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
3 - Sequent Calculus Proof Rules
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 the sequent calculus as a formal system for constructing proofs and as a basis for automated proof search. It contrasts the book’s approach with Gentzen’s original formulation. The chapter details the different types of inference rules within the sequent calculus, including structural rules (weakening, contraction), identity rules (initial, cut), and introduction rules for logical connectives. It distinguishes between additive and multiplicative rules. Finally, it defines sequent calculus proofs as trees of inference rules and briefly touches upon the properties of cut elimination. Bibliographic notes point to relevant literature.
Information
- Type
- Chapter
- Information
- Proof Theory and Logic ProgrammingComputation as Proof Search, pp. 20 - 36Publisher: Cambridge University PressPrint publication year: 2025
Accessibility standard: Inaccessible, or known limited accessibility
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this book is known to have missing or limited accessibility features.
We may be reviewing its accessibility for future improvement, but final compliance is
not yet assured and may be subject to legal exceptions. If you have any questions,
please contact
accessibility@cambridge.org.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.