In this paper logics defined by finite Sugihara matrices, as well as RM itself, are discussed both in their matrix (semantical) and in syntactical version. For each such a logic a deduction theorem is proved, and a few applications are given.

A logic is a pair (P,Q) where P is a set of formulas of a fixed propositional language and Q is a set of rules. A formula is deducible from X in the logic (P, Q) if it is deducible from XP via Q. A matrix is strongly adequate to (P, Q) if for any , X, is deducible from X iff for every valuation in , is designated whenever all the formulas in X are. It is proved in the (...) present paper that if Q = {modus ponens, adjunction } and P {E, R, E +, R +, E I, R I } then there exists a matrix strongly adequate to (P, Q). (shrink)

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.

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).

Sometimes, very often in fact, our persuasive efforts fail even though we are right and the arguments we use are logically correct. In the article we are trying to tell why this is so, and as it turns out there may be quite a few causes. First, the hearer may not be convinced because he has not been motivated to try and understand the speaker - understanding takes work, and as a rule we do not like to work. Or he (...) may not be convinced because he does not like the speaker himself. There are also many other potential causes, such as: balancing cognitive dissonance, faulty attributions, phenomena of assimilation and contrasting, or psychological mechanisms of consequence, conformism and reactance. (shrink)

The aim of this paper is to test Grice's theory of conversational implication [1], so-calledimplicature, by putting it into operation in the simplest possible formal language, that is, by constructing an adequate zero-order (sentential) logic. We are going to give a recursive formal description of Grice's maxims and show that the description cannot be made finite.

Sentences describe situations, and from the point of view of pragmatics, the situation described by a sentence depends in turn on the context of use, i.e. on the situation in which the sentence is uttered. In general, situations are abstract imaginary entitles, but some of them do actually hold; these are called facts. If a sentence A uttered in situation a describes a fact, that is, if the situation described by A actually holds in the real world, then A is (...) said to be true . Hence there are at least two ways of defining the meaning of a sentence in pragmatics; first, the meaning of A could be that function from situations into {0, 1} which takes the value l for exactly those situations in which A is true; second, the meaning of A could be that function from situations into situations which, for an argument a, takes the value b exactly in the case when A, if uttered in situation a, describes situation b. (shrink)

The aim of the paper is a popularization of a book by Dan Sperber and Deirde Wilson, which is not as well-known among logicians and philosophers as it should be. It is, apart from the famous book by Lakoff and Johnson, probably the most important work on cognitive linguistics in the last two decades. All more extensive works on pragmatics and the philosophy of language written later contain references to this book. „The relevance theory” is now a term of art, (...) explicitly and forever associated with the names of the authors. It would be very easy to criticise this work, since from the logical point of view it contains many inaccuracies and dubious ideas, some of which are simply logically fallacious. However, it is a very deep and inspiring work at the same time - also for a logician. In my paper there are no supplements nor critical remarks. It is exclusively a faithful summary of the original ideas of Sperber and Wilson. (shrink)

The subject of the paper is the ways of interpreting messages that are defective either syntactically or semantically. The formal models of communicative events in which such messages are being sent are based on a specially designed situational ontology. A situation is something of the sort of pragram, and it is meant to represent both the context of use and the meaning of an utterance. Five „economy rules” explain why (and how) language is such a user-friendly device, highly tollerant to (...) misuse: slips of the tongue, grammatical incorrectness, mistakes in meaning, etc. (shrink)