Justification Logics in a Fuzzy Setting

Abstract: Justification Logics provide a framework for reasoning about justifications and evidences. Most of the accounts of justification logics are crisp in the sense that agent's justifications for a statement is convincing or is not. In this paper, we study fuzzy variants of justification logics, in which an agent can have a justification for a statement with a certainty degree between 0 and 1. We replaced the classical base of the justification logics with some known fuzzy logics: Hajek's basic logic, {\L}ukasiewicz logic, G\"odel logic, product logic, and rational Pavelka logic. In all of the resulting systems we introduced fuzzy models (fuzzy possible world semantics with crisp accessibility relation) for our systems, and established the soundness theorems. In the extension of rational Pavelka logic we also proved a graded-style completeness theorem.