On the metamathematics of fuzzy logic. (English) Zbl 1007.03022

Hájek, Petr

Novák, Vilém (ed.) et al., Discovering the world with fuzzy logic. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 57, 155-174 (2000).

This is an invitation to the author’s book: Metamathematics of fuzzy logic [Dordrecht: Kluwer Academic Publishers, Trends in Logic, Studia Logica Library. 4 (1998; Zbl 0937.03030)]. The author first considers propositional calculi, as given by continuous generalized conjunctions over the unit real interval (t-norms), and their residuals. Hajek’s basic logic is the logic of all such conjunction connectives. The final sections are devoted to basic predicate logic, and to a list of topics not covered by the present survey. For proofs the interested reader is reffered to the above book.
For the entire collection see [Zbl 0979.00015].

Reviewer: Daniele Mundici (Milano)

MSC:

03B52	Fuzzy logic; logic of vagueness
06D35	MV-algebras
03B50	Many-valued logic

Keywords:

metamathematics of fuzzy logic; many-valued logic; MV-algebra; basic logic; survey; t-norm

Citations:

Zbl 0937.03030