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Formal Logic Mathematical Structures for Computer Science Chapter 1 Copyright  © 2006 W.H. Freeman & Co. MSCS Slides Formal Logic
Propositional Logic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Valid Argument ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Valid Argument ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Rules for Propositional Logic ,[object Object],Work only in one direction Truth preserving rules Allows new wffs  to be derived Allows individual wffs to be rewritten Inference Rules Equivalence Rules
Equivalence Rules ,[object Object],[object Object],[object Object],Equivalance - equ (P    Q) Λ ( Q    P) P  Q Double Negation- dn (R  )  R implication - imp R   V S R    S De-Morgan’s Laws De-Morgan R   Λ S  R   V S  (R V S)    (R Λ S)  Associative- ass R Λ (S Λ Q) R V (S V Q) (R V S) V Q  (R Λ S) Λ Q Commutative - comm S V R R V S Abbreviation for rule Equivalent  to Expression
Inference Rules ,[object Object],[object Object],Addition- add R  V S R Simplification- sim R, S R  Λ S Conjunction-con R  Λ S R,  S Modus Tollens- mt R  R    S, S  Modus Ponens- mp S R, R    S Abbreviation for rule Can Derive From
Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Deduction Method ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
More Inference Rules ,[object Object],Distributive - dist (P V Q)  Λ  (P  V  R) P V (Q  Λ  R) Distributive - dist (P  Λ  Q) V (P  Λ  R) P  Λ  (Q V R) Inconsistency - inc Q P, P  Exportation - exp P    (Q   R) (P  Λ  Q)    R Self-reference - self P P V P Self-reference - self P  Λ  P P Contraposition- cont P    Q Q      P  Contraposition- cont Q      P    P    Q Disjunctive syllogism- ds Q P V Q, P    Hypothetical syllogism- hs P    R P    Q, Q    R Name / Abbreviation Can Derive From
Proofs of inference rules ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Proofs using Propositional Logic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
More Proofs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Proof Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Proving Verbal Arguments ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Verbal Argument Proof ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Class Exercise ,[object Object],[object Object],[object Object],[object Object],[object Object]
Class Exercise ,[object Object],[object Object]

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CPSC 125 Ch 1 sec 2

  • 1. Formal Logic Mathematical Structures for Computer Science Chapter 1 Copyright © 2006 W.H. Freeman & Co. MSCS Slides Formal Logic
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