The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put (...) emphasis on some selected topics. Even these could not be roverrd completely, but for each topic I have attempted to present a detailed and precise t’Xposition of several basic results including some which are non-trivial. The roots of some of the central ideas in the volume go back to J. Luka siewicz’s seminar on mathematicallogi. (shrink)

In this note two notions of meaning are considered and accordingly two versions of synonymy are defined, weaker and stronger ones. A new semantic device is introduced: a matrix is said to be pragmatic iff its algebra is in fact an algebra of meanings in the stronger sense. The new semantics is proved to be universal enough (Theorem 1), and it turns out to be in some sense a generalization of Wójcicki's referential semantics (Theorem 3).

This paper was presented at the Annual Conference of the Australian Association for Logic, Melbourne, November, 1979. The present note being complementary to [1], I shall only brie y recall the key notions to be exploited here, and for more details the reader is advised to consult [1]. By a propositional logic we mean a couple , where L is a propo- sitional language and C a structural consequence de- ned on L. A couple W = is said to be (...) a referential matrix for the language L i there exists a non-empty set T such that the following two conditions are satised: i. A is an abstract algebra similar to L, whose all elements belong to f0; 1g T , i.e. they are mappings from T into the two-element set f0; 1g. ii. D = ffa 2 A : a = 1g : t 2 Tg. (shrink)

Referential matrix semantics of R. W´ojcicki [5] and [4] is extended to cover the class of all structural propositional calculi.