Logic of Implicit and Explicit Justifiers

In L. Felline, A. Ledda, F. Paoli & E. Rossanese (eds.), New Directions in Logic and the Philosophy of Science. College Publications. pp. 119-131 (2016)
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Abstract
The aim of this paper is to provide an intuitive semantics for systems of justification logic which allows us to cope with the distinction between implicit and explicit justifiers. The paper is subdivided into three sections. In the first one, the distinction between implicit and explicit justifiers is presented and connected with a proof-theoretic distinction between two ways of interpreting sequences of sentences; that is, as sequences of axioms in a certain set and as sequences proofs constructed from that set of axioms. In the second section, a basic system of justification logic for implicit and explicit justifiers is analyzed and some significant facts about it are proved. In the final section, an adequate semantics is proposed, and the system is proved to be sound and complete whit respect to it.
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