Treffer: Tableau calculi for answer set programming

We introduce a formal proof system based on tableau methods for analyzing computations made in Answer Set Programming (ASP). Our approach furnishes declarative and fine-grained instruments for characterizing operations as well as strategies of ASP-solvers. First, the granulation is detailed enough to capture the variety of propagation and choice operations of algorithms used for ASP; this also includes SAT-based approaches. Second, it is general enough to encompass the various strategies pursued by existing ASP-solvers. This provides us with a uniform framework for identifying and comparing fundamental properties of algorithms. Third, the approach allows us to investigate the proof complexity of algorithms for ASP, depending on choice operations. We show that exponentially different best-case computations can be obtained for different ASP-solvers. Finally, our approach is flexible enough to integrate new inference patterns, so to study their relation to existing ones. As a result, we obtain a novel approach to unfounded set handling based on loops, being applicable to non-SAT-based solvers. Furthermore, we identify backward propagation operations for unfounded sets.