predicate

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predicate

Sentences must always include both a subject and a predicate. The predicate is, essentially, everything in the sentences that follows the subject. It is made up of at least one finite verb, the action of which is performed by the subject.
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predicate

Logic
a. an expression that is derived from a sentence by the deletion of a name
b. a property, characteristic, or attribute that may be affirmed or denied of something. The categorial statement all men are mortal relates two predicates, is a man and is mortal
c. the term of a categorial proposition that is affirmed or denied of its subject. In this example all men is the subject, and mortal is the predicate
d. a function from individuals to truth values, the truth set of the function being the extension of the predicate

Predicate

 

the same as property. In the narrow sense, a predicate is a property of an individual object, such as the property of being human. In the broad sense, it is the property of a pair, triple, or n-tuple of objects, for example, the property of being a relative. Predicates in the broad sense are also known as relations.

Historically, the concept of the predicate came about as a consequence of the logical analysis of utterances of natural language. The concept resulted from the elucidation of the logical structure of utterances and from the elucidation of the logic that may be used to express, or formalize, the meanings of these utterances. Aristotle originated the idea of isolating the logical structure—as opposed to the grammatical structure—of speech for purposes of logical deduction. In Aristotelian and subsequent traditional logic, the predicate was construed narrowly as one of the two terms of a sentence—the term in which something is said about the subject. The form of the statement—the predicative relation—was reduced to an attributive relation, which expressed the inherent nature of some attribute of the subject. Aristotle singled out four kinds of attributes capable of acting as predicates: generic, specific, intrinsic, and casual. These are the praedicabilia, or kinds of predicates.

At the level of concepts of logical deductions that characterized Aristotelian and traditional logic, the logical analysis of phrases of a natural language was thus limited to expressing the meaning of utterances by the logic of one-place predicates—the logic of properties in the narrow sense. This greatly weakened the expressive possibilities of logic and served as an impediment to adequate formalization of the objective relations between objects; these relations, being conceivable in the form of the relations (properties in the broad sense) between the corresponding concepts, underlie the logical correctness of inferences regarding the relations—the main inferences in science. The new interpretation of predicate, which originated with G. Frege’s Begriffs-schrift (1879), was instrumental in eliminating the above-mentioned impediment and in strengthening the expressive means of the formalism of contemporary logic. The main idea behind this interpretation is that the predicative relation is considered a particular case of the functional relation. This ensures more complete representation of the content structure of the phrases of natural language in subject-predicate type formalism than does the Aristotelian representation. At the same time, it ensures a further development of this very formalism in the direction of bringing together the languages of logic and mathematics.

In natural and artificial (exact) languages, expressions of the type comprising declarative sentences containing indefinite terms—the indefinite names of subjects—serve as the basis for the functional way of viewing the predicate. These indefinite names are the variables (parameters) in the notation of assertions in mathematical language (for example, x + 2 = 4) and the various words, such as “something” and “someone,” that in a natural language act as variables in expressions of the type “some person,” “someone loves someone,” and “if someone is a person, then he is mortal.” By writing these expressions in some unique way, for example, by replacing undefined terms with gaps as is done in test questions (“… + 2 = 4,” “… person,” “… loves …,” “If … is a person, then … is mortal”) or by adopting a notation using variables as the principal one (“x + 2 = 4,” “x is a person,” “x loves y,” “if x is a person, then x is mortal”), it can readily be seen that the expressions have something in common. First, the presence of undefined terms makes these and similar expressions generally undefined both in regard to what is asserted in them and in regard to the truth-value. Second, any appropriate indication of the range of values of the undefined terms and the simultaneous quantification or substitution of the undefined terms by their values converts the corresponding expressions into meaningful propositions.

In modern logic, expressions that have the form of narrative sentences and that contain undefined terms have been given the general name of propositional functions, or, preserving the traditional term, predicates. Like numerical functions, predicates are correspondences. The undefined terms play the normal role of the arguments of a function; in contrast to numerical functions, however, propositions are the values, or meanings, of predicates. Generally, by digressing from some specific language and preserving only the functional form of notation, a predicate of n variables (n undefined terms) is expressed by the formula P(x1xn), where n ≥ 0. When n = 0 the predicate coincides with the proposition, when = 1 it is a property in the narrow sense (a one-place predicate), when n = 2 it is the property of a pair (a two-place predicate, or binary relation), when n = 3 it is the property of a triple (a three-place predicate, or ternary relation), and so forth. The expressions “x + 2 = 4,” “x is a person,” “x loves y,” and “x is the son of y and z” are examples of one-place, two-place, and three-place predicates, respectively. They may be converted into propositions by appropriate substitution, for example, “2 + 2 = 4,” “Socrates is a person,” “Xanthippe loves Socrates,” and “Sophroniscus is the son of Xanthippe and Socrates.” Alternately, they may be converted into propositions by combining the variables by means of quantifier words, for example, “∃x (x + 2 = 4)” (there exists a number which, added to 2, gives 4),“∃x (x is a person)” (people exist), and “∀xyz (x is the son of y and z)” (everyone is the son of at least two parents), where it is kept in mind that the ranges of the variables are numbers in the first case, animate beings in the second, and people in the third.

The division of a sentence into subject and predicate, which is characteristic of traditional logic, generally did not coincide with the grammatical division of a sentence into the subject and verb. To reduce the expressions of normal speech to the form of syllogistic arguments, there was a need for some transformation of these expressions, a transformation that generally changes the form of predicability. The interpretation of predicates as propositional functions, which is associated with identifying the syntactical role of subjects and complements according to whether they belong to a general semantic type of objects from the range of definition (the values of the arguments) of a propositional function, was a further digression in logic from the purely linguistic way of viewing the predicate. Nonetheless, within the framework of applied logic, it is natural to consider the predicate as a linguistic concept or, more accurately, a linguistic construct that carries an incomplete message and is described in pure logic by the concept of propositional function.

Modern set-theoretic (classical) logic has adopted an interpretation of predicate that is more abstract than the one given above and is based on the identification of propositions with their truth-values. This is permissible—but not mandatory—within the framework of this logic. The predicate then may be understood only as a logical function defined in terms of set theory, that is, as the mapping of Dn in [T, F], where n is the number of arguments in the function, D their domain, D2 the n-tuple direct product of this domain, and {T, F} the set of truth-values of the function. For example, if the values of a variable x in the expression x + 2 — 4 are defined in the set of natural numbers, then the corresponding function is that given in Table 1.

Table 1
xx + 2 = 4
0F
1F
2T
3F

The selection of a given interpretation of the concept of predicate is not arbitrary and is determined in particular by the methodological position—constructivist, intuitionist, or classical. Essentially, however, what is being dealt with here is not the claim that an interpretation has a uniquely correct description of some single essence given by the predicate but rather the agreement to use the term “predicate” in the meaning appropriate to the specific case.

REFERENCES

Markov, A. A. O logike konstruktivnoi matematiki. Moscow, 1972.
Novikov, P. S. Elementy matematicheskoi logiki, 2nd ed. Moscow, 1973.
Kleene, S. C. Matematicheskaia logika. Moscow, 1973. (Translated from English.)

M. M. NOVOSELOV


Predicate

 

one of the two principal members of a binomial sentence, the other being the subject.

The predicate is the central element of a predicate group, joining the predicate to sentence members dependent on the predicate—the object and the adverbial modifiers. The relationships that link the subject and predicate are called predicative relationships. The predicate is the bearer of “predicativity,” that is, the basic property of a sentence that distinguishes a sentence from a word or combination of words. Reduction of a sentence to its predicate does not affect the functioning of the whole; this can be seen by comparing Veter duet (“The wind is blowing”) with Duet (“[It] is blowing”). The predicate thus constitutes the functional minimum of a sentence, expressing the grammatical categories that characterize the sentence as a whole (tense, modality). It is central to the sentence because it is usually the element that expresses the message.

Although the predicate is the communicative nucleus of the sentence, it is nevertheless formally dependent on the subject, agreeing with the subject in gender, number, and person; forms of dependence are determined by the structure of individual languages. Thus, the relationships between the principal members of a sentence are diametrically opposed on different levels of analysis: the predicate is subordinated to the subject on the syntagmatic level but dominates the subject on the paradigmatic level. In the semantic sphere, the predicate serves an attributive function, indicating the existence in an object of a certain general property.

There is not only formal but also semantic agreement between the subject and the predicate: the sense categories of the predicate are determined by the sense categories of the subject. Thus, if the subject denotes a concrete object, the predicate can indicate the object’s quality, properties, state, function, activity, position, relationship to other objects, appraisal by the speaker, and so on. If the subject denotes an event, the predicate can indicate the means by which the event came about, the event’s local and temporal characteristics, the event’s bearing on reality, and so on.

A distinction is made between verbal and nominal predicates according to the part of speech that represents the predicate. The former is expressed by a finite verb, as in Mal’chik plachet (“The boy is crying”), or by a modal or phasic verb together with an infinitive, as in Mal’chik perestal plakat’ (“The boy stopped crying”). The latter is expressed by a copulative verb or a zero copula together with a noun or adjective that constitutes the nominal portion of the predicate (the predicate complement), as in Sneg bel (“The snow is white”) or Pogoda byla solnechnaia (“The weather was sunny”).

REFERENCES

Shakhmatov, A. A. Sintaksis russkogo iazyka, 2nd ed. Moscow-Leningrad, 1941.
Peshkovskii, A. M. Russkii sintaksis v nauchnom osveshchenii, 7th ed. Moscow, 1956.
Steblin-Kamenskii, M. I. “O predikativnosti.” Vestnik LGU: Seriia istorii, iazyka i literatury, 1956, no. 20, issue 4.
Kuryłowicz, J. Ocherkipo lingvistike. Moscow, 1962.
Alisova, T. B. “Opyt semantiko-grammaticheskoi klassifikatsii pros-tykh predlozhenii.” Voprosy iazykoznaniia, 1970, no. 2.
Grammatika sovremennogo russkogo literaturnogo iazyka. Moscow, 1970.

N. D. ARUTIUNOVA

predicate

[′pred·ə‚kāt]
(computer science)
A statement in a computer program that evaluates an expression in order to arrive at a true or false answer.
(mathematics)
To affirm or deny, in mathematical logic, one or more subjects. Also known as logical function; propositional function.

predicate

In programming, a statement that evaluates an expression and provides a true or false answer based on the condition of the data.