Situational logic

 Editor Aguilar, Carlos carlos.aguilar@escac.es Incorporated contributions Aguilar (11/2009, 3/2010) Usage domain Situacional Semantics Type teoría French logic situationnel German situative Logik

[Understandable but with some grammatical missteps]

Situation Theory is an attempt to provide with a mathematical formulation the Situational Semantics developed by Braswise and Perry (1983). Keith Devlin (1991) in Logic and Information dressed the Situation Theory with the mathematical necessary apparatus to be able to treat it from an own, solid and mathematically coherent perspective.

The basic ontology of the Situation Theory forms those organizations that a mental agent, with his limitations, is able to individualize and/or to discriminate. Among the objects, also known as uniformities (or regularities) we found individuals in the situational ontology, relations, locations, temporary locations, situations, types and parameters.

The framework regarding to the agent who gathers the ontology denominates “individualization scheme” (appropriate for the study of the flow of information of an agent). The information always must be information referring to a certain situation, and it takes in the form of well-known discreet items, like “infons”. An infon is an object of the form:

where R denotes a relation among n appropriate objects to describe it and denotes if these objects are in relation or they are not. The last element (1 or 0) is called “polarity” and is the one that shows the veracity if polarity is 1, or falseness if polarity is 0, of the relation R.

In terms of the Situation Theory, infons are semantic objects within the mathematical theory. They are not phrases in some language that require an interpretation. Infons are the minimum units of information.

Infons can be referred to more than a relation by operations of conjunction and disjunction. These infons are labeled "compounds infons", e.g. the one obtained representing the infon that characterizes the shout of the word fire.

The infons can include parameters as in the previous example are  and , in this case of spatial and temporary type respectively. The parameters indicate elements that do not become informational until they are anchored* to a concrete situation.

Given a situation s and an infon σ we wrote:

s╞ σ

in order to indicate that the infon σ is a “factual fact” for the situation s. In other words, we can say that σ is a information item that is a truth in the situation s. Therefore, from the situational perspective the information is treated like merchandise. Merchandise that, in addition, doesn’t have to represent always a “true” value, because for each infon exists its dual negative that can be understood as their opposite informational one and both cannot be “true”.

Situations that share common characteristics are gather in Types, giving place to entities of higher-order, situation-types. This ones are an abstract concept that gathers elements with common characteristics and always belongs relative to the agent.

In order to be able to construct the meaning, an agent must be able to settle down constraints between each one of the identified situations type, in the context of the situation. The representation of Infon gathering the constraint between two situations type s and s' is the following one:

Constraints are abstract bonds between Types of situations. They can be of diverse types: natural laws, linguistic, empirical conventions,logic relations , rules, or of any other kind. Its rol in the chain of the information is well gathered in Israel and Perry (1990) by the word “meaning”.

The constraint between two types T and T' indicates that an element of type t, will carry information of an element of the type t' within the terms determined by the situation that includes both Types.

References
• DEVLIN, Keith (1991). Logic and Information. Cambridge, UK: Cambridge University Press.
• BARWISE, J. and PERRY, J. (1983). Situations and Attitudes; Cambridge, Ma.: MIT Press.
• ISRAEL, D. y PERRY, J. (1990). What is information? In Philip Hanson (Ed.). Information, Language and Cognition. Vancouver: University of British Columbia Press, pp. 1-19.

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Incorporated entries
C. Aguilar (11/2009)

[It correspond with a prevoius version of the article directly edited by the editor/author in the left column. Renewed in 03/2010]

C. Aguilar (18/03/2010)

[It correspond with a prevoius version of the article directly edited by the editor/author in the left column. Renewed in 04/2010]

C. Aguilar (23/04/2010)

[It correspond with the review of the article directly edited by the editor/author in the left column]