Philosophy
Non-monotonic Logic and Defeasible Reasoning
Quick fact
Classical logic is monotonic: adding premises never removes conclusions. But commonsense reasoning is non-monotonic—new information can defeat old conclusions—which is why artificial intelligence systems often use non-monotonic logics like default logic to model reasoning with incomplete information.
Why this is interesting
Every day we jump to conclusions—'Tweety flies because it's a bird'—yet a single fact ('Tweety is a penguin') changes everything. How can logic handle such defeasible steps?
Read the full explanation
Understanding Non-monotonic Logic and Defeasible Reasoning
Think of classical logic as a game of LEGO: once you build a tower, adding more blocks never makes it collapse. In formal logic, this 'monotonicity' means that if a conclusion follows from a set of premises, it still follows if you add more premises. But everyday reasoning is different. We constantly make judgments that are provisional—'Birds fly' is a good rule, but it has exceptions. If I learn that a particular bird is a penguin, I must retract the inference that it flies. This is 'defeasible reasoning': drawing a conclusion that might be defeated by further evidence. Non-monotonic logic formalizes this process. Instead of guaranteeing eternal truths, it gives us rational ways to jump to conclusions and revise them when new information arrives. The key is that the logic allows a conclusion to be withdrawn when new premises are added.
A deeper explanation
The mechanism behind non-monotonic logic is the introduction of 'defeasible rules'—inference rules that apply in typical cases but can be overridden. The most influential formalization is Reiter's default logic, which adds 'default rules' of the form: 'If A is known, and it is consistent to assume B, then conclude C.' For example: 'If something is a bird, and it is consistent to assume it can fly, then conclude it flies.' When we add the fact that Tweety is a penguin, consistency check fails, and the conclusion is blocked. Another major approach is 'preferential semantics', where conclusions are those true in all 'most preferred' models—where preferred means 'most normal' or 'most typical'. This allows reasoning about normality, despite exceptions. These systems share a core idea: inference is not monotonic, but it is still rational, governed by rules that balance consistency and typicality. They are essential for modeling commonsense reasoning in AI, legal reasoning, and any domain where knowledge is incomplete or evolving.