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...

of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration...

logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure...

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 logic...

[better source needed] In formal languages, truth functions are represented by unambiguous symbols. This allows logical statements to not be understood in an...

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

disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated...

study of the laws of thought, correct reasoning, valid inference, or logical truth. It is a formal science that investigates how conclusions follow from...

said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p {\displaystyle p} and q {\displaystyle...

variables connected by logical connectives, built up in such a way that the truth of the overall formula can be deduced from the truth or falsity of each...

statement is a truth function. On the other hand, modal logic is non-truth-functional. A logical connective is truth-functional if the truth-value of a compound...

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

ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. Humans apply logical intuition in proving...

In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement)...

is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is necessary and formal, by way of...

logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts...

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...

mathematics. For non-deductive logical reasoning, the premises make their conclusion rationally convincing without ensuring its truth. This is often understood...

the truth of the premises, instead it merely necessitates that conclusion follows from the premises without violating the correctness of the logical form...

Logical equality is a logical operator that compares two truth values, or more generally, two formulas, such that it gives the value True if both arguments...

true. Negation is thus a unary logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more...

through deductively valid inferences that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific...

the relation denoted by R {\displaystyle R} . Since predicates are non-logical symbols, they can denote different relations depending on the interpretation...

reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax...

in terms of truth-values for the behaviour of the symbols "⊢" (assertion of truth), "~" (logical not), and "V" (logical inclusive OR). Truth-values: PM...

speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic. The truth of a formula such...

mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used...

rules having the property of preserving truth. The converse of soundness is known as completeness. A logical system with syntactic entailment ⊢ {\displaystyle...

logical consequence of ψ). Some of the logical symbols of a language (other than quantifiers) are truth-functional connectives that represent truth functions —...

language; in the case of predicate logic more logical axioms than that are required, in order to prove logical truths that are not tautologies in the strict...