Characterizing and Extending Answer Set Semantics using Possibility Theory

Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, where this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP, in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been accepted for publication in Theory and Practice of Logic Programming, Copyright Cambridge University Pres

Semantics for possibilistic answer set programs: uncertain rules versus rules with uncertain conclusions

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets

Logic-Based Decision Support for Strategic Environmental Assessment

Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logic-based approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages.Comment: 17 pages, 1 figure, 26th Int'l. Conference on Logic Programming (ICLP'10

Computing only minimal answers in disjunctive deductive databases

A method is presented for computing minimal answers in disjunctive deductive databases under the disjunctive stable model semantics. Such answers are constructed by repeatedly extending partial answers. Our method is complete (in that every minimal answer can be computed) and does not admit redundancy (in the sense that every partial answer generated can be extended to a minimal answer), whence no non-minimal answer is generated. For stratified databases, the method does not (necessarily) require the computation of models of the database in their entirety. Compilation is proposed as a tool by which problems relating to computational efficiency and the non-existence of disjunctive stable models can be overcome. The extension of our method to other semantics is also considered.Comment: 48 page

Magic Sets for Disjunctive Datalog Programs

In this paper, a new technique for the optimization of (partially) bound queries over disjunctive Datalog programs with stratified negation is presented. The technique exploits the propagation of query bindings and extends the Magic Set (MS) optimization technique. An important feature of disjunctive Datalog is nonmonotonicity, which calls for nondeterministic implementations, such as backtracking search. A distinguishing characteristic of the new method is that the optimization can be exploited also during the nondeterministic phase. In particular, after some assumptions have been made during the computation, parts of the program may become irrelevant to a query under these assumptions. This allows for dynamic pruning of the search space. In contrast, the effect of the previously defined MS methods for disjunctive Datalog is limited to the deterministic portion of the process. In this way, the potential performance gain by using the proposed method can be exponential, as could be observed empirically. The correctness of MS is established thanks to a strong relationship between MS and unfounded sets that has not been studied in the literature before. This knowledge allows for extending the method also to programs with stratified negation in a natural way. The proposed method has been implemented in DLV and various experiments have been conducted. Experimental results on synthetic data confirm the utility of MS for disjunctive Datalog, and they highlight the computational gain that may be obtained by the new method w.r.t. the previously proposed MS methods for disjunctive Datalog programs. Further experiments on real-world data show the benefits of MS within an application scenario that has received considerable attention in recent years, the problem of answering user queries over possibly inconsistent databases originating from integration of autonomous sources of information.Comment: 67 pages, 19 figures, preprint submitted to Artificial Intelligenc

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