predicate calculus
predicate calculus (predicate logic, firstorder logic) A fundamental notation for representing and reasoning with logical statements. It extends propositional calculus by introducing the quantifiers, and by allowing predicates and functions of any number of variables. The syntax involves terms, atoms, and formulas. An atom (or atomic formula) has the form P(t_{1},…,t_{k}), where P is a predicate symbol and t_{1},…,t_{k} are terms. Formulas may be built from these atoms in the following ways: (a) any atom is a formula;(b) formulas can be combined by the usual propositional connectives (negation, conjunction, disjunction, etc.);(c) if F is a formula, then ∀v.F and ∃v.F are also formulas (see quantifier).
A sentence is a formula with no free variables. An example of a sentence is ∀x . G(x,c) — ∀y . G(f(x,y),y)
where — signifies the biconditional and G is a predicate symbol, f is a function symbol, x and y are variables, and c is a constant symbol. The overall meaning of a sentence (true or false) depends on the interpretation given to the symbols occurring in it. For example, let G be interpreted as the predicate “greater than”, f as the operation of multiplication, and c as the number 1. Then the above sentence says that a number x is greater than 1 if and only if it has the property that, for all y, xy is greater than y. This is true if the domain of interpretation is the natural numbers, but not if it is the integers (because of the possibility of negative y).
Predicate calculus can claim to be a fundamental logical language since all the more complicated logics can, in some sense, be reduced to it. A simple but practically important extension is manysorted predicate calculus. Here there are several sorts of variables, and the operations and relations come from a manysorted signature.
Another possible extension is secondorder logic, which allows predicate and function variables, such as P in the following: ∀P . [P(a) ∧ ∀k . P(k) ⇒ P(s(k))] ⇒ ∀n . P(n)
(∧ and ⇒ signify conjunction and conditional.) This example, given the appropriate interpretation of a and s, expresses a principle of induction: if P is true for zero, and true for k+1 whenever it is true for k, then it is true for all n. Again this sentence holds for natural numbers but not integers.
Applications of predicate calculus in computer science are commonplace and include formal specification, program correctness, logic programming, and databases. See also modal logic.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"predicate calculus." A Dictionary of Computing. . Encyclopedia.com. 12 Mar. 2019 <https://www.encyclopedia.com>.
"predicate calculus." A Dictionary of Computing. . Encyclopedia.com. (March 12, 2019). https://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/predicatecalculus
"predicate calculus." A Dictionary of Computing. . Retrieved March 12, 2019 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/predicatecalculus
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.