algorithm, validity, predicate logic

An Algorithm for Evaluating the Validity of Singly-Quantified Monadic Predicate Logic Arguments Justine Leon A. Uro E-mail: justineuro@yahoo.com

An Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example/Formal Proof (  x) ( Px  Rx ) (  x) (  Rx  Qx  (  x) (Qx   Px) Q.E.D. 9. 8 E.G. 9.  (  x) (Qx   Px) 8. 6,7 Conj. 8. Qy   Py 7. 4,5 M.T. 7.  Py 6. 3 Simp. 6. Qy 5. 3 Simp. 5.  Ry 4. 1 U.I. 4. Py  Ry 3. 2 E.I. 3.  Ry  Qy 2. premise 2. (  x) (  Rx  Qx ) 1. premise 1. (  x) ( Px  Rx ) Reasons |  (  x) (Qx   Px) Steps

Step 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2 ,[object Object],[object Object],0 0 1 0 0 0 8 0 0 1 1 0 0 7 1 1 1 0 1 0 6 1 0 1 1 1 0 5 0 0 0 0 0 1 4 0 0 1 1 0 1 3 0 1 0 0 1 1 2 0 0 1 1 1 1 1 Q  P  R  Q P  R R Q P       Object Types

Step 3 ,[object Object],[object Object],0 0 1 0 0 0 8 0 0 1 1 0 0 7 1 1 1 0 1 0 6 1 0 1 1 1 0 5 0 0 0* 0 0 1 4 0 0 1 1 0 1 3 0 1 0* 0 1 1 2 0 0 1 1 1 1 1 Q  P  R  Q P  R R Q P       Object Types

Step 4 ,[object Object],[object Object],0 0 1 0 0 0 8 0 0 1 1 0 0 7 1* 1 1 0 1 0 6 1* 0 1 1 1 0 5 0 0 1 1 0 1 3 0 0 1 1 1 1 1 Q  P  R  Q P  R R Q P       Object Types

Step 5 ,[object Object],0 0 1 0 0 0 8 1 0 0 1 1 0 0 7 0 0 1 1 0 1 3 0 0 1 1 1 1 1 Q  P  R  Q P  R R Q P       Object Types

Step 6 ,[object Object],0 0 1 0 0 0 8 0 0 1 1 1 1 0 0 1 1 0 0 7 0 0 1 1 0 1 3 0 0 1 1 1 1 1 Q  P  R  Q P  R R Q P       Object Types

Step 7 ,[object Object],[object Object],[object Object],[object Object],[object Object],For this particular example, Rule II is applicable and we conclude that the argument is valid (of course, the formal proof presented earlier already shows this). 0 0 1 0 0 0 8 0 0 1 1 1 1 0 0 1 1 0 0 7 0 0 1 1 0 1 3 0 0 1 1 1 1 1 Q  P  R  Q P  R R Q P       Object Types

algorithm, validity, predicate logic

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