1,008 research outputs found
Strong normalization results by translation
We prove the strong normalization of full classical natural deduction (i.e.
with conjunction, disjunction and permutative conversions) by using a
translation into the simply typed lambda-mu-calculus. We also extend Mendler's
result on recursive equations to this system.Comment: Submitted to APA
A note on strong normalization in classical natural deduction
In the context of natural deduction for propositional classical logic, with
classicality given by the inference rule reductio ad absurdum, we investigate
the De Morgan translation of disjunction in terms of negation and conjunction.
Once the translation is extended to proofs, it obtains a reduction of
provability to provability in the disjunction-free subsystem. It is natural to
ask whether a reduction is also obtained for, say, strong normalization; that
is, whether strong normalization for the disjunction-free system implies the
same property for the full system, and whether such lifting of the property can
be done along the De Morgan translation. Although natural, these questions are
neglected by the literature. We spell out the map of reduction steps induced by
the De Morgan translation of proofs. But we need to "optimize" such a map in
order to show that a reduction sequence in the full system from a proof
determines, in a length-preserving way, a reduction sequence in the
disjunction-free system from the De Morgan translation of the proof. In this
sense, the above questions have a positive answer.This research was financed by Portuguese Funds through FCT Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013
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
Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General
This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment
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