Hence, we reduce the problem of determining the results of a belief change operation to that of satisfiability. This approach has several benefits. First, it furnishes an axiomatic specification of belief change with respect to belief change scenarios. This then leads to further insight into the belief change framework. Second, this axiomatization allows us to identify strict complexity bounds for the considered reasoning tasks. Third, we have implemented these different forms of belief change by means of existing solvers for quantified Boolean formulas. As well, it appears that this approach may be straightforwardly applied to other specific approaches to belief change

We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs.
We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P * Q. We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision.
We next consider approaches for merging a set of logic programs, P-1,...,P-n. Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program P-i those models of P-i that vary the least from models of the other programs. The second approach informally selects those models of a program P-0 that are closest to the models of programs P-1,...,P-n. In this case, P-0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets.
Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism.

Dual-normal logic programs
(2015)

Disjunctive Answer Set Programming is a powerful declarative programming paradigm with complexity beyond NP. Identifying classes of programs for which the consistency problem is in NP is of interest from the theoretical standpoint and can potentially lead to improvements in the design of answer set programming solvers. One of such classes consists of dual-normal programs, where the number of positive body atoms in proper rules is at most one. Unlike other classes of programs, dual-normal programs have received little attention so far. In this paper we study this class. We relate dual-normal programs to propositional theories and to normal programs by presenting several inter-translations. With the translation from dual-normal to normal programs at hand, we introduce the novel class of body-cycle free programs, which are in many respects dual to head-cycle free programs. We establish the expressive power of dual-normal programs in terms of SE- and UE-models, and compare them to normal programs. We also discuss the complexity of deciding whether dual-normal programs are strongly and uniformly equivalent.