Tree-Like Justification Systems are Consistent

Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are justifications for a fact and justifications for its negation suitably related. Two variants of justification theory exist: one in which justifications are trees and one in which they are graphs. In this work we resolve the consistency problem once and for all for the tree-like setting by showing that all reasonable tree-like justification systems are consistent.

On Nested Justification Systems (full version)

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).

Exploiting Game Theory for Analysing Justifications

Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification: an explanation why a property holds (or does not hold) in a model. In this paper, we continue the study of justification theory by means of three major contributions. The first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games. The established connection provides the theoretical foundations for our next two contributions. The second contribution is studying under which condition two different dialects of justification theory (graphs as explanations vs trees as explanations) coincide. The third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results. In the past proving that such semantics were consistent took cumbersome and elaborate proofs. We show that these criteria are indeed satisfied for all common semantics of logic programming. This paper is under consideration for acceptance in Theory and Practice of Logic Programming (TPLP).

Extensions to Justification Theory

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.