Young Won Lim5/14/18

Propositional Logic (3A)

Young Won Lim5/14/18

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Logic (3A)Propositional Logic 3 Young Won Lim

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Propositional Logic

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 4 Young Won Lim

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Example (1)

https://en.wikipedia.org/wiki/Propositional_calculus

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Example (2)

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 6 Young Won Lim

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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

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Inference rules and axioms

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 8 Young Won Lim

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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

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Deductive Arguments

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 11 Young Won Lim

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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

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Soundness

https://en.wikipedia.org/wiki/Soundness

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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

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Logical equivalence and bi-conditionals

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 16 Young Won Lim

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Argument Rules (1)

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 17 Young Won Lim

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Argument Rules (2)

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 18 Young Won Lim

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Argument Rules (3)

https://en.wikipedia.org/wiki/Propositional_calculus

Logic (3A)Propositional Logic 19 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 20 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 21 Young Won Lim

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Modus Tollens

https://en.wikipedia.org/wiki/Modus_tollens

Logic (3A)Propositional Logic 22 Young Won Lim

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Modus Tollens

https://en.wikipedia.org/wiki/Modus_tollens

Logic (3A)Propositional Logic 23 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 24 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 25 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 26 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 27 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 28 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Logic (3A)Propositional Logic 29 Young Won Lim

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Modus Ponens

https://en.wikipedia.org/wiki/Modus_ponens

Young Won Lim5/14/18

References

[1] http://en.wikipedia.org/[2]