This paper focuses on computing first-order theories under either stable model semantics or circumscription. A reduction from first-order theories to logic programs under stable model semantics over finite structures is proposed, and an embedding of circumscription into stable model semantics is also given. Having such reduction and embedding, reasoning problems represented by first-order theories under these two semantics can then be handled by using existing answer set solvers. The effectiveness of this approach in computing hard problems beyond NP is demonstrated by some experiments.

One criticism often advanced against abstract argumentation frameworks (AFs), is that these consider only one form of interaction between atomic arguments: specifically that an argument attacks another. Attempts to broaden the class of relationships include bipolar frameworks, where arguments support others, and abstract dialectical frameworks (ADFs). The latter, allow "acceptance'' of an argument, x, to be predicated on a given propositional function, C_x, dependent on the corresponding acceptance of its parents, i.e. those y for which occurs. Although offering a richly expressive formalism subsuming both standard and bipolar AFs, an issue that arises with ADFs is whether this expressiveness is achieved in a manner that would be infeasible within standard AFs. Can the semantics used in ADFs be mapped to some AF semantics? How many arguments are needed in an AF to "simulate'' an ADF? We show that (in a formally defined sense) any ADF can be simulated by an AF of similar size and that this translation can be realised by a polynomial time algorithm.

Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth degrees. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Lukasiewicz semantics. We obtain these results in a novel generic framework of fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities.

Many important problems can be compactly represented as quantified boolean formulas (QBF) and solved by general QBF solvers. To date QBF solvers have mainly focused on determining whether or not the input QBF is true or false. However, additional important information about an application can be gathered from its QBF formulation. In this paper we demonstrate that a circuit-based QBF solver can be exploited to obtain a Q-Resolution proof of the truth or the falsity of a QBF. QBFs have a natural interpretation as a two person game and our main result is to show how, via a simple computation, the moves for the winning player can be computed directly from these proofs. This result shows that the proof is a representation of the winning strategy. In previous approaches the winning strategy has often been represented in a way that makes it hard to verify. In our approach the correctness of the strategy follows directly from the correctness of the proof, which is relatively easy to verify.

We study the existential closures of several propositional languages L considered recently as target languages for knowledge compilation (KC), namely the incomplete fragments KROM-C, HORN-C, K/H-C, renH-C, AFF, and the corresponding disjunction closures KROM-C[V], HORN-C[V], K/H-C[V], renH-C[V], and AFF[V]. We analyze the queries, transformations, expressiveness and succinctness of the resulting languages L[E] in order to locate them in the KC map. As a by-product, we also address several issues concerning disjunction closures that were left open so far. From our investigation, the language HORN-C[V, E] (where disjunctions and existential quantifications can be applied to Horn CNF formulae) appears as an interesting target language for the KC purpose, challenging the influential DNNF languages.

In a pursuit-evasion game, one or more pursuers aim to discover the existence of, and then capture, an evader. The paper studies pursuit-evasion games in which players may have incomplete information concerning the game state. A methodology is presented for the application of a model checker for the logic of knowledge and time to verify epistemic properties in such games. Experimental results are provided from a number of case studies that validate the feasibility of the approach.

Finally, explore possible methods for decision making in general, have received a lot uses of combinatorial aggregation in sequential voting, of attention in the AI community in recent years. The reasons and discuss theoretical generalisations to more complex logical for this focus are clear: SCT provides tools for the analysis of languages and practical applications. Particularly close to the interests of AI is the to study binary aggregation procedures, inspired by research problem of social choice in combinatorial domains (Chevaleyre in AI. As long as we do not know the intended application of et al., 2008), where the space of alternatives the individuals the model, there is no appropriate set of axioms to concentrate have to choose from has a combinatorial structure. Instead, we prove characterisation results concerning one Definition 1.

The Beth definability property, a well-known property from classical logic, is investigated in the context of description logics (DLs): if a general L-TBox implicitly defines an L-concept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in DLs. In this paper a complete classification of Beth definability is provided for extensions of the basic DL ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableau-based algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in first-order logic then we show how to compute them in EXPTIME.

It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either the Delta operator or truth constants in the language, i.e. in all these cases it is PSPACE-complete.

Probabilistic logics which is followed by the development of the main methods that support reasoning with probability distributions, used in generalising probabilistic Boolean interaction, and, such as ProbLog, use an implicit definition finally, default logic is briefly discussed. We will use probabilistic of an interaction rule to combine probabilistic evidence Boolean interaction as a sound and generic, algebraic about atoms. In this paper, we show that way to combine uncertain evidence, whereas default this interaction rule is an example of a more general logic will be used as our language to implement the interaction class of interactions that can be described by nonmonotonic operators, again reflecting this double perspective on the logics. We furthermore show that such probabilistic logic. The new probabilistic logical framework local interactions about the probability of an atom is described in Section 3 and compared to other approaches can be described by convolution. The resulting extended in Section 4. The achievements of this research are reflected probabilistic logic supports nonmonotonic upon in Section 5. reasoning with probabilistic information.