On Permuting Cut with Contraction

Contraction Elimination in Sequent Based Ground Equational Calculus

In "Cut Elimination for Gentzen's Sequent Calculus with Equality and Logic of Partial Terms" LNCS 7750,161-172(2013), we have shown that the cut rule is eliminable in two ground equational sequent calculi, to be denoted by EQ_M and EQ'. In this note we prove that the contraction rule is not eliminable in EQ_M but it is eliminable in EQ'.

Contraction-free proofs and finitary games for Linear Logic

In the standard sequent presentations of Girard's Linear Logic (LL), there are two "non-decreasing" rules, where the premises are not smaller than the conclusion, namely the cut and the contraction rules. It is a universal concern to eliminate the cut rule. We show that, using an admissible modification of the tensor rule, contractions can be eliminated, and that cuts can be simultaneously limited to a single initial occurrence. This view leads to a consistent, but incomplete game model for LL with exponentials, which is finitary, in the sense that each play is finite. The game is based on a s…

On the word problem for SP-categories, and the properties of two-way communication

The word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly interpreted as processes which communicate by two-way channels. The maps of an SP-category may also be viewed as a proof theory for a simple logic with a game theoretic intepretation. The cut-elimination procedure for this logic determines equality only up to certain permuting conversions. As the equality classes under these permuting conversions are finite, it is eas…

A Cut-free sequent calculus for modal logic S5

We present the system G3S5, a Gentzen-style sequent calculus system for the modal propositional logic S5, which in a sense has the subformula property. We formulate the rules of G3 S5 in the system G3S5; which has the subformula property and prove the admissibility of the weakening, contraction and cut rules for it.

关于弱直觉时态逻辑的切割消去

On the Cut Elimination of Weak Intuitionistic Tense Logic

本文提出一种通过分裂收缩规则和切割规则来证明弱直觉时态逻辑切割消去的新方法，并展望其未来理论扩展与应用。

Classical Logic = Fibred MLL

This paper represents classical propositional proofs as *combinatorial proofs*, which are more abstract than proof nets: superposition (contraction/weakening) is modelled mathematically, as a lax form of fibration, rather than syntactically (as in proof nets, which involve contraction and weakening nodes). A combinatorial proof is a `fibred' multiplicative linear proof net, hence the slogan in the title. Cut elimination retains its richness from sequent calculus: its non-determinism does not collapse to become confluent. [Note: this is merely a 2-page synopsis, accepted for a short presentatio…