lecture 5 & 6yzhan442/teaching/cse259/lectures/cse259-… · cse 259 logic in computer science...
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Lecture 5 & 6
Natural deduction for propositional logic
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Natural Deduction Rules: Implication Introduction
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Implication Introduction Examples
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Implication Introduction Examples
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Lewis Carroll Puzzle (I) Derive an inescapable conclusion using all of these: a) All babies are illogical b) Nobody is despised who can manage a crocodile c) Illogical persons are despised
• B: it is a baby • L: it is logical • M: it can manage a crocodile • D: it is despised
a) 𝐵→¬𝐿 b) 𝑀→¬𝐷 c) ¬𝐿→𝐷
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Announcement
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• 1. Homework 2: comments on Blackboard, later will be paper-based, tonight • 2. Recitation: attend your own session unless there is a reason (in which case you
need to inform your TA (Arpit) to avoid points being deducted) • 3. Homework should be prepared in Latex on Overleaf; 50% deduction this time. • 4. Homework 3 will be there by Friday. • 5. First quiz: Monday (Feb 6) • 6. Piazza registration: 37 already registered.
CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Natural Deduction Rules: Disjunction
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Natural Deduction Rules: Disjunction
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Natural Deduction Rules: Disjunction • Example: (𝑝∨𝑞)∨𝑟⊢𝑝∨(𝑞∨𝑟)
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Natural Deduction Rules: Disjunction • Example: (𝑝∨𝑞)∨𝑟⊢𝑝∨(𝑞∨𝑟)
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Natural Deduction Rules: Negation
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Natural Deduction Rules: Negation
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CSE 259 Logic in Computer Science (Spring 2017) – Yu (“Tony”) Zhang [Slides adapted from CSE 294 Logic in Computer Science – Joohyung Lee]
Lewis Carroll Puzzle (I) Derive an inescapable conclusion using all of these: a) All babies are illogical b) Nobody is despised who can manage a crocodile c) Illogical persons are despised
• B: it is a baby • L: it is logical • M: it can manage a crocodile • D: it is despised
a) 𝐵→¬𝐿 b) 𝑀→¬𝐷 c) ¬𝐿→𝐷
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