Difference between revisions of "Sentence (logic)"
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| − | In [[mathematical logic]], a '''sentence''' of a predicate logic is a boolean-valued well-formed formula with no free variables. | + | In [[mathematical logic]], a '''sentence''' of a [[predicate logic]] is a boolean-valued [[well-formed formula]] with no [[Free variables and bound variables|free variables]]. |
== Description == | == Description == | ||
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* [[Mathematical logic]] | * [[Mathematical logic]] | ||
* [[Open sentence]] | * [[Open sentence]] | ||
| + | * [[Predicate logic]] | ||
* [[Proposition]] | * [[Proposition]] | ||
| − | * [[Statement (logic)] | + | * [[Statement (logic)]] |
== External links == | == External links == | ||
Latest revision as of 13:44, 3 September 2016
In mathematical logic, a sentence of a predicate logic is a boolean-valued well-formed formula with no free variables.
Description
A sentence can be viewed as expressing a proposition, something that may 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 sentences 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 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.
See also
External links
- Sentence (logic) @ Wikipedia.org
