Phase semantics for light linear logic

Phase semantics for light linear logic

Light linear logic 1] is a reenement of the propositions-as-types paradigm to polynomial-time computation. A semantic setting for the underlying logical system is introduced here in terms of bred phase spaces. Strong completeness is established, with a purely semantic proof of cut elimination as a consequence. A number of mathematical examples of bred phase spaces are presented that illustrate ...

Stratified coherent spaces: a denotational semantics for Light Linear Logic

We introduce a stratified version of the coherent spaces model where an object is given by a sequence of coherent spaces. The intuition behind it is that each level gives a different degree of precision on the computation, an appearance. A morphism is required to satisfy a coherence condition at each level and this setting gives a model of Elementary Linear Logic. We then introduce a measure fu...

Stratified coherence spaces: a denotational semantics for light linear logic

We introduce a stratified version of the coherent spaces model where an object is given by a sequence of coherent spaces. The intuition behind it is that each level gives a different degree of precision on the computation, an appearance. A morphism is required to satisfy a coherence condition at each level and this setting gives a model of Elementary Linear Logic. We then introduce a measure fu...

Phase Semantics for Mixed Non-Commutative Classical Linear Logic

Profunctor Semantics for Linear Logic

Linear logic is a sort of “resource-aware” logic underlying intuitionistic logic. Investigations into the proof theory of this logic typically revolve around proof nets, certain two-dimensional graphical representations of proofs. Where sequent calculus deductions enforce arbitrary distinctions between proofs and complicate these investigations, proof nets represent sequent calculus deductions ...