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A note on the normal form of closed formulas of interpretability logic

✍ Scribed by Petr Hájek; Vítězslav Švejdar

Publisher
Springer Netherlands
Year
1991
Tongue
English
Weight
183 KB
Volume
50
Category
Article
ISSN
0039-3215

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✦ Synopsis

Each dosed (i.e. variable f~ee) formula of interpretability logic is equivalent in ILF to a dosed formula of the provability logic G, thus to a Boolean combination of formulas of the form D ~ 3-. 1. Introduction. G stands for provability logic, i.e. for the modal propositional calculus whose axioms are propositional tautologies, [:](~ r --, (D T --+ De), D~o ~ E]D~ and LSb's axiom D([] T --. T) --+ [:]~ and whose rules are modus ponens and generalization. There are two propositional constants T (true) and 3-(false); a formula is closed if it contains no propositional variables, i.e. if it is built up f~om T and 3_ using Boolean connectives and D. The normal form theorem for closed formulas of G states

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