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Quantales as completions of ordered monoids. Revised semantics for intuitionistic linear logic. (English) Zbl 0963.68101

Spreen, Dieter (ed.), Domains IV. Workshop, Haus Humboldtstein, Remagen-Rolandseck, Germany, October 2-4, 1998. Amsterdam: Elsevier, Electronic Notes in Theoretical Computer Science. 35, 15 p., electronic only (2000).
Summary: The aim of this paper is to propose a unified analysis of the relationships between the notions of order and closure and to relate it to different semantics of Intuitionistic Linear Logic (ILL). We study the embedding of ordered monoids into quantales and then we propose general constructions and results about such an embedding. Therefore we obtain a new semantics based on ordered monoids and also new completeness results for ILL.
For the entire collection see [Zbl 0948.00043].

MSC:

68Q55 Semantics in the theory of computing
03B20 Subsystems of classical logic (including intuitionistic logic)
68T27 Logic in artificial intelligence
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