“Material nonimplication”的意思、由来-开放百科全书

词条

Material nonimplication

释义

Definition
Truth table Logical Equivalences
Properties
Symbol
Natural language
Grammatical Rhetorical
Computer science
See also
References

Material nonimplication or abjunction (Latin ab = "from", junctio =–"joining") is the negation of material implication. That is to say that for any two propositions and , the material nonimplication from to is true if and only if the negation of the material implication from to is true. This is more naturally stated as that the material nonimplication from to is true only if is true and is false.

It may be written using logical notation as , , or "Lpq" (in Bocheński notation), and is logically equivalent to , and .

Definition

Truth table


T	T	F
T	F	T
F	T	F
F	F	F

Logical Equivalences

Material nonimplication may be defined as the negation of material implication.

In classical logic, it is also equivalent to the negation of the disjunction of and , and also the conjunction of and

Properties

falsehood-preserving: The interpretation under which all variables are assigned a truth value of "false" produces a truth value of "false" as a result of material nonimplication.

Symbol

The symbol for material nonimplication is simply a crossed-out material implication symbol. Its Unicode symbol is 8603 (decimal).

Natural language

Grammatical

Rhetorical

"p but not q."

Computer science

Bitwise operation: A&(~B)

Logical operation: A&&(!B)

References

1 : Logical connectives

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