Some situation theoretical notions

Abstract

Situation Theory is meant to provide an adequate mathematical tool for Semantics of Natural Languages. In the last ten years it has passed through a lot of changes and it still developing. On its part Situation Theory has motivated the appearance of formalisms appropriate for modelling situation theoretical objects that are not necessarily well founded ([1,2]).

In this article we remind some situation theoretical notions, introduced in [5, 11, 12), and suggest some others such as strong/weak informativeness of a situation s' with respect to another situation s", envolving and equivalence for propositions and types. All of them and their properties are needed for the "calculations" of the interpretations of phrases generated by the grammar GR2 elaborated in [14]. One of the possibilities for representing the information transferred by uttering of natural language phrases is to accept that the models of the real situations including the situations described by the utterances are informative with respect to the situations used
in them for describing some objects. Something more; in the situation semantics, proposed by the GR2, we assume that the described situations are strongly informative with respect to the speaker's resource situations. That gives a way to conclude whether what the speaker claims by an utterance is true. An important means for representing an equivalent but differently structured information in Situation Theory is the operation absorption. of parameters (abstraction) over infons and propositions. By this operation complex relations and types are received in addition to the primitive relations and types. In this article we propose to use complex types as special
kind relations — "situated" relations that could be prescribed to objects.

The article should be considered as setting a task for modelling the introduced notions with the apparatus developed in [2] rather than a contribution to the Model Theory of Situations.