About: Sentence (mathematical logic)

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In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: As the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.

Attributes	Values
rdfs:label	Sentence (mathematical logic) (en)
rdfs:comment	In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: As the free variables of a (general) formula can range over several values, the truth value of such a formula may vary. (en)
sameAs	Sentence (mathematical logic)
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Em dbt:Reflist dbt:Logic-stub dbt:Mathematical_logic
Subject	Predicate logic Propositions
Link from a Wikipa... related subject.	dbpedia-fr:Proposition_(logique_mathématique)
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Sentence_(mathematical_logic)?oldid=1070975701&ns=0
Wikipage page ID	2129527 (xsd:integer)
page length (characters) of wiki page	3712 (xsd:nonNegativeInteger)
Wikipage revision ID	1070975701 (xsd:integer)
has abstract	In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: As the free variables of a (general) formula can range over several values, the truth value of such a formula may vary. Sentences without any logical connectives or quantifiers in them are known as atomic sentences; by analogy to atomic formula. Sentences are then built up out of atomic formulas by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory. For first-order theories, interpretations are commonly called structures. Given a structure or interpretation, a sentence will have a fixed truth value. A theory is satisfiable when it is possible to present an interpretation in which all of its sentences are true. The study of algorithms to automatically discover interpretations of theories that render all sentences as being true is known as the satisfiability modulo theories problem. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
is Wikipage redirect of	Sentence (logic) Closed sentence Logical sentence
is Link from a Wikipage to another Wikipage of	Forcing (mathematics) Formal language Formally real field Logic of graphs Non-logical symbol Number sentence Disjunction and existence properties Abstract logic Algebraic logic Atomic sentence Axiom of choice Boolean-valued function Bounded quantifier Casimir Lewy Object language Deduction theorem Lindenbaum–Tarski algebra List of first-order theories Closed sentence Compactness theorem Completeness (logic) Ehrenfeucht–Fraïssé game Elementary class Elementary diagram Elementary equivalence Embedded dependency Epistemology Equality-generating dependency First-order logic Independence (mathematical logic) Index of philosophy articles (A–C) Logical sentence Diagonal lemma Existential theory of the reals Infinitary logic Infinite chess Institution (computer science) Interpretation (logic) Model theory Multiple-conclusion logic

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