On Nested Justification Systems (full version)

TL;DR

This paper explores nested justification systems in rule-based semantics, addressing information loss issues and providing an alternative semantics characterization that enhances modularity and representational capacity.

Contribution

It introduces an equivalent alternative semantics for nested justification systems and demonstrates their ability to represent fixpoint definitions.

Findings

Alternative semantics preserve explanation-relevant information.

Nested systems enhance modularity in rule-based semantics.

Representation of fixpoint definitions is possible with nested systems.

Abstract

Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition of justification systems. This notion of nesting thus enables the modular definition of semantics of rule-based languages, and increases the representational capacities of justification theory. As we show in this paper, the original semantics for nested justification systems lead to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of semantics of nested justification systems and show that this characterization is equivalent to the original semantics. Furthermore, we show how nested justification systems allow representing fixpoint definitions (Hou and Denecker 2009).