Logic for Computer Science

  1. Advanced Topics in Logic
    1. Type Theory
      1. Simply Typed Lambda Calculus
        1. Types and Terms
          1. Typing Rules
            1. Type Checking
            2. Curry-Howard Correspondence
              1. Propositions as Types
                1. Proofs as Programs
                  1. Implications for Programming Languages
                  2. Dependent Types
                    1. Pi Types and Sigma Types
                      1. Type Families
                        1. Applications in Proof Assistants
                        2. System F
                          1. Polymorphic Types
                            1. Type Abstraction
                            2. Martin-Löf Type Theory
                            3. Temporal Logic
                              1. Linear Temporal Logic
                                1. Syntax and Semantics
                                  1. Temporal Operators
                                    1. Next Operator
                                      1. Until Operator
                                        1. Eventually Operator
                                          1. Always Operator
                                          2. Model Checking LTL
                                          3. Branching Time Logic
                                            1. Computation Tree Logic
                                              1. Path Quantifiers
                                                1. State Formulas vs Path Formulas
                                                2. Interval Temporal Logic
                                                  1. Applications
                                                    1. System Verification
                                                      1. AI Planning
                                                        1. Natural Language Processing
                                                      2. Higher-Order Logic
                                                        1. Second-Order Logic
                                                          1. Quantification over Predicates
                                                            1. Expressive Power
                                                              1. Incompleteness Results
                                                              2. Higher-Order Predicate Logic
                                                                1. Lambda Abstraction
                                                                  1. Beta Reduction
                                                                  2. Applications
                                                                    1. HOL Theorem Prover
                                                                      1. Isabelle/HOL
                                                                        1. Formalization of Mathematics
                                                                      2. Non-Classical Logics
                                                                        1. Intuitionistic Logic
                                                                          1. Constructive Proofs
                                                                            1. Brouwer-Heyting-Kolmogorov Interpretation
                                                                              1. Rejection of Law of Excluded Middle
                                                                                1. Natural Deduction for Intuitionistic Logic
                                                                                  1. Kripke Semantics for Intuitionistic Logic
                                                                                  2. Relevant Logic
                                                                                    1. Relevance Condition
                                                                                      1. Avoiding Paradoxes of Implication
                                                                                      2. Paraconsistent Logic
                                                                                        1. Handling Contradictions
                                                                                          1. Applications in AI
                                                                                          2. Fuzzy Logic
                                                                                            1. Many-Valued Logic
                                                                                              1. Fuzzy Sets and Operations
                                                                                                1. Applications in Control Systems
                                                                                                2. Quantum Logic
                                                                                                  1. Non-Distributive Logic
                                                                                                    1. Quantum Mechanics and Logic

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                                                                                                9. Applications in Database Systems

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                                                                                                1. Introduction to Logic in Computer Science