Book contents
- Frontmatter
- Contents
- List of Boxes
- Preface
- Part I Introduction
- Part II Action Notation
- Part III Semantic Descriptions
- Part IV Conclusion
- Appendices
- Appendix A AD Action Semantics
- Appendix B Action Notation
- Appendix C Operational Semantics
- Appendix D Informal Summary
- Appendix E Data Notation
- Appendix F Meta-Notation
- Appendix G Assessment
- Bibliography
- Symbol Index
- Concept Index
Appendix F - Meta-Notation
Published online by Cambridge University Press: 19 January 2010
- Frontmatter
- Contents
- List of Boxes
- Preface
- Part I Introduction
- Part II Action Notation
- Part III Semantic Descriptions
- Part IV Conclusion
- Appendices
- Appendix A AD Action Semantics
- Appendix B Action Notation
- Appendix C Operational Semantics
- Appendix D Informal Summary
- Appendix E Data Notation
- Appendix F Meta-Notation
- Appendix G Assessment
- Bibliography
- Symbol Index
- Concept Index
Summary
The meta-notation used in this book consists of positive Horn clauses, constraints, and modules, together with some convenient abbreviations.
The informal summary of the meta-notation given in this Appendix provides a concise explanation of each construct.
The description of the formal abbreviations used in the meta-notation reduces the metanotation to a simple kernel.
A context-free grammar specifies the abstract syntax of the meta-notation, and suggests its concrete syntax.
The logic used for reasoning about the meta-notation consists of the standard inference rules for Horn clause logic with equality, together with some Horn clause axioms.
The formal semantics of the meta-notation is, unfortunately, out of the scope of this book.
Informal Summary
Meta-notation is for specifying formal notation: what symbols are used, how they may be put together, and their intended interpretation.
Our meta-notation here supports a unified treatment of sorts and individuals: an individual is treated as a special case of a sort. Thus operations can be applied to sorts as well as individuals. A vacuous sort represents the lack of an individual, in particular the undefined result of a partial operation. Sorts may be related by inclusion; sort equality is just mutual inclusion. But a sort is not determined just by the set of individuals that it includes: it has an intension, stemming from the way it is expressed.
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- Information
- Action Semantics , pp. 336 - 346Publisher: Cambridge University PressPrint publication year: 1992