A graph-theoretic characterization theorem for multiplicative fragment of non-commutative linear logic

Authors:
Misao Nagayama;Mitsuhiro Okada
Affiliations:
Department of Mathematics, Tokyo Woman's Christian University, 2-6-1 Zempuku-ji, Suginami, Tokyo 167-8585, Japan;Department of Philosophy, Keio University, Japan
Venue:
Theoretical Computer Science - Linear logic
Year:
2003

Citing 4
Cited 0

Linear logic

Theoretical Computer Science
Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic

Journal of Symbolic Logic
Interpolation in fragments of classical linear logic

Journal of Symbolic Logic
Noncommutative proof nets

Proceedings of the workshop on Advances in linear logic

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Abstract

It is well known that every proof net of a non-commutative version of MLL (multiplicative fragment of commutative linear logic) can be drawn as a plane Danos-Regnier graph (drawing) satisfying the switching condition of Danos-Regnier [3]. In this paper, we study the reverse direction; we introduce a system MNCLL which is logically equivalent to the multiplicative fragment of cyclic linear logic introduced by Yetter [9], and show that any plane Danos-Regnier graph drawing with one terminal edge satisfying the switching condition represents a unique non-commutative proof net (i.e., a proof net of MNCLL). In the course of proving this, we also give the characterization of the non-commutative proof nets by means of the notion of strong planarity, as well as the notion of a certain long-trip condition, called the stack-condition, of a Danos-Regnier graph, the latter of which is related to Abrusci's balanced long-trip condition [2].