Material nonimplication
Encyclopedia
Material nonimplication or abjunction (latin
ab = "from", junctio =–"joining") is the negation
of implication
. That is to say that for any two proposition
s P and Q, if P does not imply Q, then P is the material nonimplication of Q.
It may be written using logical notation as:
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
ab = "from", junctio =–"joining") is the negation
Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...
of implication
Implication
Implication may refer to:In logic:* Logical implication, entailment, or consequence, a relation between statements* Material implication, or conditional implication, a binary truth functionIn linguistics, specifically in pragmatics:...
. That is to say that for any two proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
s P and Q, if P does not imply Q, then P is the material nonimplication of Q.
It may be written using logical notation as:
-
- p⊅q
- Lpq
- p↛q
Truth table
| p | q |  |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | F |
| F | F | F |