For other logical symbols, see List of logic symbols.
Logical connectives
AND
, , , ,
equivalent
, ,
implies
, ,
NAND
, , ,
nonequivalent
, ,
NOR
, ,
NOT
, , ,
OR
, , ,
XNOR
XOR
,
converse
, ,
Related concepts
Propositional calculus
Predicate logic
Boolean algebra
Truth table
Truth function
Boolean function
Functional completeness
Applications
Digital logic
Programming languages
Mathematical logic
Philosophy of logic
Category
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Hasse diagram of logical connectives.
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classical compositional semantics with a robust pragmatics.
A logical connective is similar to, but not equivalent to, a syntax commonly used in programming languages called a conditional operator.[1][better source needed]
^Cogwheel. "What is the difference between logical and conditional /operator/". Stack Overflow. Retrieved 9 April 2015.
and 26 Related for: Logical connective information
logic, a logicalconnective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used...
) is the truth-functional operator of conjunction or logical conjunction. The logicalconnective of this operator is typically represented as ∧ {\displaystyle...
disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logicalconnective typically notated as ∨...
false when P {\displaystyle P} is true. Negation is thus a unary logicalconnective. It may be applied as an operation on notions, propositions, truth...
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(often shortened as "iff") is paraphrased by the biconditional, a logicalconnective between statements. The biconditional is true in two cases, where...
definition, this approach to logicalconnectives permits the examination of structurally identical propositional forms in various logical systems, where somewhat...
types of logical constants are logicalconnectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant...
sentence to create a new sentence. A logicalconnective, or propositional connective, is a kind of sentential connective with the characteristic feature that...
Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation...
mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logicalconnective used to...
primitive connectives can be alternatively constructed. These axiom schemata are also used in the predicate calculus, but additional logical axioms are...
logical terms it contains which are logicalconnectives (e.g. "or", "and", and "nor"). Not all logical truths are tautologies of such a kind. Logical...
example, the expression " p ∧ q {\displaystyle p\land q} " uses the logicalconnective ∧ {\displaystyle \land } (and). It could be used to express a sentence...
linguistics, a word or phrase like "therefore" or "in other words". LogicalconnectiveConnective (botany), in the stamen of flowers, the sterile tissue that...
Logical consequence (also entailment) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement...
exactly one truth value which is either true or false, and every logicalconnective is truth functional (with a correspondent truth table), thus every...
In logic, a functionally complete set of logicalconnectives or Boolean operators is one that can be used to express all possible truth tables by combining...
operators of propositional logic are: The logical NOR, taken by itself, is a functionally complete set of connectives. This can be proved by first showing...
gate whose function is the logical complement of the Exclusive OR (XOR) gate. It is equivalent to the logicalconnective ( ↔ {\displaystyle \leftrightarrow...
either true or false, the meanings of these logicalconnectives often have the meaning of their logical counterparts. However, with descriptions of behavior...
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...
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...
disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs...
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