The ontology of justifications in the logical setting
The author deals with the question of the nature of justifications, within the context of justification logic. He notes that justifications could be interpreted as sets of formulas fulfilling certain conditions and he then characterizes a semantics in which justifications are given such an interpretation. He refers to the models of the semantics as ``modular models''. It is shown that the basic system of justification logic JCS is sound and complete with respect to the modular models semantics. The author next considers possible-worlds semantic models for justification logic. For this sort of semantics, he formulates semantical conditions that would connect justifications to the epistemic structure of the knowledge/belief semantics and characterizes a possible-worlds semantics whose models are modular, that is, they interpret justifications in a way similar to that one of the modular models. Soundness and completeness are also shown for this semantics with respect to the system JCS. The language of justification logic together with the necessity operator is also considered in the paper, and a formal system for justification logic in such a language is formulated as well. The author shows this system to be sound and complete with respect to the same modular possible-worlds semantics. Finally, connections between this modular semantics and Fitting semantics for justification logic (in terms of the notion of admissible evidence) are indicated. The author shows, on the one hand, that the set of modular models is a subclass of the set of models of Fitting semantics. On the other hand, he shows conversely that each Fitting model can be converted into a modular model. Conceptual advantages of modular semantics over Fitting semantics are also discussed.
scientific article; zbMATH DE number 6088845
scientific article