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A Survey of Abstract Algebraic Logic
Protoalgebraic logics
A wide class of deductive systems of this kind called protoalgebraic logics are considered, which include almost all (non-pathological) systems of prepositional logic that have occurred in the literature. Expand
Fregean logics
The principle of Frege’s principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. Expand
On the structure of varieties with equationally definable principal congruences IV
The notion of apseudo-interior algebra is introduced; it is a hybrid of a (topological) interior algebra and a residuated partially ordered monoid. The elementary arithmetic of pseudo-interiorExpand
Amalgamation and Interpolation in Abstract Algebraic Logic
algebraic logic provides a hierarchy of deductive systems based on how “algebra-like” their reduced semantics are. • S is protoalgebraic if Mod∗(S) is closed under subdirect products. • S isExpand
Finite basis theorems for relatively congruence-distributive quasivarieties
Q is any quasivariety. A congruence relation 0 on a mem- ber A of Q is a Q-congruence if A/0 G Q. The set CouqA. of all Q- congruences is closed under arbitrary intersection and hence forms aExpand
Abstract Algebraic Logic
The main features of the theory of abstract algebraic logic and one of its potential applications are surveyed and a uniform method of providing a formal system with algebraic semantics is found. Expand