Related papers: Strong Equivalence Made Easy: Nested Expressions a…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…
This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of 'strong equivalence' between logical programs that can be verified in 3-valued Goedel logic, G3,…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice,…
This paper shows that the semantics of programs with aggregates implemented by the solvers clingo and dlv can be characterized as extended First-Order formulas with intensional functions in the logic of Here-and-There. Furthermore, this…
Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in Answer-Set Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…
Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…
We target the problem of automatically synthesizing proofs of semantic equivalence between two programs made of sequences of statements. We represent programs using abstract syntax trees (AST), where a given set of semantics-preserving…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to…
A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than…
Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path…
We show how definite extended logic programs can be used for defining and reasoning with rough sets. Moreover, a rough-set-specific query language is presented and an answering algorithm is outlined. Thus, we not only show a possible…
Answer set programming (ASP) with disjunction offers a powerful tool for declaratively representing and solving hard problems. Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise and…
In this paper we investigate forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. The goal is to provide an approach that is syntax-independent, in that…