Tell us about Defeasible Reasoning in a few paragraphs
Ronald Loui
Ronald Loui
Ronald Loui
Published May 27, 2026
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Defeasible reasoning? From HLA Hart in legal philosophy to Ladd, Chisholm, and Pollock in epistemology, to nonmonotonic reasoning in AI starting with Doyle after McCarthy and Hayes and a few hundred others, and social construction in the hands of Nick Rescher. Probably what the post-Russell Wittgenstein had in mind.

So a big deal, right? But simple.

Most reasoning is defeasible. It's also mostly fallible (don't be so sure, feel free to use probability or some measure of confidence/belief), and corrigible (don't be afraid to revise, for example, when new observation arrives or new evidence changes the effect of probability conditioning).

So defeasibility is just one main way of escaping deductive logic. That "if p then q; p; therefore q" from freshman logic. The only worlds that really behave that way are computer circuits and mathematical proof. Everything else is something else, and often that something else is defeasible.

Defeasible simply means that if you say "if p then q", there might be an "unless" hiding somewhere. Unless r. If true, r can rebut or undercut the p-then-q rule. So it's actually an artifact of writing rules in text form. Something about the short-form of the rule means it does not carry its exceptions with it. You can see why legal reasoning has defeasible reasoning all over it. But so does analogy. And decision. And probability. Yes, to come up with a probability, that inference is probably fallible (meta-probability or confidence interval), corrigible (can be revised), and defeasible (subject to further on-paper analysis).

So you can defease/defeat an inference just by looking around at your other rules? Yes.

This is why we say defeasibility is about the nonlocality of textual respresentation, and computation upon the small pieces.

Imagine if you had to say all qualifiers explicitly. "if p and not-r then q". Even Hart early on realized this is not the same as "r defeases if-p-then-q." Why? Because you might not have computed the truth value of r. So before you do that, you are entitled to jump to the conclusion of q when p obtains. But be ready to retract it as you think harder. It's a gamble but it pays better than waiting for all r to settle.

So belief revision with no change of sensory input? Exactly.

Does it really happen? It's the basis of argument and dialectic (debate). It is how you get pro vs con in a process of justification. People who try to get there with deductive (mathematical) logic get as far as AGM (Peter and David were very nice to me!), or the obligation games, or so-called dynamic and paraconsistent logics. It's just cleaner to keep track of the inferences that get demoted, defused, deprecated, ... lots of d-words ..., annulled, overridden, rescinded, voided, etc. -- than to try to retract inferences without that gooooooood logging and tracing.

That's it. The brouhaha was over writing a clean mathematical system that modeled the phenomenon. People wanted to stay close to existing logics. But mostly the advance, which I got from Kyburg, was to step away from the logics, move to a meta-language where the derivations are the objects of discussion, and don't worry about the kinds of things logicians like, such as graphs and sets and tables for "semantics" (just a redundant structure, not actually meaning!).

There's also the question of specificity. I say penguins don't fly because penguin is more specific than bird. Some say that this preference is extra knowledge, not part of the argument system. My favorite colleagues in Europe all think it's extra knowledge. Can you believe that? I love them, but that's too timid. Penguin-based arguments defeat bird-based arguments, period!

Defeasibility opens a lot of modeling in legal philosophy, such as reasoning from precedent. But analogy works the same way. By the way, the more specific analogy defeats the less specific. Sorry, but in the .001% of cases where that's not right, you can ... write another defeater. We're talking about having the right default behavior. If some choice happens 99% of the time, make that the default and make the exception require the extra effort.

Kyburg was clear that formal languages win or lose on convenience to real users. They aren't right or wrong on objective grounds. Do people want to use specification languages where you can get to a tentative conclusion before doing exhaustive search and computation? Of course they do.

Really one of the most rewarding sights in the history of defeasibility was seeing Baude and Sachs (worked with Sachs when he was a high school freshman!) cite our work in their theory of interpretation of the US Constitution, in a big Harvard Law Review paper. Their bigger picture was about canonical background rules and burdens that are part of the meaning of text. Clever. They might not have needed the defeasibility or dialectic specifically (ha ha), but it sure helps paint the picture.

The freshman logic course you take with De Morgan's rule, the Russell-Frege conditional, and two-valued truth is doing a great disservice to understanding how inference actually works. It's sad, but won't be fixed any time soon. I'd prefer they just teach people probabilistic reasoning as the default and let Comp Eng and Pure Maths people have their old man logic as an exceptional case.