Concepts
Defeasible logic is a non-monotonic reasoning system. This chapter introduces the core concepts you need to understand Spindle.
Classical vs. Defeasible Logic
Classical (Monotonic) Logic:
- Once proven, always proven
- Adding facts only adds conclusions
- Cannot handle exceptions
Defeasible (Non-Monotonic) Logic:
- Conclusions are tentative
- New evidence can defeat existing conclusions
- Handles exceptions naturally
The Tweety Problem
The motivating example for defeasible logic:
Tweety is a bird. Tweety is a penguin. Birds fly. Penguins don’t fly. Does Tweety fly?
Classical logic produces a contradiction. Defeasible logic resolves it by recognizing that “penguins don’t fly” is a more specific rule that should override “birds fly.”
f1: >> bird
f2: >> penguin
r1: bird => flies
r2: penguin => -flies
r2 > r1
Result: Tweety doesn’t fly.
Key Terminology
| Term | Definition |
|---|---|
| Literal | An atomic proposition, possibly negated (e.g., flies, -flies) |
| Rule | A conditional statement with body and head |
| Theory | A collection of rules and superiority relations |
| Conclusion | A proven literal with a provability level |
| Defeat | When one rule blocks another’s conclusion |
| Superiority | A preference relation between rules |
Chapters
- Rules and Facts - The four rule types
- Conclusions - Understanding +D, -D, +d, -d
- Superiority - Resolving conflicts
- Negation - Strong negation in Spindle