Lambda the Ultimate

Inconsistency Robustness is not limited to belief revision.

As stated in the call:

Inconsistency Robustness 2011
Stanford University
August 16-18, 2011

Inconsistency robustness is information system performance in the face of continually pervasive inconsistencies---a shift from the previously dominant paradigms of inconsistency denial and inconsistency elimination attempting to sweep them under the rug.

Inconsistency robustness differs from previous paradigms based on belief revision, probability, and uncertainty as follows:
• Belief revision: Large information systems are continually, pervasively inconsistent and there is no way to revise them to attain consistency.
• Probability and fuzzy logic: In large information systems, there are typically several ways to calculate probability. Often the result is that the probability is both close to 0% and close to 100%!
• Uncertainty: Resolving uncertainty to determine truth is not a realistic goal in large information systems.

I read the call, and I interpreted the descriptions of belief revision, probability, fuzzy logic, and uncertainty given there as saying that those frameworks don't allow for inconsistency (the mathematical theory of probability certainly is). In particular, the sentence "Belief revision: Large information systems are continually, pervasively inconsistent and there is no way to revise them to attain consistency" seems to suggest that existing theories of belief revision cannot be applied where there is inconsistency . In contrast, Harman argues that a theory of logical entailment and are a theory of reasoning and belief revision should be two different things, with the latter often involving provisional assumption and inconsistency out of practical necessity. Dr Hewitt, I understand that you prefer to take a different path, allowing for inconsistency within a logic of entailment. Nevertheless, the conference program seemed to aim at a very broad scope and, if nothing else, Harman provides lots of good examples of "phase transition" type reasoning that various theories that may parallel phenomena found in the target domains of many approaches.

John Pollock is another philosopher who has done a lot of work on defeasible reasoning. His work is more formal an AI focused than Harman's.

Classical belief revision attempted to attain consistency by revising inconsistent theories. However, large information systems are perpetually and pervasively inconsistent.

Inconsistency robust logics have been developed because it is not safe to use classical logic for inconsistent information. For example, see the following:
Common sense for concurrency and inconsistency robustness using Direct Logic(TM) and the Actor Model

Nice links. Thank you, Josh.

Josh, if you like reading about this stuff, then you might like reading Erik Mueller's Commonsense Reasoning, too. Erik's goal was to axiomatize reasoning about subject matter.

If I understand Carl's criticisms of the other stuff, then this would also not qualify as "inconsistency robust" work.

Nevertheless, I found Erik's work, especially his test cases for his theory, very compelling. More mathematicians should demonstrate their frameworks in this way! Sounds from your comments that Harman has some test case rigor as well. I'll check it out.