Disjunctive ASP with Functions: Decidable Queries and Effective Computation

Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASP^{fs}). We show that query answering in this setting is decidable, if the query is finitely recursive (ASP^{fs}_{fr}). Our proof yields also an effective method for query evaluation. It is done by extending the magic set technique to ASP^{fs}_{fr}. We show that the magic-set rewritten program is query equivalent to the original one (under both brave and cautious reasoning). Moreover, we prove that the rewritten program is also finitely ground, implying that it is decidable. Importantly, finitely ground programs are evaluable using existing ASP solvers, making the class of ASP^{fs}_{fr} queries usable in practice.Comment: 16 pages, 1 figur

Extensions to the Estimation Calculus

Walther’s estimation calculus was designed to prove the termination of functional programs, and can also be used to solve the similar problem of proving the well-foundedness of induction rules. However, there are certain features of the goal formulae which are more common to the problem of induction rule well-foundedness than the problem of termination, and which the calculus cannot handle. We present a sound extension of the calculus that is capable of dealing with these features. The extension develops Walther’s concept of an argument bounded function in two ways: firstly, so that the function may be bounded below by its argument, and secondly, so that a bound may exist between two arguments of a predicate. Our calculus enables automatic proofs of the well-foundedness of a large class of induction rules not captured by the original calculus

A core language for fuzzy answer set programming

A number of different Fuzzy Answer Set Programming (FASP) formalisms have been proposed in the last years, which all differ in the language extensions they support. In this paperwe investigate the expressivity of these frameworks. Specificallywe showhowa variety of constructs in these languages can be implemented using a considerably simpler core language. These simulations are important as a compact and simple language is easier to implement and to reason about, while an expressive language offers more options when modeling problems