In logic, a logical constant or constant symbol of a language L {\displaystyle {\mathcal {L}}} is a symbol that has the same semantic value under every...

broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols (sometimes...

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

components (other than its logical constants). Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be...

into two sets: the logical symbols (logical constants) and the non-logical symbols. The idea behind this terminology is that logical symbols have the same...

unchanging Constant (computer programming), a value that, unlike a variable, cannot be reassociated with a different value Logical constant, a symbol in...

quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator...

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

mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given...

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

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

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...

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...

conditions a logical constant may be introduced into a new sentence of the proof. For example, the introduction rule for the logical constant " ∧ {\displaystyle...

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

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...

The axiom of determinacy The axiom of real determinacy AD+ Since 2000, logical independence has become understood as having crucial significance in the...

that can be proven in the system is logically valid with respect to the logical semantics of the system. In deductive reasoning, a sound argument is an...

In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no...

'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid...

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

language need not be symbols of anything. For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation...

language need not be symbols of anything. For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation...

regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball...

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

suffices. Other logical symbols include the following: Truth constants: T, or ⊤ for "true" and F, or ⊥ for "false". Without any such logical operators of...

plus, the increment and decrement operators in C-style languages (not in logical languages), and the successor, factorial, reciprocal, floor, ceiling, fractional...

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

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

ISBN 978-0-619-21558-3. Pudlák, Pavel (2013). "Mathematical structures". Logical foundations of mathematics and computational complexity a gentle introduction...