Tuesday, October 6, 2009

Predicate Logic

One area of semantics is predicate logic. It analyzes the internal structure of sentences. In predicate logic symbols are used to make a number of simple statements.

The sentences "Ann is sleeping" and "Joe paints" both have a simple subject-predicate structure. The subject is a referring expression (Ann, Joe) and the predicate gives information about the subject (is sleeping, paints).

The predicate can be represented by a capital letter. In the sentence "Ann is sleeping", this is "S" and in "Joe paints" this is "P".

The subject can be represented by a lowercase letter. This is called an individual constant. In "Ann is sleeping" this is "a" and in "Joe paints" this is "j".

Predicate logic forms begin with the predicate followed by the subject. The original sentences can be represented as follows:

Ann is sleeping: S (a)
Joe paints: P (j)

If one wishes to leave the identify of the subject unspecified one can use variables such as x and y. Thus, "Someone is sleeping" can be represented as S (x) and "Someone paints" as P (y).

The examples have only one noun. However, it is possible to use symbols in the analysis of sentences with more than one. For example, we can analyze sentences such as "Mark knows William" and "Helen likes Tom". These sentences have both a subject and an object.

The sentence "Mark knows William" can be represented as K (m, w) and the sentence "Helen likes Tom" can be analyzed as L (h, t). The order of the individual constants after the predicate letter mirrors English sentence structure. The subject comes before the object.

Other relational sentences can be represented in the same way. For example, "Ellen is younger than Olivia" is Y ( e, o). Here the predicate letter represents the comparative adjective "younger". Relations with three nouns are also possible. For example, the sentence "Paul prefers Danielle to Eleanore" is P (p, d, e).

Predicate logic aims to translate a sentence from an individual language into an expression in a universal metalanguage. This can be done with symbols which identify the subject-predicate structure of each sentence. It can also be viewed as a form of shorthand notation.

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