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

Abstract

Answer Set Programming (ASP) is a well-known declarative problem solving approach based on nonmonotonic logic programs, which has been successfully applied to a wide range of applications in artificial intelligence and beyond. To address the needs of modern applications, HEXprograms were introduced as an extension of ASP with external atoms for accessing information outside programs via an API style bi-directional interface mechanism. To evaluate such programs, conflict-driving learning algorithms for SAT and ASP solving have been extended in order to capture the semantics of external atoms. However, a drawback of the state-of-the-art approach is that external atoms are only evaluated under complete assignments (i.e., input to the external source) while in practice, their values often can be determined already based on partial assignments alone (i.e., from incomplete input to the external source). This prevents early backtracking in case of conflicts, and hinders more efficient evaluation of HEX-programs. We thus extend the notion of external atoms to allow for three-valued evaluation under partial assignments, while the two-valued semantics of the overall HEX-formalism remains unchanged. This paves the way for three enhancements: first, to evaluate external sources at any point during model search, which can trigger learning knowledge about the source behavior and/or early backtracking in the spirit of theory propagation in SAT modulo theories (SMT). Second, to optimize the knowledge learned in terms of so-called nogoods, which roughly speaking are impossible input-output configurations. Shrinking nogoods to their relevant input part leads to more effective search space pruning. And third, to make a necessary minimality check of candidate answer sets more efficient by exploiting early external evaluation calls. As this check usually accounts for a large share of the total runtime, optimization is here particularly important. We further present an experimental evaluation of an implementation of a novel HEX-algorithm that incorporates these enhancements using a benchmark suite. Our results demonstrate a clear efficiency gain over the state-of-the-art HEX-solver for the benchmarks, and provide insights regarding the most effective combinations of solver configurations.

Lazy-Grounding for Answer Set Programs with External Source Access

“…HEX-programs [Eiter et al, 2005;2016a] extend ordinary ASP programs by external atoms of the form &g[p](t), which enable a bidirectional interaction of a program and external computation sources. Here &g is an external predicate name, p = p 1 , .…”

“…The notion of ldesafety allows to modularly combine syntactic and/or semantic safety criteria to guarantee that a HEX-program is finitely groundable (cf. [Eiter et al, 2016b] for more details), and it is the most liberal safety notion that has been considered wrt. the HEX formalism.…”

“…HEX-programs [Eiter et al, 2005;2016a] enrich answer set programs [Gelfond and Lifschitz, 1991] with the possibility to exchange information with external sources in a bidirectional way. This greatly increases the problem solving capacity of Answer Set Programming (ASP) [Brewka et al, 2016], as in the plugin-architecture of HEX-solvers like DLVHEX, arbitrary sources can be accessed via an API style interface called external atom.…”

“…Advanced algorithms have been developed [Eiter et al, 2016a] which roughly speaking rewrite a given HEX-program into an ordinary ASP program, solve the latter using an ASP solver, and finally check whether the obtained answer sets are compatible with the external sources.…”

“…[Kaufmann et al, 2016], but the grounded program can still be (too) large. For HEX-programs, grounding is due to external atoms an even bigger challenge, which has been tackled with sophisticated program decomposition and component grounding techniques [Eiter et al, 2016a]. However, decomposition has a trade-off with efficient solving, and without decomposition exponentially many inputs to an external atom may have to be considered during grounding, e.g.…”