Abstract
AbstractEpistemic logic programs (ELPs) are an extension of answer set programming (ASP) with epistemic operators that allow for a form of meta-reasoning, that is, reasoning over multiple possible worlds. Existing ELP solving approaches generally rely on making multiple calls to an ASP solver in order to evaluate the ELP. However, in this paper, we show that there also exists a direct translation from ELPs into non-ground ASP with bounded arity. The resulting ASP program can thus be solved in a single shot. We then implement this encoding method, using recently proposed techniques to handle large, non-ground ASP rules, into the prototype ELP solving system “selp,” which we present in this paper. This solver exhibits competitive performance on a set of ELP benchmark instances.
Highlights
Epistemic logic programs (ELPs), as defined in Shen and Eiter (2016), are an extension of the well-established formalism of answer set programming (ASP)
The remainder of the paper is structured as follows: in Section 2, we introduce the formal background of ASP, ELPs, and tree decompositions; Section 3 states our reduction from ELPs to ASP, including practical considerations and a discussion of related work; Section 4 presents how quantified boolean formula (QBF) formulas can be encoded as ELP programs; Section 5 introduces our ELP solver; Section 6 presents our benchmark results, making use of results from Section 4; and Section 7 closes with some concluding remarks
For (TQ), selp can solve 6 of the 14 instances within the time limit of 12 h, whereas EP-ASP was unable to solve any instances at all. These results confirm that selp is highly competitive on well-structured problems: in the Scholarship eligibility (SE) instances, knowledge about students is not interrelated, and the graph GΠ of the ground ELP Π consists of one component for each student, having constant treewidth
Summary
Epistemic logic programs (ELPs), as defined in Shen and Eiter (2016), are an extension of the well-established formalism of answer set programming (ASP). ASP is a generic, fully declarative logic programming language that allows us to encode problems in such a way that the resulting answers (called answer sets) directly correspond to solutions of the encoded problem The default negation ¬a of an atom a is true if there is no justification for a in the same answer set, making it a “local” operator in the sense that it is defined relative to the same answer set. Epistemic negation is defined relative to a collection of answer sets, referred to as a world view. The main reasoning task for ELPs, checking that a world view exists, is Σ3P -complete (Shen and Eiter 2016)
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