Efficient HEX-Program Evaluation Based on Unfounded Sets

Abstract

HEX-programs extend logic programs under the answer set semantics with external computations through external atoms. As reasoning from ground Horn programs with nonmonotonic external atoms of polynomial complexity is already on the second level of the polynomial hierarchy, minimality checking of answer set candidates needs special attention. To this end, we present an approach based on unfounded sets as a generalization of related techniques for ASP programs. The unfounded set detection is expressed as a propositional SAT problem, for which we provide two different encodings and optimizations to them. We then integrate our approach into a previously developed evaluation framework for HEX-programs, which is enriched by additional learning techniques that aim at avoiding the reconstruction of the same or related unfounded sets. Furthermore, we provide a syntactic criterion that allows one to skip the minimality check in many cases. An experimental evaluation shows that the new approach significantly decreases runtime.

A model building framework for answer set programming with external computations

“…The results demonstrate a clear improvement using the new framework; they can often be further improved by fine-tuning the grounding and solving algorithm, and by customizing the default heuristics of the framework, as discussed by Eiter et al (2014b;2014a), and Redl (2014). However, already the default settings yield results that are significantly better than using the previous evaluation method or using no framework at all; note that the latter requires an advanced grounding algorithm as by Eiter et al (2014a), which was not available at the time the initial evaluation approach as by Schindlauer (2006) was developed.…”

“…Using decomposition techniques, evaluation units can be dynamically formed and evaluated in the framework using different heuristics, Moreover, the answer sets of the overall program can be produced in a streaming fashion. The new approach leads in combination with other techniques to significant improvements for a variety of applications, as demonstrated by Eiter et al (2014a;2014b) and Redl (2014). Notably, while our results target HEX-programs, the underlying concepts and techniques are not limited to them (e.g., to separate the evaluation and the model graph) and may be fruitfully transferred to other rule-based formalisms.…”

“…(Eiter et al 2014a) P ← GROUNDHEX(P ∪ facts(I)) // evaluate the ground program, cf. (Eiter et al 2014b), // and perform output projection return I \ I | I ∈ EVALUATEGROUNDHEX(P )…”

“…Verifying guesses of replacement atoms requires calling plugins that implement the external sources (i.e., the oracle functions F &g from Definition 3) 8 . Moreover, the Post Propagator also ensures answer set minimality by eliminating unfounded sets that are caused by external sources and therefore can not be detected by the ordinary ASP solver backend (as shown by Eiter et al (2014b)). Finally, as soon as the evaluation framework obtains an i-interpretation of the final evaluation unit u final , this i-interpretation (which is an answer set according to Proposition 6) is returned to the user 9 .…”

Exploiting Partial Assignments for Efficient Evaluation of Answer Set Programs with External Source Access

“…This basic approach has been enhanced with conflict-driven learning techniques, which learn parts of the external source semantics while the search space is traversed in order to prevent that wrong guesses reoccur (Eiter, Fink, Krennwallner, & Redl, 2012). Moreover, advanced techniques for minimality checking have been developed to boost efficiency (Eiter, Fink, Krennwallner, Redl, & Schüller, 2014a).…”