The logic of uncertain justifications (Q392291)

The author considers Artemov's justification logic \(J\) and proposes a new variant of this logic by replacing its main notion ``\(t\) is a reason that justifies a formula \(F\)'' (formally represented by the expression ``\(t:F\)'' ) by the related notion ``I have degree \(r\) of confidence that \(t\) is evidence for the truth of formula \(F\)''. A formal language for the new notion is characterized, which is basically Artemov's language for logic \(J\) with (the formal representation of) the author's new notion replacing expressions of the form ``\(t:F\)''. The author formulates a possible world semantics for his formal language. This semantics captures the intuitive content of his notion and is a modification of the Fitting-Kripke semantics for \(J\). An axiomatic system is also formulated, which is proved to be sound and complete with respect to the author's semantics. Possible variants of the author's logic are also discussed in the paper.