Abstract: "A new algebraic axiomatization of linear logic models is presented. The axioms directly reflect at the model-theoretic level the de Morgan duality exhibited by linear logic, and are considerably simpler than previous axioms. Several equationally defined classes of models are studied....

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Martí-Oliet, Narciso (VerfasserIn), Meseguer, José (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Menlo Park, Calif. 1989
Schriftenreihe:	Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL 89,11
Schlagworte:	Linear orderings Logic, Symbolic and mathematical Model theory
Zusammenfassung:	Abstract: "A new algebraic axiomatization of linear logic models is presented. The axioms directly reflect at the model-theoretic level the de Morgan duality exhibited by linear logic, and are considerably simpler than previous axioms. Several equationally defined classes of models are studied. One such class suggests a new variant of linear logic, called cancellative linear logic, in which it is always possible to cancel a proposition p (viewed as a resource) and its negation p[symbol] (viewed as a debt.) This provides a semantics for a generalization of the usual token game on Petri nets, called financial game. Poset models, called Girard algebras, are also defined equationally; they generalize for linear logic the Boolean algebras of classical logic, and contain the quantale models as a special case The proposed axiomatization also provides a simple set of categorical combinators for linear logic, extending those previously proposed by Lafont.
Beschreibung:	17 S.