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...

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

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

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...

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...

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...

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...

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

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

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

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...

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...

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...

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

Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation...

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

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

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical...

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

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...

addition where mod 2 is 1 + 1 = 0. Logical equivalence The third operation, the complement of exclusive or, is equivalence or Boolean equality: x ≡ y, or...

Gödel's completeness theorem established the equivalence between semantic and syntactic definitions of logical consequence in first-order logic. It shows...

Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that...

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...

resulting equivalences: two expressions are α-equivalent, if they can be α-converted into the same expression. β-equivalence and η-equivalence are defined...