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Susanna Cozza

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AAAI Conference 2010 Conference Paper

Enhancing ASP by Functions: Decidable Classes and Implementation Techniques

Francesco Calimeri
Susanna Cozza
Giovambattista Ianni
Nicola Leone

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.

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JELIA Conference 2006 Conference Paper

Decidable Fragments of Logic Programming with Value Invention

Francesco Calimeri
Susanna Cozza
Giovambattista Ianni

Abstract The issue of value invention in logic programming embraces many scenarios, such as logic programming with function symbols, object oriented logic languages, inter-operability with external sources of knowledge, set unification. This paper introduces a framework embedding value invention in a general context. The class of programs having a suitable (but, in general, not decidable) ‘finite grounding property’ is identified, and the class of ‘value invention restricted’ programs is introduced. Value invention restricted programs have the finite grounding property and can be decided in polynomial time. They are, in a sense, the broadest polynomially decidable class having this property, whenever no assumption can be made about the nature of invented values (while this latter is the case in the specific literature about logic programming with function symbols). Relationships with existing formalisms are eventually discussed; in particular, value invention restricted programs subsume ω -restricted programs and are incomparable with finitary programs.

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