# logical implication

## Definitions

• WordNet 3.6
• n logical implication a logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false
• ***

## Usage

### In literature:

Science, in short, signifies a realization of the logical implications of any knowledge.
"Democracy and Education" by John Dewey
There is no ambiguous implication or logical deduction.
"The Anti-Slavery Examiner, Part 3 of 4" by American Anti-Slavery Society
There is no ambiguous implication or logical deduction.
"The Anti-Slavery Examiner, Omnibus" by American Anti-Slavery Society
There is no ambiguous implication, no logical deduction.
"Abraham Lincoln" by George Haven Putnam
Indeed, the logical implication of the teaching is the reverse of eugenic.
"Applied Eugenics" by Paul Popenoe and Roswell Hill Johnson
Everything else was implication, logic, and bluff.
"Masters of Space" by Edward Elmer Smith
In ignoring this implication, does Logic oppose this implication as erroneous?
"Logic, Inductive and Deductive" by William Minto
And if Determinists do not realise this, it is because the logical implications of their doctrines have never been fully explored.
"Determinism or Free-Will?" by Chapman Cohen
But in the doctrine of implication they are just the laws of B and C respectively, though laws of A may underlie them in a logical sense.
"Spencer's Philosophy of Science" by C. Lloyd Morgan
Knowledge, it is said, is solely a matter of implication, and logic, therefore, is the science of implication simply.
"International Congress of Arts and Science, Volume I" by Various
***

### In science:

Thus subsumption is weaker than implication. A further sign of this weakness is the fact that tautologies need not be subsume-equivalent, even though they are logically equivalent.
Least Generalizations and Greatest Specializations of Sets of Clauses
Niblett's idea that the proof is simple may be due to some confusion about the relation between Herbrand models and logical implication (which is de(cid:12)ned in terms of al l models, not just Herbrand models).
Least Generalizations and Greatest Specializations of Sets of Clauses
We now proceed to de(cid:12)ne a proof procedure for logical implication between clauses, using resolution and subsumption.
Least Generalizations and Greatest Specializations of Sets of Clauses
Since C and C are not logically equivalent under implication, there is no LGI of fD; Dg in H.
Least Generalizations and Greatest Specializations of Sets of Clauses
Using his notion of term set, he de(cid:12)nes T-implication as follows: if C and D are clauses and T is a term set of fDg by some Skolem substitution (cid:27) w.r.t. fC g, then C T-implies D w.r.t. T if I (C; T ) j= D(cid:27) . T-implication is decidable, weaker than logical implication and stronger than subsumption.
Least Generalizations and Greatest Specializations of Sets of Clauses
***