Noncommutative Logic - Noncommutativity in Logic - Pomset Logic

Pomset Logic

Pomset logic was proposed by Christian Retoré in a semantic formalism with two dual sequential operators existing together with the usual tensor product and par operators of linear logic, the first logic proposed to have both commutative and noncommutative operators. A sequent calculus for the logic was given, but it lacked a cut-elimination theorem; instead the sense of the calculus was established through a denotational semantics.