Nonmonotonic Logic

This Element offers a systematic introduction to nonmonotonic logic as a model of defeasible reasoning, focussing on key methodologies.

Christian Straßer (Author)

9781009598460, Cambridge University Press

Hardback, published 13 November 2025

136 pages
23.5 x 16 x 1.3 cm, 0.34 kg

Nonmonotonic logics serve as formal models of defeasible reasoning, a type of reasoning where conclusions are drawn absent absolute certainty. Defeasible reasoning takes place when scientists interpret experiments, in medical diagnosis, and in practical everyday situations. Given its wide range of applications, nonmonotonic logic is of interest to philosophy, psychology, and artificial intelligence. This Element provides a systematic introduction to the multifaceted world of nonmonotonic logics. Part I familiarizes the reader with basic concepts and three central methodologies: formal argumentation, consistent accumulation, and semantic methods. Parts II–IV provide a deeper understanding of each of these methods by introducing prominent logics within each paradigm. Despite the apparent lack of unification in the domain of nonmonotonic logics, this Element reveals connections between the three paradigms by demonstrating translations among them. Whether you're a novice or an experienced traveler, this Element provides a reliable map for navigating the landscape of nonmonotonic logic.

Introduction
Part I. Logics for Defeasible Reasoning: 1. Defeasible reasoning
2. Central concepts
3. From knowledge bases to consequences and NMLs
4. Defeasible knowledge bases
5. Methodologies for Nonmonotonic logics
6. A roadmap
Part II. Formal Argumentation: 7. Abstract argumentation
8. ASPIC+
9. Logic-based argumentation
Part III. Consistently Accumulating Defeasible Information: 10. Consistent accumulation: general setting
11. Temperate accumulation: properties and some concrete systems
12. Greedy accumulation: properties and Reiter's default logic
Part IV. Semantic Methods: 13. A semantics for defaults
14. Quantitative methods
15. A preferential semantics for some NMLs
16. Logic programming and nonmonotonic logic
Appendix A. Proofs for Part II
Appendix B. Proofs for Part III
References.

Subject Areas: Philosophy: logic [HPL]