Manifold Answer-Set Programs for Meta-reasoning

• Authors: Wolfgang Faber;Stefan Woltran
• Venue: LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
• Year: 2009

In answer-set programming (ASP), the main focus usually is on computing answer sets which correspond to solutions to the problem represented by a logic program. Simple reasoning over answer sets is sometimes supported by ASP systems (usually in the form of computing brave or cautious consequences), but slightly more involved reasoning problems require external postprocessing. Generally speaking, it is often desirable to use (a subset of) brave or cautious consequences of a program P 1 as input to another program P 2 in order to provide the desired solutions to the problem to be solved. In practice, the evaluation of the program P 1 currently has to be decoupled from the evaluation of P 2 using an intermediate step which collects the desired consequences of P 1 and provides them as input to P 2 . In this work, we present a novel method for representing such a procedure within a single program, and thus within the realm of ASP itself. Our technique relies on rewriting P 1 into a so-called manifold program , which allows for accessing all desired consequences of P 1 within a single answer set. Then, this manifold program can be evaluated jointly with P 2 avoiding any intermediate computation step. For determining the consequences within the manifold program we use weak constraints , which is strongly motivated by complexity considerations. As an application, we present an encoding for computing the ideal extension of an abstract argumentation framework.