Infon

Francisco Salto Alemany, Carlos Aguilar Paredes (2010). Infon, GlossariumBITri, 1(1): 51.

Also available as: Infón (es)

Collection	GlossariumBITri
Author	Francisco Salto Alemany, Carlos Aguilar Paredes
Editor	Francisco Salto Alemany
Year	2010
Vol. (num.)	1(1)
ID	◀ 51 ▶
Object type	Concept
Domain	Transdisciplinar, Semántica, Lógica
es	Infón
fr	Infon
de	Infon

You being happy is a state of things composed by the object you instantiating the relation being happy. State of things such as: <<happy, you, yes>> are to be distinguished from other realities, such as the object you happy and the property of happiness-in-you. An ontology composed by things as you is distinct from another one composed by state of things.

Notice how properties and relations are in-stantiated in objects (your happiness, the red of my lips), while objects are not instatiated in other objects: they are fragments or parts, but not instances. Even if there is, throughout the milennia, no precise characterization of these basic notions of part and instance, both set theory and situation theory begin with some basic assumptions about both notions.

Now, situation semantics assumes that situations are parts of reality which also have parts being states of affairs whcih are information. They are, it is assumed, objects instantiating properties and relations. Infons are the minimal information units posed by the ontological and set theoretical tools of situation semantics. Notice that information is not only referred to a situation, but it is such situation.

Therefore, infons are states of things expressible as tuples in the form

⟨ ⟨ R, a_{1}, a_{2}, . . ., a_{n}, 1 ⟩ ⟩, ⟨ ⟨ R, a_{1}, a_{2}, . . ., a_{n}, 0 ⟩ ⟩

(1)

where $R$ is a relation between n appropiate objects denoting that such objects are or are not in the relation. The final element is called polarity and signals the veracity $⟨ ⟨ R, a_{1}, a_{2}, . . ., a_{n}, 1 ⟩ ⟩$ , or the falsity $⟨ ⟨ R, a_{1}, a_{2}, . . ., a_{n}, 0 ⟩ ⟩$ of the relation $R$ .

Given a situation s and an infon σ, we write

s ⊨ σ

(2)

if the infon σ is supported or made factual in the situation s. In other words, the situation $s$ is a fragment of reality which supports or carries the information $α$ , eventually among many other states of things that happen to be real in that situation.

Given the notion of infon, we can define the class of situations supporting such an infon. For example, <<war making, Afghanistan, western countries, yes>> is supported in distinct situations through history, as in $s_{1}$ , the 19^th century British war making, $s_{2}$ the 20^th century Russian war making, $s_{3}$ the 21^st century US war making. Different situations instantiate types of situations: given a relation $R$ , let s be an assignment of real entities instantiating $R$ . A type of situation is a pair $⟨ ⟨ R, s ⟩ ⟩$ , that can be satisfied or supported in different situations. We write:

s ⊨ ⟨ ⟨ R, s ⟩ ⟩

(3)

to indicate that the situation $s$ supports or satisfies the type $⟨ ⟨ R, s ⟩ ⟩$ .

Note that a situation not satisfying a given type does not imply it satisfying that type's negation.

The concept of type of situation makes it possible to introduce propositions in an infon setting; at least some particular family of propositions. A simple proposition is formed by a situation s and a type of situation $⟨ ⟨ R, s ⟩ ⟩$ so that: proposition $(s, ⟨ ⟨ R, s ⟩ ⟩)$ is true if and only if $s ⊨ ⟨ ⟨ R, s ⟩ ⟩$ .

Finally, an infon is a fact just in case the actual situation supports it.

References

BARWISE, J. (1989). The Situation in Logic. Stanford: CSLI.
DEVLIN, K. (1991). Logic and Information. Cambridge: Cambridge University Press.
GINZBURG, J. (2005) “Situation Semantics: the Ontological Balance Sheet”. Research on Language and Computation, 3, pp. 363-389.