Publication details

Saarland University Computer Science

Naming Proofs in Classical Propositional Logic

François Lamarche, Lutz Straßburger

Submitted., 2004

We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a ``real'' sequentialization theorem is missing, these proof nets have a grip on complexity issues. In both cases the cut elimination procedure is closely related to its equivalent in the calculus of structures, and we get ``Boolean'' categories which are not posets.

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