Complete Formal System
(Redirected from Completeness (logic))
A Complete Formal System is a mathematical formal system if every formula having the property can be derived using that system.
- Counter-Example(s):
- See: Validity (Logic), Mathematical Logic, Metalogic, Formal System, Formal Proof.
References
2023
- (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Completeness_(logic) Retrieved:2023-6-19.
- In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
The term "complete" is also used without qualification, with differing meanings depending on the context, mostly referring to the property of semantical validity. Intuitively, a system is called complete in this particular sense, if it can derive every formula that is true.
- In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.