Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs

[Abstract] Answer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied in ASP, or in the more general form of equilibrium logic, they are usually understood in the form of comparisons of the answer sets or equilibrium models of theories or programs. This is the case for strong and uniform equivalence and their relativised and projective versions. However, there are many potential areas of application of ASP for which query answering is relevant and a comparison of programs in terms of what can be inferred from them may be important. We formulate and study some natural equivalence and entailment concepts for programs and theories that are couched in terms of inference and query answering. We show that, for the most part, these new intertheory relations coincide with their model-theoretic counterparts. We also extend some previous results on projective entailment for theories and for the new connective called fork.This research has received partial support from the European Cooperation in Science & Technology (COST) Action CA17124. The third author acknowledges the funding of project PID 2020-116201GB-I00 (Ministerio de Ciencia e Innovación, Spain) and also the financial support supplied by the Consellería de Educación, Universidade e Formación Profesional (accreditations GPC ED431B 2022/23 and 2019–2022 ED431G-2019/01). The last author has been supported by the Austrian Science Fund (FWF) grant Y698Xunta de Galicia; ED431B 2022/23Xunta de Galicia; ED431G-2019/0