A Note on Fixed Points in Justification Logics and the Surprise Test Paradox
نویسنده
چکیده
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 Smoryǹski’s Diagonalization Operator Logic, and the latter is a justification version of Kozen’s modal μcalculus. 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.
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