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searching for First-order predicate 88 found (98 total)

First-order logic (12,931 words) [view diff] exact match in snippet view article find links to article

analysis of natural language needs a much richer structure than first-order predicate logic". There are many variations of first-order logic. Some of

Temperature paradox (330 words) [view diff] no match in snippet view article find links to article

systems of logic. For instance, the following formalization in first order predicate logic would be valid via Leibniz's law: t=90 R(t) R(90) (valid conclusion

Semantic reasoner (573 words) [view diff] exact match in snippet view article find links to article

language, and often a description logic language. Many reasoners use first-order predicate logic to perform reasoning; inference commonly proceeds by forward

Ideal language philosophy (221 words) [view diff] exact match in snippet view article find links to article

that these states of affairs can be expressed by the language of first-order predicate logic. Thus a picture of the universe can be construed by means

Syllogism (5,126 words) [view diff] exact match in snippet view article find links to article

Within some academic contexts, syllogism has been superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift

Metalogic (1,402 words) [view diff] exact match in snippet view article find links to article

consistency of first-order predicate logic (David Hilbert and Wilhelm Ackermann 1928) Proof of the semantic completeness of first-order predicate logic (Gödel's

Epsilon calculus (698 words) [view diff] exact match in snippet view article find links to article

operator and epsilon substitution method are typically applied to a first-order predicate calculus, followed by a demonstration of consistency. The epsilon-extended

Object–role modeling (1,414 words) [view diff] no match in snippet view article find links to article

An object–role model uses graphical symbols that are based on first order predicate logic and set theory to enable the modeler to create an unambiguous

Semantic resolution tree (145 words) [view diff] exact match in snippet view article find links to article

theoretical tool for showing the unsatisfiability of clauses in first-order predicate logic. Kundu, S (1986-12-01). "Tree resolution and generalized semantic

Consistency (2,931 words) [view diff] no match in snippet view article find links to article

1918[citation needed] and Emil Post in 1921, while the completeness of (first order) predicate calculus was proved by Kurt Gödel in 1930, and consistency proofs

Relational model (4,196 words) [view diff] exact match in snippet view article find links to article

to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar

Original proof of Gödel's completeness theorem (4,798 words) [view diff] exact match in snippet view article find links to article

not be considered a rigorous proof of the theorem. We work with first-order predicate calculus. Our languages allow constant, function and relation symbols

Parlog (114 words) [view diff] no match in snippet view article find links to article

utilization of parallel computer architectures. Its semantics is based on first order predicate logic. It expresses concurrency, interprocess communication, indeterminacy

Reification (information retrieval) (414 words) [view diff] exact match in snippet view article

meaning representations allow one to use the tools of classical first-order predicate calculus even for statements which, due to their use of tense, modality

Fril (1,000 words) [view diff] exact match in snippet view article find links to article

Fril is a programming language for first-order predicate calculus. It includes the semantics of Prolog as a subset, but takes its syntax from the micro-PROLOG [es]

Law of thought (11,576 words) [view diff] exact match in snippet view article find links to article

and exhaustive (Nagel & Newman 1958:109–113). The (restricted) "first-order predicate calculus" is the "system of logic" that adds to the propositional

Lift (mathematics) (718 words) [view diff] exact match in snippet view article

S^{2}&&\ {\text{ (sphere path)}}\end{aligned}}} The notations of first-order predicate logic are streamlined when quantifiers are relegated to established

Categorical proposition (2,492 words) [view diff] exact match in snippet view article find links to article

the increased expressive power of modern logic systems like the first-order predicate calculus, they still retain practical value in addition to their

Corresponding conditional (684 words) [view diff] exact match in snippet view article find links to article

results confirm the validity of the argument A Some arguments need first-order predicate logic to reveal their forms and they cannot be tested properly by

Lars Svenonius (668 words) [view diff] exact match in snippet view article find links to article

1959 and 1960: ℵ 0 {\displaystyle \aleph _{0}} -categoricity in first-order predicate calculus, A theorem on permutations in models, On minimal models

List of pioneers in computer science (1,578 words) [view diff] exact match in snippet view article find links to article

Internet routers 1879 Frege, Gottlob Extended Aristotelian logic with first-order predicate calculus independently of Charles Sanders Peirce, a crucial precursor

Semantic network (3,532 words) [view diff] exact match in snippet view article find links to article

independently implemented by Robert F. Simmons and Sheldon Klein, using the first-order predicate calculus as a base, after being inspired by a demonstration of Victor

Z notation (943 words) [view diff] exact match in snippet view article find links to article

mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic. All expressions in Z notation are typed, thereby avoiding

Language of thought hypothesis (2,769 words) [view diff] exact match in snippet view article find links to article

means of which these two sub-parts are combined can be expressed in first-order predicate calculus. The thought "John is tall" is clearly composed of two

Semantics of logic (707 words) [view diff] exact match in snippet view article find links to article

them to some predefined mathematical domains: an interpretation of first-order predicate logic is given by a mapping from terms to a universe of individuals

Dictum de omni et nullo (431 words) [view diff] exact match in snippet view article find links to article

valid argument form known as universal hypothetical syllogism in first-order predicate logic. Nevertheless, Aristotelean syllogistic does not employ the

Converse (logic) (1,077 words) [view diff] exact match in snippet view article

converse per accidens "Some mammals are unicorns" is clearly false. In first-order predicate calculus, All S are P can be represented as ∀ x . S ( x ) → P (

Theoria (philosophy journal) (317 words) [view diff] no match in snippet view article

Paradoxes of Confirmation, Theoria 31, 1965, 255–274. Per Lindström, First Order Predicate Logic with Generalized Quantifiers, Theoria 32, 1966, 186–195. (Lindström

Discourse representation theory (1,004 words) [view diff] exact match in snippet view article find links to article

negation, and conditionals. In one sense, DRT offers a variation of first-order predicate calculus—its forms are pairs of first-order formulae and the free

Data model (5,059 words) [view diff] exact match in snippet view article find links to article

proposed the relational model for database management based on first-order predicate logic. In the 1970s entity–relationship modeling emerged as a new

ML (programming language) (1,461 words) [view diff] exact match in snippet view article

theorem prover (whose language, pplambda, a combination of the first-order predicate calculus and the simply typed polymorphic lambda calculus, had ML

Syntax (logic) (1,052 words) [view diff] exact match in snippet view article

introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete

Notation system (1,089 words) [view diff] exact match in snippet view article find links to article

notation for specifying objects using Zermelo–Fraenkel set theory and first-order predicate logic Ordinal notation Set-builder notation, a formal notation for

Completeness (logic) (771 words) [view diff] exact match in snippet view article

introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete

Quantifier (logic) (4,559 words) [view diff] exact match in snippet view article

and y in B(y, x) is bound (i.e. non-free). An interpretation for first-order predicate calculus assumes as given a domain of individuals X. A formula A

SETL (819 words) [view diff] exact match in snippet view article find links to article

constructed using the universal and existential quantifiers of first-order predicate logic. SETL provides several iterators to produce a variety of loops

Per Lindström (230 words) [view diff] no match in snippet view article find links to article

festschrift for Lindström was published in 1986. Per Lindström, First Order Predicate Logic with Generalized Quantifiers, Theoria 32, 1966, 186–195. Per

Axiom of empty set (798 words) [view diff] exact match in snippet view article find links to article

elements that satisfy a contradictory formula. In many formulations of first-order predicate logic, the existence of at least one object is always guaranteed

László Kalmár (711 words) [view diff] exact match in snippet view article find links to article

mathematical logic, Kalmár proved that certain classes of formulas of the first-order predicate calculus were decidable. In 1936, he proved that the predicate calculus

Well-formed formula (2,164 words) [view diff] no match in snippet view article find links to article

1007/978-1-4419-1221-3, ISBN 978-1-4419-1220-6 Well-Formed Formula for First Order Predicate Logic - includes a short Java quiz. Well-Formed Formula at ProvenMath

Modus tollens (1,848 words) [view diff] exact match in snippet view article find links to article

subset of Q. x is not in Q. Therefore, x is not in P.") Also in first-order predicate logic: ∀ x : P ( x ) → Q ( x ) {\displaystyle \forall x:~P(x)\to

Configuration management database (1,137 words) [view diff] exact match in snippet view article find links to article

and a semantic data model. Relational data models are based on first-order predicate logic and all data is represented in terms of tuples that are grouped

Willard Van Orman Quine (6,471 words) [view diff] exact match in snippet view article find links to article

philosophy students did not do justice to quantification theory or first-order predicate logic. Quine wrote this book in 6 weeks as an ad hoc solution to

First-order inductive learner (1,312 words) [view diff] exact match in snippet view article find links to article

Ross Quinlan, FOIL learns function-free Horn clauses, a subset of first-order predicate calculus. Given positive and negative examples of some concept and

Cylindric algebra (1,156 words) [view diff] exact match in snippet view article find links to article

algebra.[example needed] It is easier to connect the semantics of first-order predicate logic with cylindric set algebra. (For more details, see § Further

Guarded logic (812 words) [view diff] exact match in snippet view article find links to article

Mathematical logic and database theory (Artificial Intelligence) were first-order predicate logic. Both terms found sub-classes of first-class logic and efficiently

Gödel's completeness theorem (2,330 words) [view diff] exact match in snippet view article find links to article

the other).[citation needed] We first fix a deductive system of first-order predicate calculus, choosing any of the well-known equivalent systems. Gödel's

Definite clause grammar (1,902 words) [view diff] exact match in snippet view article find links to article

as a "formalism ... in which grammars are expressed clauses of first-order predicate logic" that "constitute effective programs of the programming language

Paradoxes of set theory (2,657 words) [view diff] exact match in snippet view article find links to article

logician Thoralf Skolem showed in 1922 that every consistent theory of first-order predicate calculus, such as set theory, has an at most countable model. However

Philosophy of logic (11,722 words) [view diff] exact match in snippet view article find links to article

to a logical contradiction. Higher-order logics extend classical first-order predicate logic by including new forms of quantification. In first-order logic

Navigational database (1,167 words) [view diff] exact match in snippet view article find links to article

inherently recursive: the mathematics underpinning SQL (specifically, first-order predicate calculus) does not have sufficient power to support recursive queries

Database normalization (2,918 words) [view diff] exact match in snippet view article find links to article

universal data sub-language based on an applied predicate calculus. A first-order predicate calculus suffices if the collection of relations is in normal form

Lindström quantifier (1,192 words) [view diff] no match in snippet view article find links to article

"strongest" logic having both properties. Lindstrom, P. (1966). "First order predicate logic with generalized quantifiers". Theoria. 32 (3): 186–195. doi:10

Unifying Theories of Programming (853 words) [view diff] exact match in snippet view article find links to article

available on the web. The semantic foundation of the UTP is the first-order predicate calculus, augmented with fixed point constructs from second-order

Ω-consistent theory (1,988 words) [view diff] exact match in snippet view article find links to article

The system of ω-logic includes all axioms and rules of the usual first-order predicate logic, together with, for each T-formula P(x) with a specified free

Finite model theory (3,107 words) [view diff] exact match in snippet view article find links to article

предикатов" [Volume and fraction of satisfiability of formulae of the first-order predicate calculus]. Kibernetika. 5 (2): 17–27. Also available as;"Range and

Ontology engineering (1,660 words) [view diff] exact match in snippet view article find links to article

Cyc project has its own ontology language called CycL, based on first-order predicate calculus with some higher-order extensions. The Gellish language

Automated theorem proving (2,933 words) [view diff] exact match in snippet view article find links to article

algorithms are believed to exist for general proof tasks. For a first-order predicate calculus, Gödel's completeness theorem states that the theorems

Outline of databases (3,487 words) [view diff] exact match in snippet view article find links to article

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

Procedural reasoning system (1,168 words) [view diff] no match in snippet view article find links to article

components: Database for beliefs about the world, represented using first order predicate calculus. Goals to be realized by the system as conditions over

Inductive logic programming (4,245 words) [view diff] exact match in snippet view article find links to article

ISBN 0-262-19218-7. Muggleton, S.H.; Buntine, W. (1988). "Machine invention of first-order predicate by inverting resolution". Proceedings of the 5th International Conference

Semantic interoperability (2,477 words) [view diff] exact match in snippet view article find links to article

purpose language such as XML. Languages with the full power of first-order predicate logic may be required for many tasks. Human languages are highly

Database (9,580 words) [view diff] exact match in snippet view article find links to article

operations to be defined in terms of the established discipline of first-order predicate calculus; because these operations have clean mathematical properties

Ontology (information science) (6,194 words) [view diff] exact match in snippet view article

Cyc project has its own ontology language called CycL, based on first-order predicate calculus with some higher-order extensions. DOGMA (Developing Ontology-Grounded

Resolution (logic) (4,063 words) [view diff] exact match in snippet view article

not be used as p {\displaystyle p} due to its syntactic form. For first-order predicate logic, Murray's rule is generalized to allow distinct, but unifiable

Truth-bearer (4,888 words) [view diff] exact match in snippet view article find links to article

and is therefore a truth-bearer. For example, a language in the first-order predicate calculus might include one or more predicate symbols and one or

Prolog (8,098 words) [view diff] exact match in snippet view article find links to article

certainty about the result. Pure Prolog is based on a subset of first-order predicate logic, Horn clauses, which is Turing-complete. Turing completeness

Prolog syntax and semantics (1,964 words) [view diff] exact match in snippet view article find links to article

Prolog is restricted to Horn clauses, a Turing-complete subset of first-order predicate logic. There are two types of clauses: Facts and rules. A rule is

Deepak Kapur (1,936 words) [view diff] exact match in snippet view article find links to article

(18 August 1985). "An equational approach to theorem proving in first-order predicate calculus". Proceedings of the 9th International Joint Conference

Semantics of Business Vocabulary and Business Rules (2,611 words) [view diff] no match in snippet view article find links to article

any OMG modeling language. The logics supported by SBVR are typed first order predicate logic with equality, restricted higher order logic (Henkin semantics)

Equality (mathematics) (7,684 words) [view diff] exact match in snippet view article

convenience, as noted by Azriel Lévy. "The reason why we take up first-order predicate calculus with equality is a matter of convenience; by this, we save

Intuitionistic logic (8,022 words) [view diff] exact match in snippet view article find links to article

FALSE: ⊥ → ϕ {\displaystyle \bot \to \phi } To make this a system of first-order predicate logic, the generalization rules ∀ {\displaystyle \forall } -GEN:

Sequent calculus (5,904 words) [view diff] exact match in snippet view article find links to article

A {\displaystyle A} and B {\displaystyle B} denote formulas of first-order predicate logic (one may also restrict this to propositional logic), Γ , Δ

Meaning (philosophy) (6,511 words) [view diff] exact match in snippet view article

semantics. He proposed simply translating natural languages into first-order predicate calculus in order to reduce meaning to a function of truth. Saul

Legal informatics (4,083 words) [view diff] no match in snippet view article find links to article

documents bears a close resemblance to the Horn clause subset of first order predicate calculus. Moreover, it identified the need to extend the use of

Analytic philosophy (10,876 words) [view diff] exact match in snippet view article find links to article

states of affairs can be expressed and mirrored by the language of first-order predicate logic. Thus, a picture of the universe can be constructed by expressing

Lambda cube (3,237 words) [view diff] no match in snippet view article find links to article

Propositional Calculus λω Higher Order Propositional Calculus λP (First order) Predicate Logic λP2 Second-order Predicate Calculus λPω Weak Higher Order

Principia Mathematica (9,477 words) [view diff] exact match in snippet view article find links to article

and consistent. In 1930, Gödel's completeness theorem showed that first-order predicate logic itself was complete in a much weaker sense—that is, any sentence

Logic programming (10,767 words) [view diff] exact match in snippet view article find links to article

is a relational expression, which is similar to an expression in first-order predicate logic. Other relational programming languages are based on the relational

Diploma in Computer Science (2,731 words) [view diff] exact match in snippet view article find links to article

breakthroughs in logic itself. The traditional generalisations of first-order predicate calculus are insufficient to support the new applications. New developments

Giorgi Japaridze (2,628 words) [view diff] no match in snippet view article find links to article

algebras and proof-theoretic ordinals). Japaridze has also studied the first-order (predicate) versions of provability logic. He came up with an axiomatization

RDFLib (3,219 words) [view diff] no match in snippet view article find links to article

Notation 3 that go beyond the RDF model to provide a framework for First Order Predicate Logic processing and persistence. Context A named, unordered set

Logic of graphs (5,029 words) [view diff] no match in snippet view article find links to article

Koncewicz, Leszek (1973), "Definability of classes of graphs in the first order predicate calculus with identity", Polish Academy of Sciences, 32: 159–190

Von Neumann–Bernays–Gödel set theory (15,666 words) [view diff] exact match in snippet view article find links to article

Mendelson's modification. This means that NBG is an axiomatic system in first-order predicate logic with equality, and its only primitive notions are class and

Glossary of artificial intelligence (29,481 words) [view diff] exact match in snippet view article find links to article

language, and often a description logic language. Many reasoners use first-order predicate logic to perform reasoning; inference commonly proceeds by forward

Method of analytic tableaux (11,782 words) [view diff] exact match in snippet view article find links to article

gives an assignment that falsifies A. Tableaux are extended to first-order predicate logic by two rules for dealing with universal and existential quantifiers

History of the function concept (10,688 words) [view diff] no match in snippet view article find links to article

(in Halmos), they will see no mention of "proposition" or even "first order predicate calculus". In their place are "expressions of the object language"

History of ontology (5,990 words) [view diff] exact match in snippet view article find links to article

to determine this is by translating the theory in question into first-order predicate logic. Of special interest in this translation are the logical constants