# Volume II: Predicate Logic

- Page ID
- 1799

The first part of Volume II lays out predicate logic, including identity, functions, and definite descriptions. The second part introduces metatheory, including mathematical induction, soundness, and completeness. A predicate is commonly understood to be a Boolean-valued function P: X→ {true, false}, called the predicate on X. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory.

- 1: Predicate Logic - Syntax
- 2: Predicate Logic - Semantics and Validity
- 3: More about Quantifiers
- 4: Transcription
- 5: Natural Deduction for Predicate Logic - Fundamentals
- 6: More on Natural Deduction for Predicate Logic
- 7: Truth Trees for Predicate Logic - Fundamentals
- 8: More on Truth Trees for Predicate Logic
- 9: Identity, Functions, and Definite Descriptions
- 10: Metatheory - The Basic Concepts
- 11: Mathematical Induction
- 12: Soundness and Completeness for Sentence Logic Tree
- 13: Soundness and Completeness for Sentence Logic Derivation
- 14: Compactness, and Generalization to Infinite Sets of Premises
- 15: Interpretations, Soundness, and Completeness for Predicate Logic

### Contributors

Paul Teller (UC Davis). The Primer was published in 1989 by Prentice Hall, since acquired by Pearson Education. Pearson Education has allowed the Primer to go out of print and returned the copyright to Professor Teller who is happy to make it available without charge for instructional and educational use.