Frege's Begriffsschrift ( 1879 ) introduced both a complete propositional calculus and what is essentially modern predicate logic.

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

In linguistics, a copula ( plural: copulas or copulae ) is a word used to link the subject of a sentence with a predicate ( a subject complement ).

Every effectively calculable function ( effectively decidable predicate ) is general recursive italics

Every effectively calculable function ( effectively decidable predicate ) is general recursive.

Each category is that one predicate which is common to multiple empirical concepts.

Rather, we say that a real a is definable in the language of arithmetic ( or arithmetical ) if its Dedekind cut can be defined as a predicate in that language ; that is, if there is a first-order formula φ in the language of arithmetic, with two free variables, such that

Likewise, in the sentence, " here, there is a pot ", " here " is the bearer of the property " pot-existence " – this shows that the categories of property and property-bearer are closer to those of a logical predicate and its subject-term, and not to a grammatical predicate and subject.

The two terms are joined by the verb " is " ( or " is not ", if the predicate is denied of the subject ).

Kant also argued that existence is not a " real " predicate, but gave no explanation of how this is possible.

This is the case of the Mycin and Dendral expert systems, and of, for example, fuzzy logic, predicate logic ( Prolog ), symbolic logic and mathematical logic.

It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic ( a less precise term ).

In first-order logic, however, the sentences can be expressed in a more parallel manner using the predicate Phil ( a ), which asserts that the object represented by a is a philosopher.

Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.

) In addition to specifying the meaning of predicate symbols such as Person and Time, an interpretation must specify a nonempty set, known as the domain of discourse or universe, as a range for the quantifiers.

* Filter ( higher-order function ), a higher-order function that processes a data structure ( typically a list ) in some order to produce a new data structure containing exactly those elements of the original data structure for which a given predicate returns the boolean value true

In practice, one would have a predicate for specifying when an action is executed and a rule for specifying the effects of actions.

It would have been nice to have a predicate Q ' so that for every x, Q '( x, y ) would be true if and only if y is the required one to make ( something ) true.

First-order predicate calculus is commonly used as a mathematical basis for these systems, to avoid excessive complexity.

The language ’ s grammar is based on predicate logic, which is why it was named Loglan, an abbreviation for " logical language ".

Each predicate has its argument structure with places for arguments, which may be variables.

Alfred Tarski diagnosed the paradox as arising only in languages that are " semantically closed ", by which he meant a language in which it is possible for one sentence to predicate truth ( or falsehood ) of another sentence in the same language ( or even of itself ).

The analogue of conjunction for a ( possibly infinite ) family of statements is universal quantification, which is part of predicate logic.

The question of whether or not existence is a predicate has been discussed since the Early Modern period, not least in relation to the ontological argument for the existence of God.

Many jurisdictions adopt a list of specific predicate crimes for money laundering prosecutions, while others criminalize the proceeds of any serious crime.

Historically, ML stands for metalanguage: it was conceived to develop proof tactics in the LCF theorem prover ( whose language, pplambda, a combination of the first-order predicate calculus and the simply typed polymorphic lambda calculus, had ML as its metalanguage ).

One extreme is predicate nominalism, which states that Fluffy and Kitzler, for example, are both cats simply because the predicate ' is a cat ' applies to both of them.

IST is an extension of Zermelo-Fraenkel set theory ( ZF ) in that alongside the basic binary membership relation, it introduces a new unary predicate standard which can be applied to elements of the mathematical universe together with some axioms for reasoning with this new predicate.

By contrast, when Bertrand Russell writes, in The Principles of Mathematics, " A class [...] is neither a predicate nor a class-concept, for different predicates and different class-concepts may correspond to the same class.

The built-in Prolog predicate provides negation as failure, which allows for non-monotonic reasoning.

:" We were justified intuitionistically in using the classical 2-valued logic, when we were using the connectives in building primitive and general recursive predicates, since there is a decision procedure for each general recursive predicate ; i. e. the law of the excluded middle is proved intuitionistically to apply to general recursive predicates.

:" Now if Q ( x ) is a partial recursive predicate, there is a decision procedure for Q ( x ) on its range of definition, so the law of the excluded middle or excluded " third " ( saying that, Q ( x ) is either t or f ) applies intuitionistically on the range of definition.

Although some of the RICO predicate acts are extortion and blackmail, one of the most successful applications of the RICO laws has been the ability to indict or sanction individuals for their behavior and actions committed against witnesses and victims in alleged retaliation or retribution for cooperating with federal law enforcement or intelligence agencies.

The relational model for database management is a database model based on first-order predicate logic, first formulated and proposed in 1969 by Edgar F. Codd.

On the other hand, a non-logical predicate symbol such as Phil ( x ) could be interpreted to mean " x is a philosopher ", " x is a man named Philip ", or any other unary predicate, depending on the interpretation at hand.

In fact, the model of any theory containing PA obtained by the systematic construction of the arithmetical model existence theorem, is always non-standard with a non-equivalent provability predicate and a non-equivalent way to interpret its own construction, so that this construction is non-recursive ( as recursive definitions would be unambiguous ).

Under such conditions every formula of the form, where ( T ) is a string of quantifiers containing all quantifiers in ( S ) and ( S ') interleaved among themselves in any fashion, but maintaining the relative order inside ( S ) and ( S '), will be equivalent to the original formula Φ '( this is yet another basic result in first-order predicate calculus that we rely on ).

He then proposes that " there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate " ( Book IV, CH 7, p. 531 ).

So we can identify the " class of all sets " with the predicate x = x or any equivalent predicate.

The jury acquitted Barger on the RICO charges with a hung jury on the predicate acts: " There was no proof it was part of club policy, and as much as they tried, the government could not come up with any incriminating minutes from any of our meetings mentioning drugs and guns.

The content of the database at any given time is a finite ( logical ) model of the database, i. e. a set of relations, one per predicate variable, such that all predicates are satisfied.

Crispin Wright argued in his 1992 book Truth and Objectivity that any predicate which satisfied certain platitudes about truth qualified as a truth predicate.

Notice that truth never gets defined for sentences like This sentence is false, since it was not in the original subset and does not predicate truth of any sentence in the original or any subsequent set.

According to the Ness-Ity-Hood Principle, a name for any universal may be formed that is distinctive, " of left-handers " may be formed by taking the predicate " left-handed " and adding " ness ", which yields the name " left-handedness ".

where P is any unary predicate that does not mention A, to define a unique set whose members are precisely the sets satisfying the predicate.

nomo: no / any more ( placed before the predicate )

: Given any x and y, x = y if, given any predicate P, P ( x ) if and only if P ( y ).

This is because denotes the empty set, and no x of any description – let alone an x fulfilling a given predicate P ( x ) – exist in the empty set.