Resolution refutation is a powerful reasoning technique employed in many automated theorem provers. Various enhancements to resolution have enabled it to be used as a general question answering mechanism. Question answering systems employing resolution as the basic reasoning technique have been used to provide both "intensional" and "extensional" answers to questions by considering a theorem to be proven as a question. An intensional answer is a rule, such as "for all x and for all y if x is a cat and y is a dog then x detests y', and an extensional answer is a fact, such as "Rachel detests Fido". The notion of what constitutes an answer can be expanded so that, as resolution proceeds, the intermediate results generated on the way to finding an intensional or extensional answer may be regarded as answers. This view of resolution as answer generation, and resolvants as answers, requires an expanded notion of what constitutes an answer. A class of "hypothetical" answers is proposed, having the general form X Y, where X can not be proven based on the information in the knowledge base.

Renkens, Joris (Katholieke Universiteit Leuven) | Kimmig, Angelika (Katholieke Universiteit Leuven) | Broeck, Guy Van den (Katholieke Universiteit Leuven) | Raedt, Luc De (Katholieke Universiteit Leuven)

Probabilistic inference can be realized using weighted model counting. Despite a lot of progress, computing weighted model counts exactly is still infeasible for many problems of interest, and one typically has to resort to approximation methods. We contribute a new bounded approximation method for weighted model counting based on probabilistic logic programming principles. Our bounded approximation algorithm is an anytime algorithm that provides lower and upper bounds on the weighted model count. An empirical evaluation on probabilistic logic programs shows that our approach is effective in many cases that are currently beyond the reach of exact methods. (To be published at AAAI14)

Renkens, Joris (KULeuven) | Kimmig, Angelika (KULeuven) | Broeck, Guy Van den (KULeuven) | Raedt, Luc De (KULeuven)

Probabilistic inference can be realized using weighted model counting. Despite a lot of progress, computing weighted model counts exactly is still infeasible for many problems of interest, and one typically has to resort to approximation methods. We contribute a new bounded approximation method for weighted model counting based on probabilistic logic programming principles. Our bounded approximation algorithm is an anytime algorithm that provides lower and upper bounds on the weighted model count. An empirical evaluation on probabilistic logic programs shows that our approach is effective in many cases that are currently beyond the reach of exact methods.

Bartholomew, Michael (Arizona State University) | Lee, Joohyung (Arizona State University)

Recently there has been an increasing interest in incorporating "intensional" functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being pre-defined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of "Answer Set Programming Modulo Theories (ASPMT)" — a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that "tight" ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT.