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Representation Theorems for Quantales
Author(s) -
Valentini Silvio
Publication year - 1994
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19940400205
Subject(s) - mathematics , isomorphism (crystallography) , commutative property , mathematics subject classification , pure mathematics , algebra over a field , representation (politics) , order (exchange) , subject (documents) , discrete mathematics , computer science , chemistry , crystal structure , finance , politics , library science , political science , law , economics , crystallography
In this paper we prove that any quantale Q is (isomorphic to) a quantale of suitable relations on Q. As a consequence two isomorphism theorems are also shown with suitable sets of functions of Q into Q. These theorems are the mathematical background one needs in order to give natural and complete semantics for (non‐commutative) Linear Logic using relations. Mathematics Subject Classification: 06D05, 06D10, 06D20, 03G25.