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

Misao Nagayama, Mitsuhiro Okada

研究成果: Conference article査読

1 被引用数 (Scopus)

抄録

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].

本文言語English
ページ(範囲)551-573
ページ数23
ジャーナルTheoretical Computer Science
294
3
DOI
出版ステータスPublished - 2003 2月 18
外部発表はい
イベントLinear Logic - Tokyo, Japan
継続期間: 1996 3月 281996 4月 2

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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