In recent years, *semantical partiality* has emerged as an important concept in philosophical logic as well in the study of natural language semantics. Despite the many applications, however, a number of mathematically intriguing questions associated with this concept have received only very limited attention.

*Partiality, Truth and Persistence* is a study in the theory of partially defined models. Langholm compares in detail the various alternatives for extending the definition of truth or falsity that holds with classical, complete models to partial models. He also investigates the monotonicity of truth and other nonexpressible conditions. These discussions culminate with a combined Lindstrom and persistence characterization theorem.

Tore Langholm is a research fellow in mathematics at the University of Oslo.

- Preface
- Introduction
- 1 Propositional Logic
- 1.1 Basic Notions
- 1.2 Compositionality
- 1.3 Encoding in Classical Logic
- 1.4 Extending the Language
- 1.5 The “Cut-and-Glue” Theorem: Statement
- 1.6 Alternative Truth Definitions
- 1.7 Predicative and Saturated Sentences

- 2 The Strong Kleene Truth Definition
- 2.1 Basic Notions
- 2.2 Interpolation
- 2.3 Domain Persistence
- 2.4 Compactness
- 2.5 Semantical Equivalence for Structures
- 2.6 The Skolem Property

- 3 Alternative Truth Definitions
- 3.1 The Generalized Strong Kleene Truth Definitions
- 3.2 Syntactic Closures
- 3.3 Neighborhood Assignments
- 3.4 The Skolem Property
- 3.5 Semantical Equivalence for Structure
- 3.6 Predictive and Saturated Formulas

- 4 Extending the Language
- 4.1 Semantical Equivalence for L ∽
- 4.2 Maximality of L ∽
- 4.3 Relation of L to L ∽
- 4.4 Maximality of L
- 4.5 Truth Functional Extentions of L
- 4.6 Other Extensions of L

- Further Directions
- References
- Index of Symbols
- General Index

1/1/1988