The paper is a brief survey of the most important semantic constructions founded on the concept of possible world. It is impossible to capture in one short paper the whole variety of the problems connected with manifold applications of possible worlds. Hence, after a brief explanation of some philosophical matters I take a look at possible worlds from rather technical standpoint of logic and focus on the applications in formal semantics. In particular, I would like to focus on the fruitful (...) marriage of possible world semantics and algebra and its evolution leading to very general construction of Wójcicki called referential semantics and some of its refinements. The presentation is informal and sketchy; the main purpose is to put in one place a short, and readable I hope, description of the most important constructions and to point out the main sources of these solutions. (shrink)

Referential semantics importantly subscribes to the programme of theory of logical calculi. Defined by Wójcicki in [8], it has been subsequently studied in a series of papers of the author, till the full exposition of the framework in [9] and its intuitive characterisation in [10]. The aim of the article is to present several generalizations of referential semantics as compared and related to the matrix semantics for propositional logics. We show, in a uniform way, some own generalizations of referentiality: the (...) first, directed to unrestricted cluster referential semantics, [4], its "discrete" version, a counterpart of algebraic semantics and a many-valued referentiality based on matrices, whose elements are functions from the set of indices to a finite n-element set of values, n≥2, [3]. Next to this we outline pragmatic matrices introduced by Tokarz in [6] as an alternative for cluster referential approach and discuss together all presented versions of referential semantics. (shrink)

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)

One of the generalizations of R. W´ojcicki’s concept of referential matrix is so-called pseudo-referential matrix . G. Malinowski, who introduced that concept, also considers a particular case of pseudo-referential matrices called discrete pseudo-referential matrices . In this note we want to show how any generalized matrix determines a semantically equivalent discrete pseudo-referential matrix.