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Infons

An infon is sometimes written:

where p is one of -,+. The expressions:

are intended to convey the information that are (are not, respectively) related by q. We might think of + as the basic polarity, then - expresses the notion of complement.

It is not clear to me whether or not situation theory requires q to have an explicit arity.

We could implement infons as pairings of terms.gif Alternatively, we could have a primitive class of infons and their complements, or primitive relational expressions from which we can form positive and negative infons. The last two options allow us to ignore the question of the arity of an infon for the moment.

A term r is a relational expression iff:

If r is a relational expression, then +r,-r are infons:

The terms +r,-r are intended to be used in place of expressions of the form

We can form the conjunction and disjunction of infons. For the moment we will add the operators . Depending upon how we model Austinian Propositions, it may be possible to make these definitional. However implemented, they must satisfy the closure conditions

A situation-theoretic relation can be encoded as -abstracts of infons. Then we can have:

Note that expressions of are also called situation-theoretic properties.



Chris Fox , 4th October 1995