Structures for Semantics

One: Logic and Set Theory.- 1.1. First Order Logic.- 1.1.1. Basic Concepts.- 1.1.2. Metalogic.- 1.2. Second Order Logic.- 1.2.1. Basic Concepts.- 1.2.2. The Expressive Power of Second Order Logic.- 1.3. First Order Theories.- 1.3.1. Some Examples of First Order Theories.- 1.3.2. Peano Arithmetics (PA).- 1.4. Zermelo-Fraenkel Set Theory.- 1.4.1. Basic Set Theory.- 1.4.2. The Set Theoretic Universe.- Two: Partial Orders.- 2.1. Universal Algebra.- 2.2. Partial Orders and Equivalence Relations.- 2.3. Chains and Linear Orders.- Three: Semantics with Partial Orders.- 3.1. Instant Tense Logic.- 3.2. Algebraic Semantics, Functional Completeness and Expressibility.- 3.3. Some Linguistic Considerations Concerning Instants.- 3.4. Information Structures.- 3.5. Partial Information and Vagueness.- Four: Constructions with Partial Orders.- 4.1. Period Structures.- 4.2. Event Structures.- Five: Intervals, Events and Change.- 5.1. Interval Semantics.- 5.2. The Logic of Change in Interval Semantics.- 5.3. The Moment of Change.- 5.4. Supervaluations.- 5.5. Kamp's Logic of Change.- Six: Lattices.- 6.1. Basic Concepts.- 6.2. Universal Algebra.- 6.3. Filters and Ideals.- Seven: Semantics with Lattices.- 7.1. Boolean Types.- 7.2. Plurals.- 7.3. Mass Nouns.- Answers To Exercises.- References.