Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Terms, Formulas, and Sequents
- 3 Sequent Calculus Proof Rules
- 4 Classical and Intuitionistic Logics
- 5 Two Abstract Logic Programming Languages
- 6 Linear Logic
- 7 Formal Properties of Linear Logic Focused Proofs
- 8 Linear Logic Programming
- 9 Higher-Order Quantification
- 10 Specifying Computations Using Multisets
- 11 Collection Analysis for Horn Clauses
- 12 Encoding Security Protocols
- 13 Formalizing Operational Semantics
- Solutions to Selected Exercises
- References
- Index
6 - Linear Logic
Published online by Cambridge University Press: 01 December 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Terms, Formulas, and Sequents
- 3 Sequent Calculus Proof Rules
- 4 Classical and Intuitionistic Logics
- 5 Two Abstract Logic Programming Languages
- 6 Linear Logic
- 7 Formal Properties of Linear Logic Focused Proofs
- 8 Linear Logic Programming
- 9 Higher-Order Quantification
- 10 Specifying Computations Using Multisets
- 11 Collection Analysis for Horn Clauses
- 12 Encoding Security Protocols
- 13 Formalizing Operational Semantics
- Solutions to Selected Exercises
- References
- Index
Summary
This chapter introduces linear logic, highlighting its unique approach to resource management. It presents sequent calculus proof systems for linear logic. The chapter discusses the polarity of logical connectives in linear logic and the concept of multi-zone sequents. It provides an informal semantics of resource consumption to illustrate the meaning of linear logic connectives. The chapter also touches upon the implementation of proof search in linear logic, mentioning techniques like lazy splitting of multisets. Bibliographic notes guide the reader to key literature on linear logic and its proof theory.
Information
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- Chapter
- Information
- Proof Theory and Logic ProgrammingComputation as Proof Search, pp. 107 - 142Publisher: Cambridge University PressPrint publication year: 2025
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