# Founded World Views with Autoepistemic Equilibrium Logic

## TL;DR

This paper introduces a formal property called foundedness for epistemic logic programs, proposes a new semantics combining Autoepistemic and Equilibrium Logic, and shows it accurately captures the intended world views without self-support.

## Contribution

It extends unfounded set concepts to epistemic logic, defines foundedness, and proposes a new semantics that ensures only founded world views are derived.

## Key findings

- The new semantics captures all founded G91 world views.
- Previous approaches violate foundedness, leading to self-supported world views.
- Formalizes the notion of foundedness in epistemic logic programming.

## Abstract

Defined by Gelfond in 1991 (G91), epistemic specifications (or programs) are an extension of logic programming under stable models semantics that introducessubjective literals. A subjective literal al-lows checking whether some regular literal is true in all (or in some of) the stable models of the program, being those models collected in a setcalledworld view. One epistemic program may yield several world views but, under the original G91 semantics, some of them resulted from self-supported derivations. During the last eight years, several alternative approaches have been proposed to get rid of these self-supported worldviews. Unfortunately, their success could only be measured by studying their behaviour on a set of common examples in the literature, since no formal property of "self-supportedness" had been defined. To fill this gap, we extend in this paper the idea of unfounded set from standard logic programming to the epistemic case. We define when a world view is founded with respect to some program and propose the foundedness property for any semantics whose world views are always founded. Using counterexamples, we explain that the previous approaches violate foundedness, and proceed to propose a new semantics based on a combination of Moore's Autoepistemic Logic and Pearce's Equilibrium Logic. The main result proves that this new semantics precisely captures the set of founded G91 world views.