In this paper a very general fuzzy extension is proposed of logical systems of Natural Deduction. Given a complete lattice L with max and min, and the formulas of a logical system, the notions of L-rules (inference and deduction rules), L-natural syntax and fuzzy-deduction are introduced, by means of which it can be defined the value of a deduction with respect to a given L-set of assumptions, and the Consequence Operator, that assigns to every L-set of assumptions the corresponding L-set of its consequences. Then the problems of compactness and completeness for a given L-natural syntax are studied, and finally the results obtained are recognized as true extensions of already known both classical and fuzzy results.
Fuzzy Natural Deduction / G., Gerla; Tortora, Roberto. - In: ZEITSCHRIFT FÜR MATHEMATISCHE LOGIK UND GRUNDLAGEN DER MATHEMATIK. - ISSN 0044-3050. - STAMPA. - 36:(1990), pp. 67-77.
Fuzzy Natural Deduction
TORTORA, ROBERTO
1990
Abstract
In this paper a very general fuzzy extension is proposed of logical systems of Natural Deduction. Given a complete lattice L with max and min, and the formulas of a logical system, the notions of L-rules (inference and deduction rules), L-natural syntax and fuzzy-deduction are introduced, by means of which it can be defined the value of a deduction with respect to a given L-set of assumptions, and the Consequence Operator, that assigns to every L-set of assumptions the corresponding L-set of its consequences. Then the problems of compactness and completeness for a given L-natural syntax are studied, and finally the results obtained are recognized as true extensions of already known both classical and fuzzy results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
