6,387 research outputs found
Strong Normalization for HA + EM1 by Non-Deterministic Choice
We study the strong normalization of a new Curry-Howard correspondence for HA
+ EM1, constructive Heyting Arithmetic with the excluded middle on
Sigma01-formulas. The proof-term language of HA + EM1 consists in the lambda
calculus plus an operator ||_a which represents, from the viewpoint of
programming, an exception operator with a delimited scope, and from the
viewpoint of logic, a restricted version of the excluded middle. We give a
strong normalization proof for the system based on a technique of
"non-deterministic immersion".Comment: In Proceedings COS 2013, arXiv:1309.092
Proof-graphs for Minimal Implicational Logic
It is well-known that the size of propositional classical proofs can be huge.
Proof theoretical studies discovered exponential gaps between normal or cut
free proofs and their respective non-normal proofs. The aim of this work is to
study how to reduce the weight of propositional deductions. We present the
formalism of proof-graphs for purely implicational logic, which are graphs of a
specific shape that are intended to capture the logical structure of a
deduction. The advantage of this formalism is that formulas can be shared in
the reduced proof.
In the present paper we give a precise definition of proof-graphs for the
minimal implicational logic, together with a normalization procedure for these
proof-graphs. In contrast to standard tree-like formalisms, our normalization
does not increase the number of nodes, when applied to the corresponding
minimal proof-graph representations.Comment: In Proceedings DCM 2013, arXiv:1403.768
Strong normalization of lambda-Sym-Prop- and lambda-bar-mu-mu-tilde-star- calculi
In this paper we give an arithmetical proof of the strong normalization of
lambda-Sym-Prop of Berardi and Barbanera [1], which can be considered as a
formulae-as-types translation of classical propositional logic in natural
deduction style. Then we give a translation between the
lambda-Sym-Prop-calculus and the lambda-bar-mu-mu-tilde-star-calculus, which is
the implicational part of the lambda-bar-mu-mu-tilde-calculus invented by
Curien and Herbelin [3] extended with negation. In this paper we adapt the
method of David and Nour [4] for proving strong normalization. The novelty in
our proof is the notion of zoom-in sequences of redexes, which leads us
directly to the proof of the main theorem
- …