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Back to the Future: Explicit Logic for Computer Science [chapter]

Sergei Artemov
2003 Lecture Notes in Computer Science  
• Big distraction and big help: Provability Logic with 2F ∼ Provable(F) (Solovay, Boolos, de Jongh, Visser, Magari, Sambin, Montagna, S.A., Beklemishev, et al.) is modal system GL incompatible with  ...  t a proof of t:F (New) "+" is union: takes union (concatenation) of two proofs The Logic of Proofs LP The language of LP = that of the classical propositional logic + additional atoms p:F , where p is  ...  Basic Logic of Proofs = operation free versions for major classes of proof predicates, pre-LP studies. Artemov, T.  ... 
doi:10.1007/978-3-540-45220-1_4 fatcat:d65z6j7igfedppyfx53aaitudi

On Two Models of Provability [chapter]

Sergei Artemov
Mathematical Problems from Applied Logic II  
Gödel's modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models.  ...  These two models complement each other and cover a wide range of applications, from traditional proof theory to λ-calculi and formal epistemology.  ...  Several groups of researchers in the USA (Solovay, Boolos, Smoryński) , the Netherlands (D. de Jongh, Visser), Italy (Magari, Montagna, Sambin, Valentini), and the former USSR (Artemov and his students  ... 
doi:10.1007/978-0-387-69245-6_1 fatcat:yqlmr4lkzzg75ei3inpaqossda