Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Which are the True Defeasible Logics?

Michael J. Maher

TL;DR

This work addresses the unclear boundaries of defeasible logics by proposing a unified, well-behaved class that preserves coherence and computationally desirable properties. It formalizes defeasible theories and two key logics, ${DL}(\partial)$ and ${DL}(\partial_{||})$, and identifies problems that arise when naively extending their features. The authors introduce strict criteria for applicability conditions, stability, and a revised strong-negation principle, culminating in the notion of well-behaved defeasible logics, which are proven to be coherent. The framework is designed to be largely syntax-agnostic with respect to the defeasible theories and aims to accommodate existing logics while guiding future extensions, including distributed reasoning and connections to default and modal defeasible frameworks.

Abstract

The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new features to such logics, which have repercussions that we explore. In particular, we define a class of logics that accommodates the new logic while retaining the traditional properties of defeasible logics.

Which are the True Defeasible Logics?

TL;DR

This work addresses the unclear boundaries of defeasible logics by proposing a unified, well-behaved class that preserves coherence and computationally desirable properties. It formalizes defeasible theories and two key logics, and , and identifies problems that arise when naively extending their features. The authors introduce strict criteria for applicability conditions, stability, and a revised strong-negation principle, culminating in the notion of well-behaved defeasible logics, which are proven to be coherent. The framework is designed to be largely syntax-agnostic with respect to the defeasible theories and aims to accommodate existing logics while guiding future extensions, including distributed reasoning and connections to default and modal defeasible frameworks.

Abstract

The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic introduced new features to such logics, which have repercussions that we explore. In particular, we define a class of logics that accommodates the new logic while retaining the traditional properties of defeasible logics.
Paper Structure (14 sections, 14 theorems, 5 equations)

This paper contains 14 sections, 14 theorems, 5 equations.

Table of Contents

  1. Introduction
  2. Defeasible Logics
  3. Defeasible Theories
  4. The Logic ${ DL}(\partial)$
  5. The Logic ${ DL}(\partial_{||})$
  6. Properties of Defeasible Logics
  7. The Principle of Strong Negation
  8. Problems
  9. What is a defeasible logic?
  10. Language of Applicability Conditions
  11. Stability
  12. Revision of Strong Negation
  13. Well-behaved Defeasible Logics
  14. Conclusion

Key Result

proposition 1

There is an inference rule that is applicability persistent but not stable.

Theorems & Definitions (29)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • proposition 1
  • proof
  • proposition 2
  • proof
  • proposition 3
  • proof
  • ...and 19 more