equivalent if they have the same truth value in every model. The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed...

In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication...

European Union law Logical equivalence, where two statements are logically equivalent if they have the same logical content Material equivalence, a relationship...

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can...

and logical equivalence) and the symbols for the quantifiers "for all" and "there exists". The equality symbol is sometimes treated as a non-logical symbol...

suggested set of logical symbols Logic gate § Symbols Logical connective Mathematical operators and symbols in Unicode Non-logical symbol Polish notation...

for the conditional. Truth tables can be used to prove many other logical equivalences. For example, consider the following truth table: This demonstrates...

first, like the boolean logical operators XOR, AND, OR, and NOT, relational operators can be designed to have logical equivalence, such that they can all...

1962:11) and logical product defined as p . q .=. ~(~p ∨ ~q) Df. (PM 1962:12) Equivalence: Logical equivalence, not arithmetic equivalence: "≡" given as...

Philosophy portal Psychology portal Boolean function If and only if Logical equivalence Logical biconditional Propositional calculus Keeton, Brian; Cavaness...

disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs...

to the original and is logically equivalent to it. Due to their logical equivalence, stating one effectively states the other; when one is true, the...

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth...

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments...

Tarski asserts that the notion of IDENTITY (as distinguished from LOGICAL EQUIVALENCE) lies outside the propositional calculus; however, he notes that...

of "implies". ⇔ 1.  Denotes logical equivalence, and is read "is equivalent to" or "if and only if". If P and Q are logical predicates, P ⇔ Q {\displaystyle...

be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation. Like the law of the excluded middle...

Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That...

no mistakes were made, a verification step is needed to check the logical equivalence of the final version of the netlist to the original description of...

Definition Equivalence relation Logical biconditional Logical equality Logical equivalence If and only if in logic programs Polysyllogism "Logical Connectives"...

hand, an interpretation does not have anything to say about logical symbols, e.g. logical connectives " a n d {\displaystyle \mathrm {and} } ", " o r...

unbounded dense linear ordering. This is sufficient to ensure elementary equivalence, because the theory of unbounded dense linear orderings is complete,...

\wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ∧ {\displaystyle...

with the deductive nature of the system. The logical consequence (or entailment) of the system by its logical foundation is what distinguishes a formal system...

assumed to show equivalence, especially in order of magnitude, when equivalence is not necessarily the logical result. False equivalence is a common result...

for reasoning. In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are taken to be true within the system of logic...

graph-theoretic formulation for finite graphs are equivalent. The same equivalence extends to infinite families of finite sets and to certain infinite graphs...

choice function. Formally, this may be derived making use of the logical equivalence of ¬ ∀ X [ P ( X ) → Q ( X ) ] ⟺ ∃ X [ P ( X ) ∧ ¬ Q ( X ) ] . {\displaystyle...

validity, and logical consequence. While logical syntax concerns the formal rules for constructing well-formed expressions, logical semantics establishes...

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition...