Propositional Logic (3A) - Wikimedia · 14/05/2018  · Logic (3A) Propositional Logic 3 Young Won...

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Young Won Lim 5/14/18 Propositional Logic (3A)

Transcript of Propositional Logic (3A) - Wikimedia · 14/05/2018  · Logic (3A) Propositional Logic 3 Young Won...

Page 1: Propositional Logic (3A) - Wikimedia · 14/05/2018  · Logic (3A) Propositional Logic 3 Young Won Lim 5/14/18 Propositional Logic

Young Won Lim5/14/18

Propositional Logic (3A)

Page 2: Propositional Logic (3A) - Wikimedia · 14/05/2018  · Logic (3A) Propositional Logic 3 Young Won Lim 5/14/18 Propositional Logic

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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Propositional Logic

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

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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

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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: ⊥)

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Inference rules and axioms

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

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Argument

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

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Terminology

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

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Deductive Arguments

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

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Inductive Arguments

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

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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

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Logical equivalence and bi-conditionals

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

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Argument Rules (1)

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

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Argument Rules (2)

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

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Argument Rules (3)

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

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Modus Ponens

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

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Modus Ponens

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

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Modus Tollens

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

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Modus Tollens

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

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Modus Ponens

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

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Modus Ponens

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

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Modus Ponens

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

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Modus Ponens

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

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Modus Ponens

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

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Modus Ponens

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

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Modus Ponens

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

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References

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


Propositional Logic - Engineeringlucia/courses/2101-10/... · Propositional Logic Basics Propositional Equivalences Normal forms Boolean functions and digital circuits Propositional

Propositional Logic - Engineeringlucia/courses/2101-10/... · Propositional Logic Basics Propositional Equivalences Normal forms Boolean functions and digital circuits Propositional

1 Propositional Logic Introduction. 2 What is propositional logic? Propositional Logic is concerned with propositions and their interrelationships.

1 Propositional Logic Introduction. 2 What is propositional logic? Propositional Logic is concerned with propositions and their interrelationships.

Propositional Logic - Open Logic Projectbuilds.openlogicproject.org/content/propositional-logic/... · 2020-05-15 · propositional logic we leave out of consideration any further

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Arti cial Intelligence - cms.sic.saarland · Introduction Propositional Logic Resolution Wumpus ConclusionReferences Propositional Logic and Its Applications!Propositional logic =

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Propositional Logic - Brooklyn Collegechipp/cis32/lectures/Lecture...Propositional Logic • The simplest, and most abstract, logic we can study is called propositional logic. •

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First-Order Logic. Pros and cons of propositional logic Propositional logic is declarative Not procedural Propositional logic allows partial/disjunctive/negated.

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The Foundation: Logic Propositional Logic, Propositional Equivalence Muhammad Arief download dari .

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Propositional Logic - im.ntu.edu.tw

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12 Propositional Logic

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Propositional Logic – Language - Brandeiscs112/readings2008/PropositionalLogic.pdfInput A propositional logic formula F. Output A propositional logic formula G in conjunctive normal

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