IASCAR: Incremental Answer Set Counting by Anytime Refinement
This work addresses the expensive counting problem in ASP navigation for users of declarative programming, but it appears incremental as it builds on existing knowledge compilation methods.
The paper tackles the problem of efficiently counting answer sets under assumptions for answer set programming (ASP) navigation by introducing an incremental counting technique that uses knowledge compilation and the inclusion-exclusion principle, showing promising results with quick recounting after an offline compilation phase.
Answer set programming (ASP) is a popular declarative programming paradigm with various applications. Programs can easily have many answer sets that cannot be enumerated in practice, but counting still allows quantifying solution spaces. If one counts under assumptions on literals, one obtains a tool to comprehend parts of the solution space, so-called answer set navigation. However, navigating through parts of the solution space requires counting many times, which is expensive in theory. Knowledge compilation compiles instances into representations on which counting works in polynomial time. However, these techniques exist only for CNF formulas, and compiling ASP programs into CNF formulas can introduce an exponential overhead. This paper introduces a technique to iteratively count answer sets under assumptions on knowledge compilations of CNFs that encode supported models. Our anytime technique uses the inclusion-exclusion principle to improve bounds by over- and undercounting systematically. In a preliminary empirical analysis, we demonstrate promising results. After compiling the input (offline phase), our approach quickly (re)counts.