Indexical Entailment

next up previous
Next: Nonmonotonic Entailment Up: Semantics Previous: Logical Entailment

Indexical Entailment

In the definition of logical entailment, all interpretations are taken into account; there is no constraint. In certain situations, it is desirable to restrict the possible interpretations to those in which certain constants are assigned values having to do with the set of sentences itself. In this case, the constants are said to be indexical. An interpretation then is indexical if and only if it assigns these indexical constants correctly.

In KIF, there is a single indexical constant, viz. the object constant knowedge-base. An indexical interpretation of a knowledge base is one in which this constant is assigned as value. This one indexical makes it possible for the user to write sentences that depend on the knowledge base within which the sentences are contained.

Finally, we say that a set of sentences indexically entails a conclusion if and only if every indexical interpretation and variable assignment that satisfies the set of sentences also satisfies the conclusion.

Vishal I. Sikka
Wed Dec 7 13:23:42 PST 1994