Semantics



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Semantics

Intuitively, the semantics of KIF is very simple. Unfortunately, the formal details are quite complex. Consequently, we proceed gradually in our presentation. In this chapter, we introduce the basic notions underlying the semantics of KIF (in particular, the notions of interpretation, variable assignment, semantic value, truth value, and various types of entailment).

The basis for KIF semantics is a correlation between the terms and sentences of the language and a conceptualization of the world. Every term denotes an object in the universe of discourse associated with the conceptualization, and every sentence is either true or false.

When we encode knowledge in KIF, we select constants on the basis of our understanding of their meanings. In some cases (e.g. the basic constants of the language), these meanings are fixed in the definition of the language. In other cases (i.e. the non-basic constants), the meanings can vary from one user to another.

Given exact meanings for the constants of the language (whether they are the meanings in the definition of the language or our own concoctions), the semantics of KIF tells us the meaning of its complex expressions. We can unambiguously determine the referent of any term, and we can unambiguously determine the truth or falsity of any sentence.

Unfortunately, few of us have complete knowledge about the world. In keeping with traditional logical semantics, this is equivalent to not knowing the exact referent for every constant in the language. In such situations, we write sentences that reflect all of the meanings consistent with whatever knowledge we have. In such situations, the semantics of the language cannot pick out exact meanings for all expressions in the language, but it does place constraints on the meanings of complex expressions.

And, of course, the meanings we ascribe to non-basic constants may differ from those ascribed by others. However, we can convey our meanings to others by writing sentences to constrain those meanings in accordance with our usage. By writing more and more sentences, the set of possible referents for our constants is decreased.

In the remainder of this section, we provide precise definitions for the ideas just introduced. We start off with a definition for the interpretation of constants, and we introduce the related notion of variable assignment. We then show how these concepts are used in defining the semantic value of terms and the truth value of sentences. Finally, we introduce several approaches to entailment, which eliminates the dependence of meaning on the interpretation of non-basic constants.





next up previous
Next: Interpretation Up: No Title Previous: Functions and Relations



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