Proof normalization modulo

Proof Normalization Modulo

We define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theories having a so-called pre-model. As a corollary, we retrieve cut elimination for several axiomatic theories, including Church’s simple type theory. Deduction modulo [11] is a formulation of first-order logic, that g...

A proof of strong normalization by reducibility modulo for λσw

1 A proof of strong normalization of λσw We admit all along this proof the following properties: • Confluence and termination of the substitution part of λσw written −→es [ACCL90]. • Subject reduction of λσw [ACCL90] The scheme of the proof is the following one: 1. We (re-)define λσw and it’s typing system and remark that this version of λσw has the subject reduction property. 2. We define a ne...

Strong Normalization of Proof Nets Modulo Structural Congruences

This paper proposes a notion of reduction for the proof nets of Linear Logic modulo an equivalence relation on the contraction links, that essentially amounts to consider the contraction as an associative commutative binary operator that can float freely in and out of proof net boxes. The need for such a system comes, on one side, from the desire to make proof nets an even more parallel syntax ...

Languages Modulo Normalization

We propose a new class of tree automata, called tree automata with normalization (TAN). This framework extends equational tree automata, and improved the results of them: recognized tree languages modulo the idempotency f(x, x) = x are closed under complement, besides we do not lose an important decidability result. In the paper, first we investigate the closure properties of this class for Boo...

Proof Normalization and Normal Proofs