Implies Grice

From:

Weisstein, Eric W. "Implies."
From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/Implies.html

Weisstein writes:

""Implies" is the connective in propositional
calculus which has the meaning "if p, q" In
formal terminology, the term "conditional" is often
used to refer to this connective
(Mendelson 1997, p. 13)."

"The symbol used to denote "implies" is [)]"
(Carnap 1958, p. 8; Mendelson 1997, p. 13), or >."

"The Mathematica command Experimental`ImpliesRealQ[ineqs1, ineqs2]
can be used to determine if the system of real algebraic equations
and inequalities ineqs1 implies the system of real
algebraic equations and inequalities ineqs2."

"In classical logic, p)q is an abbreviation ~pvq, where ~ denotes NOT
and v denotes OR (though this is not the case, for example, in intuitionistic logic)."

vide Dummett.

") is a binary operator that is implemented in Mathematica as
Implies[A, B], and can not be extended to more than
two arguments."

" ) has the following truth table (Carnap 1958, p. 10; Mendelson 1997, p. 13).
T T T
T F F
F T T
F F T
If p ) q and q ) p, then p and q are said to be equivalent, a relationship which is written symbolically as p )( q (Carnap 1958, p. 8)."

SEE ALSO: Connective, Equivalent, Exists, For All, Quantifier
REFERENCES:
Carnap, R. Introduction to Symbolic Logic and Its Applications.
New York: Dover, p.8, 1958.
Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.