ANon commutative Extension of MELL Alessio Guglielmi and Lutz Straßburger

Niveau: Supérieur
ANon-commutative Extension of MELL Alessio Guglielmi and Lutz Straßburger Technische Universitat Dresden Fakultat Informatik - 01062 Dresden - Germany and Abstract We extend multiplicative exponential linear logic (MELL) by a non-commutative, self-dual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We should then be able to extend the range of applications of MELL, by modelling a broad notion of sequentiality and providing new properties of proofs. We show some proof theoretical results: decomposition and cut elimination. The new operator represents a significant challenge: to get our results we use here for the first time some novel techniques, which constitute a uniform and modular approach to cut elimination, contrary to what is possible in the sequent calculus. 1 Introduction Non-commutative logical operators have a long tradition [12, 22, 2, 13, 16, 3], and their proof theoretical properties have been studied in the sequent calculus [7] and in proof nets [8]. Recent research has shown that the sequent calculus is not adequate to deal with very simple forms of non-commutativity [9, 10, 21].

• logic


• commutative operator


• can collectively


• rules become mutually


• system


• logical relations


• rules


• nel