Axiomatization of semigroup consequences (Q1263575)

A semigroup connective is a binary connective which is associative and properly binary. Of the 16 binary connectives only 10 are properly binary and of these only: \(\wedge\), \(\vee\), \(\leftrightarrow\), \(+\), are associative. With logics represented as rules placing conditions on consequence relations, a general problem is to specify the common rules for two or more semigroup connectives. A more specific problem is to specify conditions for a finitely based set of common rules. The author uses matrix semantics to show: The consequence relation determined by a variety V of algebraic semigroup matrices is finitely based iff V is finitely based. He then proves that the common rules for the connectives: \(\wedge\), \(\vee\), \(\leftrightarrow\), \(+\) are finitely based. The first line of Section 1 on p. 115 should read: We are now going to construct an effective base.