Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms

In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negation-as-failure (naf) atoms, make use of an immediate consequence operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly well-supported models, are generalizations of the notion of well-supported models of normal logic programs to the case of programs with c-atoms. As for the case of fixpoint-based semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) well-supported models of a program, thus generalizing the theorem on the correspondence between stable models and well-supported models of a normal logic program to the class of programs with c-atoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with c-atoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature

Proving Correctness and Completeness of Normal Programs - a Declarative Approach

We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the operational semantics, in particular on the selection rule. We show how to deal with correctness and completeness in a declarative way, treating programs only from the logical point of view. Specifications used in this approach are interpretations (or theories). We point out that specifications for correctness may differ from those for completeness, as usually there are answers which are neither considered erroneous nor required to be computed. We present proof methods for correctness and completeness for definite programs and generalize them to normal programs. For normal programs we use the 3-valued completion semantics; this is a standard semantics corresponding to negation as finite failure. The proof methods employ solely the classical 2-valued logic. We use a 2-valued characterization of the 3-valued completion semantics which may be of separate interest. The presented methods are compared with an approach based on operational semantics. We also employ the ideas of this work to generalize a known method of proving termination of normal programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP). 44 page

CASP Solutions for Planning in Hybrid Domains

CASP is an extension of ASP that allows for numerical constraints to be added in the rules. PDDL+ is an extension of the PDDL standard language of automated planning for modeling mixed discrete-continuous dynamics. In this paper, we present CASP solutions for dealing with PDDL+ problems, i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP CASP solver in order to solve CASP programs arising from PDDL+ domains. An experimental analysis, performed on well-known linear and non-linear variants of PDDL+ domains, involving various configurations of the EZCSP solver, other CASP solvers, and PDDL+ planners, shows the viability of our solution.Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

Correctness and completeness of logic programs

We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we show how to prove completeness and correctness in the presence of SLD-tree pruning, and point out that approximate specifications simplify specifications and proofs. We compare the proof methods to declarative diagnosis (algorithmic debugging), showing that approximate specifications eliminate a major drawback of the latter. We argue that our proof methods reflect natural declarative thinking about programs, and that they can be used, formally or informally, in every-day programming.Comment: 29 pages, 2 figures; with editorial modifications, small corrections and extensions. arXiv admin note: text overlap with arXiv:1411.3015. Overlaps explained in "Related Work" (p. 21

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks

05171 Abstracts Collection -- Nonmonotonic Reasoning, Answer Set Programming and Constraints

From 24.04.05 to 29.04.05, the Dagstuhl Seminar 05171 ``Nonmonotonic Reasoning, Answer Set Programming and Constraints\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available