A Non-commutative Extension of MELL
نویسندگان
چکیده
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.
منابع مشابه
A System of Interaction and Structure IV: The Exponentials
We study some normalisation properties of the deep-inference proof system NEL, which can be seen both as 1) an extension of multiplicative exponential linear logic (MELL) by a certain non-commutative self-dual logical operator; and 2) an extension of system BV by the exponentials of linear logic. The interest of NEL resides in: 1) its being Turing complete, while the same for MELL is not known,...
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