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Propositional Logic Part 4: Proving the Completeness Theorem for Propositional Logic
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In this video we define the value of a sentence using truth tables. Then, we prove that a sentence is true in all models exactly when the value of the sentence is true regardless of assignment. This gives us an easy way to determine the validity of a sentence: using truth tables.
0:00 Introduction
1:03 Motivation for a Syntactic Definition of Truth
4:59 Definition of Assignment
7:20 Definition of Value
11:40 Disambiguation of Syntax and Semantics
15:00 Definition of a Tautology
17:00 Statement of the Completeness Theorem
23:51 Proof of our Lemma
29:58 Proof of the Completeness Theorem
0:00 Introduction
1:03 Motivation for a Syntactic Definition of Truth
4:59 Definition of Assignment
7:20 Definition of Value
11:40 Disambiguation of Syntax and Semantics
15:00 Definition of a Tautology
17:00 Statement of the Completeness Theorem
23:51 Proof of our Lemma
29:58 Proof of the Completeness Theorem
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