Partially commutative linear logic: sequent calculus and phase semantics
نویسنده
چکیده
In this short paper we introduce a variant of intuitionistic multiplicative linear logic that features both commutative and non-commutative connectives. This new logic extends conservatively both Girard’s multiplicative linear logic [2] and Lambek’s syntactic calculus [3]. Ultimately, our goal will be to fulfil the programme achieved by Girard in [2], i.e., to provide our system with: (1) a sequent calculus, (2) a proof-net syntax together with a correctness criterion and a sequentialisation theorem, (3) semantics of provability together with a completeness theorem, (4) denotational semantics, i.e., semantics of proofs. Nevertheless, in this first report, we only concentrate on (1) and (3). Related works on mixing commutativity and non-commutativity in linear logic include [1] and [5].
منابع مشابه
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