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.

Recently, a prototype for an interactive decision enactment system for notaries was developed. This prototype follows the Knowledge Base Paradigm (KBP): it consists of purely declarative domain knowledge, to which various logical inference methods can be applied. This paper extends that work in two ways. First, we experimentally validate the claim that the KBP leads to highly maintainable software. Second, we extend the number of additional logical inferences, which allow us to address a number of usability concerns. This provides further evidence for the claim that the KBP is indeed a viable method of developing interactive software systems. The resulting decision enactment prototype is a fully generic system, that can be applied to other domains with minimal effort.

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Approximation Fixpoint Theory (AFT) and Justification Theory (JT) are two frameworks to unify logical formalisms. AFT studies semantics in terms of fixpoints of lattice operators, and JT in terms of so-called justifications, which are explanations of why certain facts do or do not hold in a model. While the approaches differ, the frameworks were designed with similar goals in mind, namely to study the different semantics that arise in (mainly) non-monotonic logics. The First contribution of our current paper is to provide a formal link between the two frameworks. To be precise, we show that every justification frame induces an approximator and that this mapping from JT to AFT preserves all major semantics. The second contribution exploits this correspondence to extend JT with a novel class of semantics, namely ultimate semantics: we formally show that ultimate semantics can be obtained in JT by a syntactic transformation on the justification frame, essentially performing some sort of resolution on the rules.