Non-commutative logic III: focusing proofs

Authors:
Roberto Maieli;Paul Ruet
Affiliations:
Dipartimento di Informatica, Universit di Rome "La Sapienza", Via Salaria 113, Rome 00198, Italy;CNRS, Institut de Mathématiques de Luminy, 163 avenue de Luminy, Case 907, FR-13288 Marseille Cedex 9, France
Venue:
Information and Computation
Year:
2003

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Abstract

It is now well-established that the so-called focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for non-commutative logic (NL) which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying the permutabilities of rules for NL and showing that all permutabilities of linear logic involved in focalization can be lifted to NL permutabilities. These results are based on a study of the partitions of partially ordered sets modulo entropy.