Deduction

Inference by Hypothetical Proposition

 

For those of you working on AI engines, here is a starting set of deductive processes.
P, q, r, and s are propositions. > means implies, - means not, v means or, & means and.
These methods can be used to create or validate arguments, or infer propositions.

 

Name	Rule
Modus Ponens	p > q, p; therefore q
Modus Tollens	p > q, -q; therefore -p
Chain	p > q, q > r; therefore p > r
Disjunctive1	p v q, p; therefore -q
Disjunctive2	p v q, q; therefore -p
Addition1	p; therefore p v q
Addition2	q; therefore p v q
Conjunctive1	-(p & q), p; therefore -q
Conjunctive2	-(p & q), q; therefore -p
Simplification1	(p & q); therefore p
Simplification2	(p & q); therefore q
Adjunction	p, q; therefore p & q
Reductio1	p > -p; therefore -p
Reductio2	p > (q & -q); therefore -p
Complex constructive	p > q, r > s, p v r; therefore q v s
Complex destructive	p > q, r > s, -q v -s; therefore -p v -r
Simple constructive	p > q, r > q, p v r; therefore q
Simple destructive	p > q, p > r, -q v -r; therefore -p

 

Applied Categorical Dilemma rules

• Jane is a Human. Humans are male or female, then remember Jane is male or female.

• if Jane is male and Jane is male or female then forget Jane is male or female.

• if Jane is female and Jane is male or female then forget Jane is male or female.

• if Jane is not male and Jane is male or female then remember Jane is female and forget Jane is male or female and forget Jane is not male.

• if Jane is not female and Jane is male or female then remember Jane is male and forget Jane is male or female and forget Jane is not female.

 

Creating and resolving a dilemma or disjunction is the other side of the opposition situation. The question is, do we report or respond to the discovery of the dilemma or just remember it until more information is provided to resolve the issue?  Here are some possible conversations.   T is the tester and R is the responder.

 

Test 1: report dilemma

Given: humans are male or female.

T: Jane is human.

R: Jane is male or female.

 

Test 2: ask for resolution of dilemma

Given: humans are male or female.

T: Jane is human.

R: Is Jane is male or female?

T: Jane is female.

R: Jane is female.

T: describe Jane.

R: Jane is a female human.

 

Test 3: recall dilemma

Given: humans are male or female.

T: Jane is human.

R: Jane is human.

T: describe Jane.

R: Jane is a male or female human.

 

Test 4: resolve dilemma with positive

Given: humans are male or female.

T: Jane is human.

R: Jane is human.

T: Jane is female.

R: Jane is female.

T: describe Jane.

R: Jane is a female human.

 

Test 5: resolve dilemma with negative

Given: humans are male or female.

T: Jane is human.

R: Jane is human.

T: Jane is not male.

R: Jane is not male.

T: describe Jane.

R: Jane is a female human.