"Logical conditional" redirects here. For other related meanings, see Conditional statement.
Not to be confused with Material inference or Material implication (rule of inference).
Material conditional
IMPLY
Definition
Truth table
Logic gate
Normal forms
Disjunctive
Conjunctive
Zhegalkin polynomial
Post's lattices
0-preserving
no
1-preserving
yes
Monotone
no
Affine
no
v
t
e
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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The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum.[citation needed]
Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language.
and 26 Related for: Material conditional information
The materialconditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol → {\displaystyle \rightarrow...
a conditional, and proves that the antecedent leads to the consequent Strict conditional, in philosophy, logic, and mathematics Materialconditional, in...
A conditional statement may refer to: A conditional formula in logic and mathematics, which can be interpreted as: Materialconditional Strict conditional...
The paradoxes of material implication are a group of true formulae involving materialconditionals whose translations into natural language are intuitively...
logical connective of modal logic. It is logically equivalent to the materialconditional of classical logic, combined with the necessity operator from modal...
language. They were first discussed as a problem for the materialconditional analysis of conditionals, which treats them all as trivially true. Starting in...
Conditional sentences are natural language sentences that express that one thing is contingent on something else, e.g. "If it rains, the picnic will be...
truth value of the consequent. In essence, a conditional statement, that is based on the materialconditional, is true when the antecedent ("Tokyo is in...
connective is biconditional (a statement of material equivalence), and can be likened to the standard materialconditional ("only if", equal to "if ... then")...
identified indicative conditionals with the logical operation known as the materialconditional. According to the materialconditional analysis, an indicative...
expressions P, Q have side effects. Also, a conditional, which in some sense corresponds to the materialconditional connective, is essentially non-Boolean...
the materialconditional, since the natural language conditional is not the materialconditional. (See also the paradoxes of the materialconditional for...
others Materialconditional (also material implication), a logical connective and binary truth function typically interpreted as "If p, then q" Material implication...
The conditional mood (abbreviated cond) is a grammatical mood used in conditional sentences to express a proposition whose validity is dependent on some...
the only case where a logical biconditional is different from a materialconditional is the case where the hypothesis (antecedent) is false but the conclusion...
connective introduced by Alonzo Church a rule in classical logic that the materialconditional ¬p → q is equivalent to the disjunction p ∨ q, so that these two...
Material implication may refer to: Materialconditional, a logical connective Material implication (rule of inference), a rule of replacement for some...
antecedent is false. The ordinary indicative conditional has somewhat more structure than the materialconditional. For instance, although the first is the...
In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome...
of material implication (a materialconditional is equivalent to the disjunction of the negation of its antecedent and its consequence) and material equivalence...
In logic, the corresponding conditional of an argument (or derivation) is a materialconditional whose antecedent is the conjunction of the argument's...
\to } \to or \rightarrow ⊃ {\displaystyle \supset } \supset materialconditional (material implication) implies, if P then Q, it is not the case that P...
Wiktionary, the free dictionary. Condition or conditions may refer to: Materialconditional, a logical connective used to form "if...then..." statements Necessary...
premise is a conditional ("if–then") claim, namely that P implies Q. The second premise is an assertion that P, the antecedent of the conditional claim, is...
truth-functional interpretation of the materialconditional by introducing the additional requirement of relevance: for the conditional to be true, its antecedent...
as protective as a legally mandated OEL for the bulk form of the material (conditional recommendation, low-quality evidence). If specific OELs for MNMs...
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