# Extensions to Justification Theory

## TL;DR

This paper discusses potential extensions to justification theory, a framework for understanding semantics in various non-monotonic logics, with applications in logic programming and answer set programming.

## Contribution

It proposes new directions and possible extensions to the existing justification theory framework for broader applicability and improved computational methods.

## Key findings

- Justification theory unifies semantics for multiple non-monotonic logics.
- Justifications are used in modern ASP solvers and lazy grounding algorithms.
- Extensions could enhance the theory's applicability and computational efficiency.

## Abstract

Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge representation languages covered by justification theory include logic programs, argumentation frameworks, inductive definitions, and nested inductive and coinductive definitions. In addition, justifications are also used for implementation purposes. They are used to compute unfounded sets in modern ASP solvers, can be used to check for relevance of atoms in complete search algorithms, and recent lazy grounding algorithms are built on top of them. In this extended abstract, we lay out possible extensions to justification theory.