1 research outputs found
A Note on Fixed Points in Justification Logics and the Surprise Test Paradox
In this note we study the effect of adding fixed points to justification
logics. We introduce two extensions of justification logics: extensions by
fixed point (or diagonal) operators, and extensions by least fixed points. The
former is a justification version of Smory\`nski's Diagonalization Operator
Logic, and the latter is a justification version of Kozen's modal
-calculus. We also introduce fixed point extensions of Fitting's
quantified logic of proofs, and formalize the Knower Paradox and the Surprise
Test Paradox in these extensions. By interpreting a surprise statement as a
statement for which there is no justification, we give a solution to the
self-reference version of the Surprise Test Paradox in quantified logic of
proofs. We also give formalizations of the Surprise Test Paradox in timed modal
epistemic logics, and in G\"odel-L\"ob provability logic.Comment: 40 pages. In version 3, Mkrtychev models for QLP are adde