Search results
Results from the WOW.Com Content Network
The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, after which an element ϕ ∈ T {\displaystyle \phi \in T} of a deductively closed theory T {\displaystyle T} is then called a theorem of the theory.
Löb's theorem A theorem in mathematical logic that provides conditions under which a statement about its own provability is provable, related to Gödel's incompleteness theorems. logic The systematic study of the form of valid inference, including the structures that allow or compel particular conclusions given certain premises. logic gate
Löb's theorem (mathematical logic) Lochs's theorem (number theory) Looman–Menchoff theorem (complex analysis) Łoś' theorem (model theory) Lovelock's theorem ; Löwenheim–Skolem theorem (mathematical logic) Lucas's theorem (number theory) Lukacs's proportion-sum independence theorem (probability) Lumer–Phillips theorem (semigroup theory)
Semantic completeness is the converse of soundness for formal systems. A formal system is complete with respect to tautologousness or "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system ...
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
The deduction theorem for predicate logic is similar, but comes with some extra constraints (that would for example be satisfied if is a closed formula). In general a deduction theorem needs to take into account all logical details of the theory under consideration, so each logical system technically needs its own deduction theorem, although ...
The definition is slightly more ... Provability logic is a ... theories have analogues in provability logic. For example, it is a theorem in GL that if a ...