Logic for Computer Science

  1. Proof Systems for Propositional Logic
    1. Introduction to Proof Theory
      1. Syntax vs Semantics
        1. Distinction and Relationship
          1. Syntactic Proofs vs Semantic Truth
          2. Soundness and Completeness
            1. Definition of Soundness
              1. Definition of Completeness
                1. Importance in Logic Systems
              2. Natural Deduction
                1. Basic Concepts
                  1. Assumptions and Conclusions
                    1. Proof Structure
                      1. Discharge of Assumptions
                      2. Inference Rules
                        1. Introduction Rules
                          1. Conjunction Introduction
                            1. Disjunction Introduction
                              1. Implication Introduction
                                1. Biconditional Introduction
                                  1. Negation Introduction
                                  2. Elimination Rules
                                    1. Conjunction Elimination
                                      1. Disjunction Elimination
                                        1. Implication Elimination
                                          1. Biconditional Elimination
                                            1. Negation Elimination
                                          2. Proof Construction
                                            1. Forward and Backward Reasoning
                                              1. Proof Strategies
                                                1. Common Proof Patterns
                                                2. Fitch-Style Proofs
                                                  1. Structure and Notation
                                                    1. Subproofs and Indentation
                                                      1. Example Proofs
                                                    2. Sequent Calculus
                                                      1. Sequents and Interpretation
                                                        1. Definition of Sequents
                                                          1. Reading and Writing Sequents
                                                            1. Antecedent and Consequent
                                                            2. Rules of Inference
                                                              1. Initial Sequents
                                                                1. Structural Rules
                                                                  1. Weakening
                                                                    1. Contraction
                                                                      1. Exchange
                                                                      2. Logical Rules
                                                                        1. Left Rules
                                                                          1. Right Rules
                                                                        2. Cut Rule and Cut Elimination
                                                                          1. The Cut Rule
                                                                            1. Cut-Elimination Theorem
                                                                              1. Significance in Proof Theory
                                                                            2. Resolution Method
                                                                              1. Clausal Form
                                                                                1. Definition of Clauses
                                                                                  1. Converting to Clausal Form
                                                                                    1. Unit Clauses and Empty Clause
                                                                                    2. Resolution Rule
                                                                                      1. Binary Resolution
                                                                                        1. Resolving Clauses
                                                                                          1. Unification in Propositional Logic
                                                                                          2. Resolution as Refutation
                                                                                            1. Proof by Contradiction
                                                                                              1. Deriving the Empty Clause
                                                                                                1. Completeness of Resolution
                                                                                                2. Resolution Strategies
                                                                                                  1. Unit Resolution
                                                                                                    1. Input Resolution
                                                                                                      1. Linear Resolution
                                                                                                      2. Applications
                                                                                                        1. Automated Theorem Proving
                                                                                                          1. SAT Solvers
                                                                                                            1. Limitations and Strengths

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                                                                                                        2. Propositional Logic

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                                                                                                        4. First-Order Logic