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Paper detail

Constructive Provability Logic

We present constructive provability logic, an intuitionstic modal logic that validates the Löb rule of Gödel and Löb's provability logic by permitting logical reflection over provability. Two distinct variants of this logic, CPL and CPL*, are presented in natural deduction and sequent calculus forms which are then shown to be equivalent. In addition, we discuss the use of constructive provability logic to justify stratified negation in logic programming within an intuitionstic and structural proof theory.

preprint2012arXivOpen access
Robert J. SimmonsBernardo Toninho
Logic in Computer ScienceProgramming Languages
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Robert J. SimmonsBernardo Toninho

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