Departamento de Inteligencia Artificial

A logic program 1 is said to be equivalent to a logic program 2 in the sense of the answer set semantics if 1 and 2 have the same answer sets. We are interested in the following stronger condition: for every logic program , 1 ∪ has the same answer sets as 2 ∪ . The study of strong equivalence is important, because we learn from it how one can simplify a part of a logic program without looking at the rest of it. The main theorem shows that the verification of strong equivalence can be accomplished by checking the equivalence of formulas in a monotonic logic, called the logic of here-and-there, which is intermediate between classical logic and intuitionistic logic.

This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics. We define a nonmonotonic logic, called equilibrium logic, based on the least constructive extension, N2, of the intermediate logic of “here-and-there”. We show that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz. We thereby obtain a very simple characterisation of answer set semantics as a form of minimal model reasoning in N2, while equilibrium logic itself provides a natural generalisation of this semantics to arbitrary theories. We discuss briefly some consequences and applications of this result.

This volume contains the papers presented at the third international workshop on Applications of Logic Programming to the (Semantic) Web and Web Services (ALPSWS2008) held on the 12h of December 2008 in Udine, Italy, as part of the 24thInternational Conference on Logic Programming (ICLP 2008).

Abstract. We introduce and study a modal logic wK4F which is closely related to the logic S4F that is important in the context of epistemic logics for representing and reasoning about an agent's knowledge. It is obtained by adding the axiom F to the modal logic wK4, or dropping from S4F the T axiom. We show that wK4F is sound and complete with respect to the class of all minimal topological spaces ie topological spaces with only three open sets.

In the early stages of quantum mechanics, a widely accepted heuristic principle played a very important role. It says that a future theory has to be a generalisation of a classical theory in the sense of yielding it as a special, or 'limiting', case. This principle is especially associated with ~iels Bohr. He already used it in his e~rlier papers~ but explicitly mentions it in his [3], where he calls it 'Korrespondenzprinzip'. It is known that the principle was very extensively used in the development of quantum mechanics. Thus according to van der Waerden [22] (p. 28):

Abstract. Many answer set solvers deal with programs with variables by requiring a safety condition on rules: any variable in a rule must appear in its positive body. This idea of safety has recently been extended to cover more general kinds of rules or first-order formulas that might be accepted by existing or future generation ASP systems [4, 12, 7]. In this paper we continue the study of the generalised safety concept recently proposed in [7].

Abstract We propose a solution to a long-standing problem in the foundations of well-founded semantics (WFS) for logic programs. The problem addressed is this: which (non-modal) logic can be considered adequate for well-founded semantics in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program?

Though formal metascience has made rapid advances over the past few decades, it has seldom been seen to contribute much to the rational reconstruction of scientific development; for the most part, logical concepts have found application in the synchronic analysis of scientific theories.

Interpretability and Equivalence in Quantified Equilibrium Logic David Pearce1* and Agustın Valverde2** 1 Computing Science and Artificial Intelligence, Univ. Rey Juan Carlos,(Móstoles, Madrid), Spain. davidandrew. pearce@ urjc. es 2 Dept. of Applied Mathematics, Univ. of Málaga, Spain. a valverde@ ctima. uma. es Abstract. The study of synonymy among propositional theories in equilibrium logic, begun in [36], is extended to the first-order case.

Abstract. For a given semantics, two nonmonotonic theories Π1 and Π2 can be said to be equivalent if they have the same intended models and strongly (resp., uniformly) equivalent if for any Σ, Π1∪ Σ and Π2∪ Σ are equivalent, where Σ is a set of sentences (resp., literals). In the general case, no restrictions are placed on the language (signature) of Σ. Relativised notions of strong and uniform equivalence are obtained by requiring that Σ belongs to a specified sublanguage L of the theories Π1 and Π2.

The nonmonotonic formalism of partial equilibrium logic (PEL) has recently been proposed as a logical foundation for the partial stable and well-founded semantics of logic programs [1, 2]. We study certain logical properties of PEL and some techniques to compute partial equilibrium models.

/Motivation Though possible worlds semantics has long been established as the dominant research tradition in philosophical logic and its applications, its various theories, background assumptions, and norms have seldom been systematically investigated from a methodological point of view. By way of illustration, consider the matter of semantic adequacy.

Abstract In the ongoing discussion about rule extensions for Ontology languages on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view.

Summary This project deals with the study of mathematical foundations, as well as deduction and programming, for several types of non-classical logics, especially multiple-valued logics and intermediate logics, with the aim of providing means for intelligent management of information. The classical problem of deduction is, given explicit knowledge expressed in a given formalism together with a set of inference rules, to deduce the implicit knowledge which could be relevant for applications.

Abstract The project develops logical and programming tools for knowledge representation and reasoning tasks oriented towards practical application domains such as program verification, Semantic Web services and the modelling of virtual organisations.

Abstract. A formalism called partial equilibrium logic (PEL) has recently been proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. In PEL one defines a class of minimal models, called partial equilibrium models, in a non-classical logic, HT2. On logic programs partial equilibrium models coincide with Przymusinski's partial stable (p-stable) models, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories.

Abstract We de ne a logical semantics called back-and-forth, applicable to normal and disjunctive datalog programs as well as to programs possessing a second, explicit orstrong'negation operator. We show that on normal programs it is equivalent to the well-founded semantics (WFS), and that on disjunctive programs it is equivalent to the P-stable semantics of Eiter, Leone and Sacc a, hence to Przymusinski's 3-valued stable semantics.

Abstract. The study of strong equivalence between logic programs or nonmonotonic theories under answer set semantics, begun in [18], is extended to the case where the programs or theories concerned are formulated in different languages. We suggest that theories in different languages be considered equivalent in the strong sense or synonymous if and only if each is bijectively interpretable (hence translatable) into the other.

When the new research area of logic programming and non-monotonic reasoning emerged at the end of the 1980s, it focused notably on the study of mathematical relations between different non-monotonic formalisms, especially between the semantics of stable models and various non-monotonic modal logics. Given the many and varied embeddings of stable models into systems of modal logic, the modal interpretation of logic programming connectives and rules became the dominant view until well into the new century.

Abstract. The nonmonotonic formalism of partial equilibrium logic (PEL) was introduced and studied in [1, 2] and proposed as a logical foundation for the partial stable and well-founded semantics of logic programs. Here we study further logical properties of PEL and some techniques to compute partial equilibrium models.