Situation theory
Encyclopedia
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.
Types in the theory are defined by applying two forms of type abstraction, starting with an initial collection of basic types.
Basic types
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.
Situation semantics
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 theoretical linguistics, philosophy, or applied natural language...
, and was developed by writers such as Jon Barwise
Jon Barwise
Kenneth Jon Barwise was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used....
and Keith Devlin
Keith Devlin
Keith J. Devlin is a British mathematician and popular science writer. He has lived in the USA since 1987 and has dual American-British citizenship.- Biography :...
in the 1980s. Due to certain foundational problems, the mathematics was framed in a non-well-founded set theory
Non-well-founded set theory
Non-well-founded set theories are variants of axiomatic set theory which allow sets to contain themselves and otherwise violate the rule of well-foundedness...
. One could think of the relation of situation theory to situation semantics as like that of type theory
Type theory
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
to Montague semantics.
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.