Core Fuzzy Answer Set Programming

Abstract

The study of extensions of classical ASP has received a great deal of attention over the past years, including the efforts of the European Working Group on Answer Set Programming (WASP) (Niemelä 2003). The main objectives of such a study are (1) researching the complexity and additional expressivity which certain extensions bring; (2) investigating whether extensions can be compiled to a core language that is easy to implement, or is already implemented. Certain interesting links have been brought to light in this research. For example, it has been shown that nested expressions can be translated to disjunctive logic programs (Pearce et al. 2002) and that aggregates can be translated to normal logic programs (Pelov et al. 2003). Next to these general extensions of ASP, the translation of other frameworks to ASP has also been studied. For example DLV supports abduction with penalization (Perri et al. 2005) through its front-end by compiling this framework to a logic program with weak constraints (Buccafurri et al. 2000). For preferences in ASP a common implementation method is to use a meta-formalism and first generate all answer sets for a program, and then filter the most preferred ones. Though the preference extensions have a higher complexity, this method ensures that programs with preferences can still be solved using off the shelf ASP solvers such as Smodels (Simons and Niemelä 2000) and DLV (Faber and Pfeifer 2005).