ISSN:
1572-8730
Keywords:
algebraizable logics
;
equivalential logics
;
implicative logics
;
protoalgebraic logics
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Philosophy
Notes:
Abstract The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to the theory of equivalential logics in the sense of Prucnal and Wroński [18], and it is extended to nonfinitary logics. The main result states that a logic is algebraizable (p.i.-algebraizable) iff it is finitely equivalential (equivalential) and the truth predicate in the reduced matrix models is equationally definable.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00370843
