# Situation theory

Situation theory provides the mathematical foundations to situation semantics, and was developed by writers such as Jon Barwise and Keith Devlin in the 1980s. Due to certain foundational problems, the mathematics was framed in a non-well-founded set theory. One could think of the relation of situation theory to situation semantics as like that of type theory to Montague semantics.

## Basic types

Types in the theory are defined by applying two forms of type abstraction, starting with an initial collection of basic types.

Basic types:

• TIM: the type of a temporal location
• LOC: the type of a spatial location
• IND: the type of an individual
• RELn: the type of an n-place relation
• SIT: the type of a situation
• INF: the type of an infon
• TYP: the type of a type
• PAR: the type of a parameter
• POL: the type of a polarity (i.e. 0 or 1)

Infons are made of basic types. For instance: If l is a location, then l is of type LOC, and the infon <<of-type, l, LOC, 1>> is a fact.

## References

• Jon Barwise. "Situations and small worlds", in: In The Situation in Logic, number 17 in CSLI Lecture Notes, pp. 79–92, 1987.
• Keith Devlin. Logic and Information, pp. 49–51, 1991.