Structures for Semantics offers an advanced course in logical and mathematical techniques and structures that are used in semantics, in relation to their semantic applications. The book helps students with a background in semantics to develop their skills of formalization and it makes research in semantics accessible. Workers in other disciplines will use it to discover more about the role of formal modelling in current semantic research, and about semantics itself. Following a chapter on logic and set theory there are three parts of chapters: two pairs of chapters on partial order and equivalence relations in relation to semantic analyses of tense, partial information and vagueness; two chapters on methods for creating ordered structures in relation to intervals, events, and the semantics of change; two chapters on lattices and Boolean algebras in relation to types for noun phrases and verbs, and the semantics of plurals and mass nouns. For upper-level undergraduate students and graduate students in semantics: theoretical linguists, logicians, philosophers of language, computer scientists interested in natural language 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.
Series: Studies in Linguistics and Philosophy
Number Of Pages: 371
Published: 31st October 1991
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6
Weight (kg): 0.72