WordNet
- a system of symbolic logic that represents individuals and predicates and quantification over individuals (as well as the relations between propositions) (同)functional calculus
- make the (grammatical) predicate in a proposition; "The predicate `dog is predicated of the subject `Fido in the sentence `Fido is a dog"
- one of the two main constituents of a sentence; the predicate contains the verb and its complements (同)verb phrase
- (logic) what is predicated of the subject of a proposition; the second term in a proposition is predicated of the first term by means of the copula; "`Socrates is a man predicates manhood of Socrates"
- affirm or declare as an attribute or quality of; "The speech predicated the fitness of the candidate to be President" (同)proclaim
- a hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body; "renal calculi can be very painful" (同)concretion
- the branch of mathematics that is concerned with limits and with the differentiation and integration of functions (同)infinitesimal_calculus
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For the specific term, see First-order logic.
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic, or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified. Two common quantifiers are the existential ∃ ("there exists") and universal ∀ ("for all") quantifiers. The variables could be elements in the universe under discussion, or perhaps relations or functions over that universe. For instance, an existential quantifier over a function symbol would be interpreted as modifier "there is a function". The foundations of predicate logic were developed independently by Gottlob Frege and Charles Peirce.[1]
In informal usage, the term "predicate logic" occasionally refers to first-order logic. Some authors consider the predicate calculus to be an axiomatized form of predicate logic, and the predicate logic to be derived from an informal, more intuitive development.[2]
Predicate logics also include logics mixing modal operators and quantifiers. See Modal logic, Saul Kripke, Barcan Marcus formulae, A. N. Prior, and Nicholas Rescher.
See also[edit]
- First-order logic
- Propositional logic
[edit]
- ^ Eric M. Hammer: Semantics for Existential Graphs, Journal of Philosophical Logic, Volume 27, Issue 5 (October 1998), page 489: "Development of first-order logic independently of Frege, anticipating prenex and Skolem normal forms"
- ^ Among these authors is Stolyar, p. 166. Hamilton considers both to be calculi but divides them into an informal calculus and a formal calculus.
References[edit]
- A. G. Hamilton 1978, Logic for Mathematicians, Cambridge University Press, Cambridge UK ISBN 0-521-21838-1
- Abram Aronovic Stolyar 1970, Introduction to Elementary Mathematical Logic, Dover Publications, Inc. NY. ISBN 0-486-645614
- George F Luger, Artificial Intelligence, Pearson Education, ISBN 978-81-317-2327-2
- Hazewinkel, Michiel, ed. (2001), "Predicate calculus", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
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- Cohen PJ1.
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Japanese Journal
- An extension to predicate logic of $\lambda\rho$-calculus (Logics, Algebras and Languages in Computer Science)
- An Algebraic Method to Identify Classes of Formulas in Calculus of Predicates(<Special Issue>Bilevel Programming, Optimization Methods, and Applications to Economics)
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- NAID 110009661064
Related Links
- Predicate calculus definition, functional calculus. See more. Thesaurus Translate Puzzles & Games Word of the Day Blog Slideshows Apps by Dictionary My Account Log Out Log In follow Dictionary.com Dictionary Thesaurus ...
- A formal axiomatic theory; a calculus intended for the description of logical laws (cf. Logical law) that are true for any non-empty domain of objects with ... How to Cite This Entry: Predicate calculus. Encyclopedia of Mathematics.
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- ～を(～の)属性であると断定する(of)。～を(～だと)断言する(to be)。～だと断言する(that節)
- ～の根拠を(～に)置く(=base)(on)
- In these individuals, survival after delivery is predicated on maintenance of ductal patency through the intravenous infusion of prostaglandin E1 initiated in the delivery suite often through an umbilical vein catheter.
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