Soundness and Completeness Propositional Logic

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Soundness and Completeness Propositional Logic
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Overview
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Propositional Formulas
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Natural Deduction
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Basic Rules
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Proof
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Proof
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Reasoning vs. Reality
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Soundness, Completeness, and Auto Mechanics
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Semantics
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Truth Tables
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Meaning of a Formula
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Semantic Entailment
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Example
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Example
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Soundness and Completeness
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Soundness
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Proof Inductive Definition
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Base Case
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Induction Case
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Rule ?-i
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Rule ?-i
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Rule ?-i
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Rule -e
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Rule -e
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Rule -e
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Completeness
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Completeness Proof Structure
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Eliminating Premises
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Showing Provability
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Example
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Proof
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Negation
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Negation, Continued
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Implication
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Use of the Induction Hypothesis
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Use of the Induction Hypothesis
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Cases
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Combining Sequents
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Proof Idea
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Reintroducing Premises
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Proof
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Summary