The first-order hypothetical logic of proofs

The Propositional Logic of Proofs (LP) is a modal logic in which the modality □A is revisited as [[t]]A, t being an expression that bears witness to the validity of A. It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs (⊢A impli...

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Detalles Bibliográficos
Autores principales: Steren, G., Bonelli, E.
Formato: JOUR
Materias:
Curry howard isomorphism
First-order logic of proofs
Lambda calculus
Natural deduction
Calculations
Computer circuits
Differentiation (calculus)
Semantics
Curry-Howard correspondence
Curry-Howard isomorphism
First order logic
Provability semantics
Soundness and completeness
Strong normalization
Formal logic
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0955792X_v27_n4_p1023_Steren
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:The Propositional Logic of Proofs (LP) is a modal logic in which the modality □A is revisited as [[t]]A, t being an expression that bears witness to the validity of A. It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs (⊢A implies ⊢[[t]]A, for some t). A presentation of first-order LP has recently been proposed, FOLP, which enjoys arithmetical soundness and has an exact provability semantics. A key notion in this presentation is how free variables are dealt with in a formula of the form [[t]]A(i). We revisit this notion in the setting of a Natural Deduction presentation and propose a Curry-Howard correspondence for FOLP. A term assignment is provided and a proof of strong normalization is given. © The Author, 2016.

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