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 the ...
, 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
He was born in Indepen ...
and
Keith Devlin
Keith James 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. One could think of the relation of situation theory to situation semantics as like that of
type theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems.
Some type theories serve as alternatives to set theory as a foundation of ...
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.
See also
* State of affairs (philosophy)
In philosophy, a state of affairs (), also known as a situation, is a way the actual world must be in order to make some given ''proposition'' about the actual world true; in other words, a state of affairs is a ''truth-maker'', whereas a proposit ...
References
* 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
He was born in Indepen ...
. "Situations and small worlds", in: ''In The Situation in Logic'', number 17 in CSLI Lecture Notes, pp. 79–92, 1987.
* Keith Devlin
Keith James 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.
Further reading
* Edward N. Zalta. "Twenty-Five Basic Theorems in Situation and World Theory", ''Journal of Philosophical Logic'' 22 (1993): 385–428.
Semantics
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