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Young Won Lim5/14/18
Propositional Logic (3A)
Young Won Lim5/14/18
Copyright (c) 2015 - 2018 Young W. Lim.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".
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Logic (3A)Propositional Logic 3 Young Won Lim
5/14/18
Propositional Logic
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 4 Young Won Lim
5/14/18
Example (1)
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 5 Young Won Lim
5/14/18
Example (2)
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 6 Young Won Lim
5/14/18
Valid, Satisfiable, and Unsatisfiable Formulas
https://en.wikipedia.org/wiki/Propositional_calculus
A formula is valid iffIts truth value is T in all interpretations (tautology: ⊤)
A formula is satisfiable iffIts truth value is T in at least one interpretation
A formula is unsatisfiable iffIts truth value is F in all interpretations (contradiction: ⊥)
Logic (3A)Propositional Logic 7 Young Won Lim
5/14/18
Inference rules and axioms
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 8 Young Won Lim
5/14/18
Argument
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 9 Young Won Lim
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Terminology
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 10 Young Won Lim
5/14/18
Deductive Arguments
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 11 Young Won Lim
5/14/18
Inductive Arguments
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 12 Young Won Lim
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Validity
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 13 Young Won Lim
5/14/18
Soundness
https://en.wikipedia.org/wiki/Soundness
Logic (3A)Propositional Logic 14 Young Won Lim
5/14/18
Valid and Sound Arguments
https://en.wikipedia.org/wiki/Soundness
H 1=TH 2=T
C=T
H 2=T
F T F T F T FT F F T T F F
T T T T T T T
T T T F F F F
H 1=TH 2=T
C=F
H 2=T
a valid argument
a sound argument
a invvalid argument
Logic (3A)Propositional Logic 15 Young Won Lim
5/14/18
Logical equivalence and bi-conditionals
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 16 Young Won Lim
5/14/18
Argument Rules (1)
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 17 Young Won Lim
5/14/18
Argument Rules (2)
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 18 Young Won Lim
5/14/18
Argument Rules (3)
https://en.wikipedia.org/wiki/Propositional_calculus
Logic (3A)Propositional Logic 19 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 20 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 21 Young Won Lim
5/14/18
Modus Tollens
https://en.wikipedia.org/wiki/Modus_tollens
Logic (3A)Propositional Logic 22 Young Won Lim
5/14/18
Modus Tollens
https://en.wikipedia.org/wiki/Modus_tollens
Logic (3A)Propositional Logic 23 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 24 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 25 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 26 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 27 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 28 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Logic (3A)Propositional Logic 29 Young Won Lim
5/14/18
Modus Ponens
https://en.wikipedia.org/wiki/Modus_ponens
Young Won Lim5/14/18
References
[1] http://en.wikipedia.org/[2]