Quantified Modal Justification Logic with Existence Predicate

Systems of explicit modal logic provide a powerful framework for characterizing modal concepts as arising from the existence of appropriate sources. In what follows, we will construct a system of quantified modal logic of justification, endowed with a specific predicate of existence, which can help us to model both situations where the distinction between actual and potential possession of a justification is crucial and situations where sources of knowldge are subjected to change. The paper is structured as follows. In section 2 the basic system of quantified modal justification logic we are interested in is introduced from an axiomatic point of view. In section 3 the system previously introduced is proved to be sound and complete with respect to a suitable possibile world semantics. Finally, the system is extended in order to incorporate a predicate of existence, to be intended as indicating acknowledged existence, and some observations are made on its usefulness.