Dynamic Magic Sets for Super-Consistent Answer Set Programs

TL;DR

This paper extends the Dynamic Magic Sets technique for ASP to super-consistent programs, enabling more efficient query answering through dynamic pruning, with formal correctness proofs and empirical validation.

Contribution

It formally proves the correctness of DMS for super-consistent ASP programs, broadening its applicability beyond stratified negation.

Findings

DMS is sound and complete for super-consistent ASP programs.

Experimental results show significant performance improvements.

The approach generalizes to all odd-cycle-free programs.

Abstract

For many practical applications of ASP, for instance data integration or planning, query answering is important, and therefore query optimization techniques for ASP are of great interest. Magic Sets are one of these techniques, originally defined for Datalog queries (ASP without disjunction and negation). Dynamic Magic Sets (DMS) are an extension of this technique, which has been proved to be sound and complete for query answering over ASP programs with stratified negation. A distinguishing feature of DMS is that the optimization can be exploited also during the nondeterministic phase of ASP engines. In particular, after some assumptions have been made during the computation, parts of the program may become irrelevant to a query under these assumptions. This allows for dynamic pruning of the search space, which may result in exponential performance gains. In this paper, the correctness of DMS is formally established and proved for brave and cautious reasoning over the class of super-consistent ASP programs (ASP^{sc} programs). ASP^{sc} programs guarantee consistency (i.e., have answer sets) when an arbitrary set of facts is added to them. This result generalizes the applicability of DMS, since the class of ASP^{sc} programs is richer than ASP programs with stratified negation, and in particular includes all odd-cycle-free programs. DMS has been implemented as an extension of DLV, and the effectiveness of DMS for ASP^{sc} programs is empirically confirmed by experimental results with this system.