A Note on the Fixed Points in Justification Logics

Por • 26 mar, 2014 • Sección: Educacion

Meghdad Ghari

Abstract: 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\`{n}ski’s Diagonalization Operator Logic, and the latter is a justification version of Kozen’s modal μ  -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.

arXiv:1403.4407v1 [math.LO]

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