Difference between revisions of "Propositional formula"
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| − | In [[propositional calculus]], a '''propositional formula''' is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula. | + | In [[propositional calculus]], a '''propositional formula''' is a type of syntactic formula which is [[Well-formed formula|well formed]] and has a [[truth value]]. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula. |
== Description == | == Description == | ||
Latest revision as of 07:09, 7 September 2016
In propositional calculus, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula.
Description
A propositional formula is constructed from simple propositions, such as "five is greater than three" or propositional variables such as P and Q, using connectives such as NOT, AND, OR, and IMPLIES; for example: (P AND NOT Q) IMPLIES (P OR Q).
In mathematics, a propositional formula is often more briefly referred to as a "proposition", but, more precisely, a propositional formula is not a proposition but a formal expression that denotes a proposition, a formal object under discussion, just like an expression such as "x + y" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importance.
See also
External links
- Propositional formula @ Wikipedia
