This paper summarizes our line of research about the introduction of function symbols (functions) in Answer Set Programming (ASP) – a powerful language for knowledge representation and reasoning. The undecidability of reasoning on ASP with functions, implied that functions were subject to severe restrictions or disallowed at all, drastically limiting ASP applicability. We overcame most of the technical difficulties preventing this introduction, and we singled out a highly expressive class of programs with functions (FG-programs), allowing the (possibly recursive) use of function terms in the full ASP language with disjunction and negation. Reasoning on FG-programs is decidable, and they can express any computable function (causing membership in this class to be semi-decidable). We singled out also FD-programs, a subset of FG-programs which are effectively recognizable, while keeping the computability of reasoning. We implemented all results into the DLV system, thus obtaining an ASP system allowing to encode any computable function in a rich and fully declarative KRR language, ensuring termination on every FG program. Finally, we singled out the class of DFRP programs, where decidability of reasoning is guaranteed and Prolog-like functions are allowed.

We introduce DTProbLog, a decision-theoretic extension of Prolog and its probabilistic variant ProbLog. DTProbLog is a simple but expressive probabilistic programming language that allows the modeling of a wide variety of domains, such as viral marketing. In DTProbLog, the utility of a strategy (a particular choice of actions) is defined as the expected reward for its execution in the presence of probabilistic effects. The key contribution of this paper is the introduction of exact, as well as approximate, solvers to compute the optimal strategy for a DTProbLog program and the decision problem it represents, by making use of binary and algebraic decision diagrams.  We also report on experimental results that show the effectiveness and the practical usefulness of the approach.

A general game player is a system that understands the rules of unknown games and learns to play these games well without human intervention. A major challenge for research in General Game Playing is to endow a player with the ability to extract and prove game-specific knowledge from the mere game rules. We define a formal language to express temporally extended — yet local — properties of games. We also develop a provably correct proof theory for this language using the paradigm of Answer Set Programming, and we report on experiments with a practical implementation of this proof system in combination with a successful general game player.

We consider problems where several individuals each need to make a yes/no choice regarding a number of issues and these choices then need to be aggregated into a collective choice. Depending on the application at hand, different combinations of yes/no may be considered rational. We can describe such rationality assumptions in terms of a propositional formula. The question then arises whether or not a given aggregation procedure will lift the rationality assumptions from the individual to the collective level, i.e., whether the collective choice will be rational whenever all individual choices are. To address this question, for each of a number of simple fragments of the language of propositional logic, we provide an axiomatic characterisation of the class of aggregation procedures that will lift all rationality assumptions expressible in that fragment.

The stable model semantics was recently generalized by Ferraris, Lee and Lifschitz to the full first-order language with a syntax translation approach that is very similar to McCarthy's circumscription. In this paper, we investigate the decidability and undecidability of various fragments of first-order language under both semantics of stable models and circumscription. Some maximally decidable classes and undecidable classes are identified. The results obtained in the paper show that the boundaries between decidability and undecidability for these two semantics are very different in spite of the similarity of definition. Moreover, for all fragments considered in the paper, decidability under the semantics of circumscription coincides with that in classical first-order logic. This seems rather counterintuitive due to the second-order definition of circumscription and the high undecidability of first-order circumscription.

We show how the situation calculus can be reformulated in terms of the first-order stable model semantics. A further transformation into answer set programs allows us to use an answer set solver to perform propositional reasoning about the situation calculus. We also provide an ASP style encoding method for Reiter's basic action theories, which tells us how the solution to the frame problem in ASP is related to the solution in the situation calculus.

An answer set program with variables is first-order definable on finite structures if the set of its finite answer sets can be captured by a first-order sentence, otherwise this program is first-order indefinable on finite structures. In this paper, we study the problem of first-order indefinability of answer set programs. We provide an Ehrenfeucht-Fraisse game-theoretic characterization for the first-order indefinability of answer set programs on finite structures. As an application of this approach, we show that the well-known finding Hamiltonian cycles program is not first-order definable on finite structures. We then define two notions named the 0-1 property and unbounded cycles or paths under the answer set semantics, from which we develop two sufficient conditions that may be effectively used in proving a program's first-order indefinability on finite structures under certain circumstances.

The study of node-selection query languages for (finite) trees has been a major topic in the recent research on query lan- guages for Web documents. On one hand, there has been an extensive study of XPath and its various extensions. On the other hand, query languages based on classical logics, such as first-order logic (FO) or monadic second-order logic (MSO), have been considered. Results in this area typically relate an Xpath-based language to a classical logic. What has yet to emerge is an XPath-related language that is expressive as MSO, and at the same time enjoys the computational proper- ties of XPath, which are linear query evaluation and exponen- tial query-containment test. In this paper we propose μXPath, which is the alternation-free fragment of XPath extended with fixpoint operators. Using two-way alternating automata, we show that this language does combine desired expressiveness and computational properties, placing it as an attractive can- didate as the definite query language for trees.

In this paper, we propose a translation from normal first-order logic programs under the answer set semantics to first-order theories on finite structures. Specifically, we introduce ordered completions which are modifications of Clark's completions with some extra predicates added to keep track of the derivation order, and show that on finite structures, classical models of the ordered-completion of a normal logic program correspond exactly to the answer sets (stable models) of the logic program.

Temporal conceptual data models (TCMs) can be encoded Conceptual data modelling formalisms such as the Entity-in various temporal description logics (TDLs), which Relationship model (ER) and Unified Modelling Language have been designed and investigated since the seminal paper (UML) have become a de facto standard in database design (Schild 1993) with the aim of understanding the computational by providing visual means to describe application domains price of introducing a temporal dimension in DLs; in a declarative and reusable way. On the other hand, both see (Lutz, Wolter, & Zakharyaschev 2008) for a recent survey. ER and UML turned out to be closely connected with description A general conclusion one can draw from the obtained logics (DLs) developed in the area of knowledge results is that--as far as there is nontrivial interaction between representation, underpinned by formal semantics and thus the temporal and DL components--TDLs based on capable of providing services for effective reasoning over full-fledged DLs like ALC turn out to be too complex for conceptual models; see, e.g., (Berardi, Calvanese, & De Giacomo effective reasoning (see the end of this section for details).