Quantitative and Stream Extensions of Answer Set Programming

Abstract

While propositional Answer Set Programming (ASP) is already NP-hard and therefore powerful enough to express many challenging problems, their specification can be tedious and complicated. Further, there are relevant problems that require higher expressivity or reasoning over data that changes with time. This and the practical usage of ASP gave rise to a need for a simpler, more expressive, and more concise specification language [1, 11]. Thus, ASP was extended in multiple directions. We focus on the following ones: 1. Time Domain (TD): In [5] ASP-semantics were combined with a temporal context resulting in the Logic-based framework for Analytic Reasoning over Streams (LARS). Here, interpretations assign possibly different sets of facts to time points. Accordingly, the input language was extended with operators like ♦, corresponding to existential quantification over time points. Another temporal extension of ASP is Temporal Equilibrium Logic (TEL) [9]. 2. Quantitative Reasoning over Models (QM): Given a program we may not only be interested in its answer sets but also in reasoning with quantities associated with them. Commonly this includes: