We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premise-based procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms.

Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision Diagram (BDD) for the constraint, and then encode the BDD into a propositional formula. These BDD-based approaches have some important advantages, such as not being dependent on the size of the coefficients, or being able to share the same BDD for representing many constraints. We first focus on the size of the resulting BDDs, which was considered to be an open problem in our research community. We report on previous work where it was proved that there are Pseudo-Boolean constraints for which no polynomial BDD exists. We also give an alternative and simpler proof assuming that NP is different from Co-NP. More interestingly, here we also show how to overcome the possible exponential blowup of BDDs by \emph{coefficient decomposition}. This allows us to give the first polynomial generalized arc-consistent ROBDD-based encoding for Pseudo-Boolean constraints. Finally, we focus on practical issues: we show how to efficiently construct such ROBDDs, how to encode them into SAT with only 2 clauses per node, and present experimental results that confirm that our approach is competitive with other encodings and state-of-the-art Pseudo-Boolean solvers.

We explore applicability of the situation calculus, the well-known logical framework developed in Artificial Intelligence for representation of dynamic systems, to the task of representing knowledge about processes, actions and events in the natural sciences. In this paper, we concentrate on a case study in the area of organic chemistry. More specifically, we adapt the situation calculus to the task of automating organic synthesis planning on a qualitative level, where the objective is to identify a chain of chemical reactions transforming the given initial molecules into the desired goal molecule. We present two approaches for reasoning about reactions in organic chemistry: a “micro” approach and a “macro” approach. The “micro” approach is a low level approach that explicitly represents the most elementary interactions between molecules during a single chemical reaction, namely the splitting and forming of bonds between atoms. In contrast, the“macro” approach is a higher level approach that treats each chemical reaction (a set of splits and formation of bonds) as an elementary action. Both approaches are implemented in PROLOG. Declarative heuristics are defined to reduce the search space and help the program to find the correct synthesis routes more quickly. We hope that the lessons learned from our successful case study can have discovery potential in other bio-medical sciences. We discuss briefly how the proposed approaches can contribute to solving other research problems and to communicating pathways.

Rules complement and extend ontologies on the Semantic Web. We refer to these rules as onto-relational since they combine DL-based ontology languages and Knowledge Representation formalisms supporting the relational data model within the tradition of Logic Programming and Deductive Databases. Rule authoring is a very demanding Knowledge Engineering task which can be automated though partially by applying Machine Learning algorithms. In this chapter we show how Inductive Logic Programming (ILP), born at the intersection of Machine Learning and Logic Programming and considered as a major approach to Relational Learning, can be adapted to Onto-Relational Learning. For the sake of illustration, we provide details of a specific Onto-Relational Learning solution to the problem of learning rule-based definitions of DL concepts and roles with ILP.

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague's use of lambda calculus formulas as meaning of words and phrases. With ASP as the target language the meaning of words and phrases are ASP-lambda formulas. In an earlier work we illustrated our approach by manually developing a dictionary of words and their ASP-lambda formulas. However such an approach is not scalable. In this paper our focus is on two algorithms that allow one to construct ASP-lambda formulas in an inverse manner. In particular the two algorithms take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F such that F with input as G, denoted by F@G, is equal to H; and similarly G@F = H. We present correctness and complexity results about these algorithms. To do that we develop the notion of typed ASP-lambda calculus theories and their orders and use it in developing the completeness results. (To appear in Theory and Practice of Logic Programming.)

We present CLP(BN), a novel approach that aims at expressing Bayesian networks through the constraint logic programming framework. Arguably, an important limitation of traditional Bayesian networks is that they are propositional, and thus cannot represent relations between multiple similar objects in multiple contexts. Several researchers have thus proposed first-order languages to describe such networks. Namely, one very successful example of this approach are the Probabilistic Relational Models (PRMs), that combine Bayesian networks with relational database technology. The key difficulty that we had to address when designing CLP(cal{BN}) is that logic based representations use ground terms to denote objects. With probabilitic data, we need to be able to uniquely represent an object whose value we are not sure about. We use {sl Skolem functions} as unique new symbols that uniquely represent objects with unknown value. The semantics of CLP(cal{BN}) programs then naturally follow from the general framework of constraint logic programming, as applied to a specific domain where we have probabilistic data. This paper introduces and defines CLP(cal{BN}), and it describes an implementation and initial experiments. The paper also shows how CLP(cal{BN}) relates to Probabilistic Relational Models (PRMs), Ngo and Haddawys Probabilistic Logic Programs, AND Kersting AND De Raedts Bayesian Logic Programs.

We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of {m P}{cal C}+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.

This paper is directed towards combining Pearl's structural-model approach to causal reasoning with high-level formalisms for reasoning about actions. More precisely, we present a combination of Pearl's structural-model approach with Poole's independent choice logic. We show how probabilistic theories in the independent choice logic can be mapped to probabilistic causal models. This mapping provides the independent choice logic with appealing concepts of causality and explanation from the structural-model approach. We illustrate this along Halpern and Pearl's sophisticated notions of actual cause, explanation, and partial explanation. This mapping also adds first-order modeling capabilities and explicit actions to the structural-model approach.

Generalized relational theories with null values in the sense of Reiter are first-order theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption.

We are proud to introduce this special issue of the Journal of Theory and Practice of Logic Programming (TPLP), dedicated to the full papers accepted for the 28th International Conference on Logic Programming (ICLP). The ICLP meetings started in Marseille in 1982 and since then constitute the main venue for presenting and discussing work in the area of logic programming. We contributed to ICLP for the first time in 1991. The first guest-editor had a paper on logic programming with sets, and the second had two papers on the parallel implementation of the Andorra model. Since then, we continued pursuing research in this exciting area and ICLP has always been the major venue for our work.