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...

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

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...

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

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

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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

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

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...

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

types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant...

the subject. Every categorical proposition can be reduced to one of four logical forms, named A, E, I, and O based on the Latin affirmo (I affirm), for...

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

introduced the arrow symbol representing logical implication. The double-headed arrow representing logical equivalence was introduced by Albrecht Becker in...

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