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...

way. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives. For...

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

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

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

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...

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...

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

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

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...

negatum. Negation is a unary logical connective. It may furthermore be applied not only to propositions, but also to notions, truth values, or semantic values...

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...

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...

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

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...

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...

section on syntax. The logical constants, by contrast, have the same meaning in all interpretations. They include the symbols for truth-functional connectives...

semantics (i.e. what they mean). A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive...

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

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...

of truth value or factual content. Despite its ambition to overhaul philosophy by mimicking the structure and process of empirical science, logical positivism...

general, truth requires a proper fit of elements within a whole system. Very often, coherence is taken to imply something more than simple logical consistency;...

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

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

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...

a compound proposition to be true, the truth values of its constituent parts must satisfy the relevant logical connectives that occur in it (most commonly:...