Search results
Results from the WOW.Com Content Network
In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of what a ball is ...
However, the term tautology is also commonly used to refer to what could more specifically be called truth-functional tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. " every ", " some ", and "is"), a truth-functional tautology is true because of the logical terms it ...
In propositional logic, tautology is either of two commonly used rules of replacement. [ 1 ] [ 2 ] [ 3 ] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs .
The tee (⊤, \top in LaTeX), also called down tack (as opposed to the up tack) or verum, [1] is a symbol used to represent: . The top element in lattice theory.; The truth value of being true in logic, or a sentence (e.g., formula in propositional calculus) which is unconditionally true.
A less trivial example of a redundancy is the classical equivalence between and . Therefore, a classical-based logical system does not need the conditional operator " → {\displaystyle \to } " if " ¬ {\displaystyle \neg } " (not) and " ∨ {\displaystyle \vee } " (or) are already in use, or may use the " → {\displaystyle \to } " only as a ...
This example argument will be reused when explaining § Formalization. ... Definition 1: Atomic ... (tautology): A sentence of is ...
In Łukasiewicz's Ł3 the designated value is True, meaning that only a proposition having this value everywhere is considered a tautology. For example, A → A and A ↔ A are tautologies in Ł3 and also in classical logic. Not all tautologies of classical logic lift to Ł3 "as is".
Tautology may refer to: Tautology (language) , a redundant statement in literature and rhetoric Tautology (logic) , in formal logic, a statement that is true in every possible interpretation