Situation theory provides the mathematical foundations to

situation semantics In situation theory, situation semantics (pioneered by Jon Barwise and John Perry in the early 1980s) attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theor ...

, and was developed by writers such as

Jon Barwise Kenneth Jon Barwise (; June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used. Education and career Born in Independence, ...

and

Keith Devlin Keith J. Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.

in the 1980s. Due to certain foundational problems, the mathematics was framed in a

non-well-founded set theory Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axio ...

. One could think of the relation of situation theory to situation semantics as like that of

type theory In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a founda ...

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 <> is a fact.

References

. "Situations and small worlds", in: ''In The Situation in Logic'', number 17 in CSLI Lecture Notes, pp. 79–92, 1987. *

Keith Devlin Keith J. Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.

. ''Logic and Information'', pp. 49–51, 1991.

Basic types

See also

References

Further reading