arXiv subjects

Stefania Costantini

Publications and source records attributed to Stefania Costantini.

21 records · Page 2Linked to original sources

arXiv2014

Characterizing and computing stable models of logic programs: The non-stratified case

Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-free logic program encoding the problem itself. Several implementations now exist for stable logic programming, and their performance is rapidly improving. To make SLP generally applicable, it should be possible to check for consistency (i.e., existence of stable models) of the input program before attempting to answer queries. In the literature, only rather strong sufficient conditions have been proposed for consistency, e.g., stratification. This paper extends these results in several directions. First, the syntactic features of programs, viz. cyclic negative dependencies, affecting the existence of stable models are characterized, and their relevance is discussed. Next, a new graph representation of logic programs, the Extended Dependency Graph (EDG), is introduced, which conveys enough information for reasoning about stable models (while the traditional Dependency Graph does not). Finally, we show that the problem of the existence of stable models can be reformulated in terms of coloring of the EDG.

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arXiv2004

On the existence of stable models of non-stratified logic programs

This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is given a syntactic characterization. This condition may have a practical importance both for defining new algorithms for checking consistency and computing answer sets, and for improving the existing systems. The approach of this paper is to introduce a new canonical form (to which any logic program can be reduced to), to focus the attention on cyclic dependencies. The technical result is then given in terms of programs in canonical form (canonical programs), without loss of generality. The result is based on identifying the cycles contained in the program, showing that stable models of the overall program are composed of stable models of suitable sub-programs, corresponding to the cycles, and on defining the Cycle Graph. Each vertex of this graph corresponds to one cycle, and each edge corresponds to onehandle, which is a literal containing an atom that, occurring in both cycles, actually determines a connection between them. In fact, the truth value of the handle in the cycle where it appears as the head of a rule, influences the truth value of the atoms of the cycle(s) where it occurs in the body. We can therefore introduce the concept of a handle path, connecting different cycles. If for every odd cycle we can find a handle path with certain properties, then the existence of stable model is guaranteed.

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arXiv2004

Normal forms for Answer Sets Programming

Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is useful for studying existence and number of answer sets. A kernel program is composed of the atoms which are undefined in the Well-founded semantics, which are those that directly affect the existence of answer sets. The body of rules is composed of negative literals only. Thus, the kernel form tends to be significantly more compact than other formulations. Also, it is possible to check consistency of kernel programs in terms of colorings of the Extended Dependency Graph program representation which we previously developed. The second normal form is called {\em 3-kernel.} A 3-kernel program is composed of the atoms which are undefined in the Well-founded semantics. Rules in 3-kernel programs have at most two conditions, and each rule either belongs to a cycle, or defines a connection between cycles. 3-kernel programs may have positive conditions. The 3-kernel normal form is very useful for the static analysis of program consistency, i.e., the syntactic characterization of existence of answer sets. This result can be obtained thanks to a novel graph-like representation of programs, called Cycle Graph which presented in the companion article \cite{Cos04b}.

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