Light linear logics with controlled weakening: Expressibility, confluent strong normalization

Expressibility results for linear-time and branching-time logics

Linear Logic and Strong Normalization

Strong normalization for linear logic requires elaborated rewriting techniques. In this paper we give a new presentation of MELL proof nets, without any commutative cut-elimination rule. We show how this feature induces a compact and simple proof of strong normalization, via reducibility candidates. It is the first proof of strong normalization for MELL which does not rely on any form of conflu...

Strong Normalization with Singleton

Confluent Term Rewriting for Only-knowing Logics

Combining term rewriting and modal logics, this paper addresses confluence and termination of rewrite systems introduced for only-knowing logics. The rewrite systems contain a rule scheme that gives rise to an infinite number of critical pairs, hence we cannot check the joinability of every critical pair directly, in order to establish local confluence. We investigate conditions that are suffic...

Strong Normalization with Singleton Types

This paper presents a new lambda-calculus with singleton types, called λ ≤{}. The main novelty of λ ≤{} is the introduction of a new reduction, the δ-reduction, replacing any variable declared of singleton type by its value, and the definition of equality as the syntactic equality of βδ-normal forms. The δ-reduction has a very odd behavior on untyped terms, which renders its metatheoretical stu...