Founded (Auto)Epistemic Equilibrium Logic Satisfies Epistemic Splitting

Abstract

In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.

Autoepistemic equilibrium logic and epistemic specifications

“…13 The other semantics that passes the epistemic splitting test is Truszczyński's approach [10]. 14 Very recently, Cabalar et al [36] have proposed a new epistemic extension of equilibrium logic called founded autoepistemic equilibrium logic, and Fandinno [37] has proved that it also satisfies epistemic splitting.…”

eclingo : A Solver for Epistemic Logic Programs

“…There exist several implemented solvers for epistemic logic programs -see (Leclerc and Kahl 2018) for a recent survey. Although there is no solver for FAEEL yet, the closest existing tools are those based on G91, since both semantics coincide in all epistemic logic programs whose subjective literals do not form positive cycles (Fandinno 2019). This suggests that a solver for FAEEL can be constructed by applying an extra foundedness check on top of a G91 solver.…”