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In answer set programming systems like Smodels and some SAT solvers, constraint propagation is carried out by a mechanism called lookahead. The question arises as what is the pruning power of lookahead, and how such pruning power fares in comparison with the consistency techniques in solving CSPs. In this paper, we study the pruning power of lookahead by relating it to local consistencies under two different encodings from CSPs to answer set programs. This leads to an understanding of how the search space is pruned in an answer set solver with lookahead for solving CSPs. On the other hand, lookahead as a general constraint propagation mechanism provides a uniform algorithm for enforcing a variety of local consistencies. We also study the impact on the search efficiency under these encodings.

Nested logic programs and epistemic logic programs are two important extensions of answer set programming. However, the relationship between these two formalisms is rarely explored. In this paper we first introduce the epistemic HT-logic, and then propose a more general extension of logic programs called . The semantics of this extension – named – is defined on the basis of the epistemic HT-logic. We prove that equilibrium view semantics extends both the answer sets of nested logic programs and the world views of epistemic logic programs. Therefore, our work establishes a unifying framework for both nested logic programs and epistemic logic programs. Furthermore, we also provide a characterization of the strong equivalence of two nested epistemic logic programs.

ID-logic uses ideas from the field of logic programming to extend second order logic with non-monotone inductive defintions. In this work, we reformulate the semantics of this logic in terms of approximation theory, an algebraic theory which generalizes the semantics of several non-monotonic reasoning formalisms. This allows us to apply certain abstract modularity theorems, developed within the framework of approximation theory, to ID-logic. As such, we are able to offer elegant and simple proofs of generalizations of known theorems, as well as some new results.

The main construction in this paper is an encoding of default logic into an “only knowing” logic with degrees of confidence. By imposing simple and natural constraints on the encoding we show that the “only knowing” logic can accommodate ordered default theories and that the constrained encoding implements a prescriptive interpretation of preference between defaults. An advantage of the encoding is that it provides a transparent formal rendition of such a semantics. A feature of the construction is that the generation of extensions can be carried out within the “only knowing” logic, using object level concepts alone.

As in human world many of our goals could not be achieved without interacting with other people, in case many agents are part of the same environment one agent should be aware that he is not alone and he cannot assume other agents sharing his own goals. Moreover, he may be required to interact with other agents and to reason about their mental state in order to find out potential friends to join with (or opponents to fight against). In this paper we focus on a language derived from logic programming which both supports the representation of mental states of agent communities and provides each agent with the capability of reasoning about other agents’ mental states and acting accordingly. The proposed semantics is shown to be translatable into stable model semantics of logic programs with aggregates.

Two approaches to logic programming with probabilities emerged over time: bayesian reasoning and probabilistic satisfiability (PSAT). The attractiveness of the former is in tying the logic programming research to the body of work on Bayes networks. The second approach ties computationally reasoning about probabilities with linear programming, and allows for natural expression of imprecision in probabilities via the use of intervals.

In this paper we construct precise semantics for one PSAT-based formalism for reasoning with inteval probabilities, probabilistic logic programs (p-programs), orignally considered by Ng and Subrahmanian. We show that the probability ranges of atoms and formulas in p-programs cannot be expressed as single intervals. We construct the prescise description of the set of models of p-programs and study the computational complexity if this problem, as well as the problem of consistency of a p-program. We also study the conditions under which our semantics coincides with the single-interval semantics originally proposed by Ng and Subrahmanian for p-programs. Our work sheds light on the complexity of construction of reasoning formalisms for imprecise probabilities and suggests that interval probabilities alone are inadequate to support such reasoning.

We present an alternative model theory for answer sets based on the possible worlds semantics proposed by Routley (1974) as a framework for the propositional logics of Fitch and Nelson. By introducing a falsity constant or second negation into Routley models, we show how paraconsistent as well as ordinary answer sets can be represented via a simple minimality condition on models. This means we can define a paraconsistent version of equilibrium logic, or paraconsistent answer sets (PAS) for propositional theories. The underlying logic of PAS is denoted by . We characterise it axiomatically and algebraically, showing it to be the least conservative extension of the logic of here-and-there with strong negation. In addition, we show that captures the strong equivalence of programs in the paraconsistent case and can thus serve as a useful mathematical foundation for PAS. We end by showing that has the Interpolation Property.

are a paradigm which allows to express (partially) hierarchically ordered evolving knowledge bases through (partially) ordered multi sets of logic programs and allowing to solve contradictions among rules in different programs by allowing rules in more important programs to reject rules in less important ones. This class of programs extends the class of that provides meaning and semantics to . Recently a semantics named has fixed some counterintuitive behaviour of previously existing semantics for dynamic logic programs. However, it is not possible to directly extend the definitions and concepts of the refined semantics to the multidimensional case and hence more sophisticated principles and techniques are in order. In this paper we face the problem of defining a proper semantics for multidimensional dynamic logic programs by extending the idea of well supported model to this class of programs and by showing that this concept alone is enough for univocally characterizing a proper semantics. We then show how the newly defined semantics coincides with the refined one when applied to sequences of programs.

Evolution is an important sub-area of study in biological science, where given a set of taxa, the goal is to reconstruct their evolutionary history, or phylogeny. One very recent approach is to predict a local phylogeny for every subset of 4 taxa, called a quartet topology, and then to assemble a phylogeny for the whole set of taxa satisfying these predicted quartet topologies. In general, the predicted quartet topologies might not always agree with each other, and thus the objective function becomes to satisfy a maximum number of them. This is the well known Maximum Quartet Consistency (MQC) problem. In the past, the MQC problem has been solved by dynamic programming and the so-called fixed-parameter method. Recently, we have proposed to solve the MQC in answer set programming. In this note, we summarize the theoretical results of this approach and report new experimental results for the purpose of comparison, which show that our approach in answer set programming is favored over the existing approaches based on dynamic programming and fixed-parameter method. In particular, some of the hard instances (where the error ratio is high) that were not reported to be solved in other approaches can now be solved in our approach.

ACMI is a decision support system for the checking of medical invoices in a German health insurance company. We present a brief overview of the system and its implementation in DLV.