Mathematical Logic

1. Related Topics
   1. Non-Classical Logic
      1. Modal Logic
         1. Syntax and Semantics
            1. Possible Worlds Semantics
            2. Kripke Frames and Models
         2. Types of Modal Logic
            1. Alethic Modalities (Necessity and Possibility)
            2. Temporal Modal Logic
            3. Deontic Logic
            4. Epistemic Logic
      2. Intuitionistic Logic
         1. Differences from Classical Logic
            1. Law of Excluded Middle
            2. Double Negation
         2. Brouwer-Heyting-Kolmogorov Interpretation
         3. Kripke Semantics for Intuitionistic Logic
         4. Applications
            1. Constructive Mathematics
            2. Type Theory
      3. Fuzzy Logic
         1. Gradual Truth Values
            1. Membership Functions
            2. Fuzzy Sets
         2. Fuzzy Logic Systems
            1. Fuzzy Rule-based Systems
            2. Fuzzy Control Systems
         3. Applications of Fuzzy Logic
            1. Control Systems
            2. Approximate Reasoning
   2. Category Theory
      1. Connections with Logic
         1. Functorial Semantics
         2. Cartesian Closed Categories
         3. Topos Theory
      2. Categorical Logic
         1. Internal Logic of a Category
         2. Categorical Interpretation of Logic Theories
         3. Adjunctions in Logic
   3. Algebraic Logic
      1. Relation Algebras
         1. Operations on Relations
            1. Composition
            2. Converse
         2. Uses of Relation Algebras
            1. Database Theory
            2. Temporal Logic
      2. Cylindric Algebras
         1. Algebraic Structures
            1. Variables and Substitution
         2. Applications of Cylindric Algebras
            1. Model Theory
            2. Representation Theory