Using the notion of an elementary loop, Gebser and Schaub refined the theorem on loop formulas due to Lin and Zhao by considering loop formulas of elementary loops only. In this article, we reformulate their definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we show that the corresponding problem is {\sf coNP}-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs due to Ben-Eliyahu and Dechter. Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.

Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the non-monotonic system of equilibrium logic, establishing weaker or stronger forms of interpolation depending on the precise interpretation of the inference relation. These results also yield a form of interpolation for ground logic programs under the answer sets semantics. For disjunctive logic programs we also study the property of uniform interpolation that is closely related to the concept of variable forgetting.

In this report, we propose a quick survey of the currently known techniques for encoding a Boolean cardinality constraint into a cnf formula, and we discuss about the relevance of these encodings. We also propose models to facilitate analysis and design of cnf encodings for Boolean constraints.

Temporal Logic Model Checking is a verification method in which we describe a system, the model, and then we verify whether some properties, expressed in a temporal logic formula, hold in the system. It has many industrial applications. In order to improve performance, some tools allow preprocessing of the model, verifying on-line a set of properties reusing the same compiled model; we prove that the complexity of the Model Checking problem, without any preprocessing or preprocessing the model or the formula in a polynomial data structure, is the same. As a result preprocessing does not always exponentially improve performance. Symbolic Model Checking algorithms work by manipulating sets of states, and these sets are often represented by BDDs. It has been observed that the size of BDDs may grow exponentially as the model and formula increase in size. As a side result, we formally prove that a superpolynomial increase of the size of these BDDs is unavoidable in the worst case. While this exponential growth has been empirically observed, to the best of our knowledge it has never been proved so far in general terms. This result not only holds for all types of BDDs regardless of the variable ordering, but also for more powerful data structures, such as BEDs, RBCs, MTBDDs, and ADDs.

We present a probabilistic logic programming framework to reinforcement learning, by integrating reinforce-ment learning, in POMDP environments, with normal hybrid probabilistic logic programs with probabilistic answer set seman-tics, that is capable of representing domain-specific knowledge. We formally prove the correctness of our approach. We show that the complexity of finding a policy for a reinforcement learning problem in our approach is NP-complete. In addition, we show that any reinforcement learning problem can be encoded as a classical logic program with answer set semantics. We also show that a reinforcement learning problem can be encoded as a SAT problem. We present a new high level action description language that allows the factored representation of POMDP. Moreover, we modify the original model of POMDP so that it be able to distinguish between knowledge producing actions and actions that change the environment.

In this paper we consider a logical treatment for the ordered disjunction operator 'x' introduced by Brewka, Niemel\"a and Syrj\"anen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic programming under the answer set semantics. Their semantics is defined by first translating the LPOD into a set of normal programs (called split programs) and then imposing a preference relation among the answer sets of these split programs. We concentrate on the first step and show how a suitable translation of the ordered disjunction as a derived operator into the logic of Here-and-There allows capturing the answer sets of the split programs in a direct way. We use this characterisation not only for providing an alternative implementation for LPODs, but also for checking several properties (under strongly equivalent transformations) of the 'x' operator, like for instance, its distributivity with respect to conjunction or regular disjunction. We also make a comparison to an extension proposed by K\"arger, Lopes, Olmedilla and Polleres, that combines 'x' with regular disjunction.

In this paper we propose a middleware to reuse multimedia resources in order to produce new types of multimedia artifacts. In this work we adopt some basic concepts of film theory, such as the notions of plot, fabula and, in particular, diegetic time. The techniques we use are located within the area of artificial intelligence, using an explicit representation of time. The middleware consists of several modules, some devoted to the semantic annotation of multimedia components, and others to their visualization. Some modules regard the analysis of temporal connectivity and consistency of events. From a methodological point of view, an important module of the middleware contains the representation of a story (time of the narration and time of the story) and the temporal reasoning services, which are both implemented using a logic programming language (Flora2). Finally, there is a module in the middleware that translates the logical representation (in Flora2 language) into SMIL language, which allows the use of the final composition by a standard player.

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic constructs in the semantics and needs to axiomatize validity as part of the logic. It is also not clear how to generalize their ideas to a first-order case. In this paper, we propose a new account of multi-agent only-knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. We then provide, for the propositional fragment, a sound and complete axiomatization that faithfully lifts Levesque's proof theory to the many agent case. We also discuss comparisons to the earlier approach by Halpern and Lakemeyer.

In this short position paper we briefly review the development history of automated inductive theorem proving and computer-assisted mathematical induction. We think that the current low expectations on progress in this field result from a faulty narrow-scope historical projection. Our main motivation is to explain--on an abstract but hopefully sufficiently descriptive level--why we believe that future progress in the field is to result from human-orientedness and descente infinie.

We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. Our example is a formalism aiming at capturing causal explanations from causal information. We show the naturalness and relative efficiency of this translation job. We are interested in the ease for writing an ASP program. Limitations of the earlier systems made that in practice, the ``declarative aspect'' was more theoretical than practical. We show how recent improvements in working ASP systems facilitate the translation.