Default reasoning using maximum entropy and variable strength defaults

symbols are not loaded with intuitive interpretations. While it is true that a ) c is not an "-consequence of , since it is not probabilistically sound, both falsifying models of a ) c, must either falsify a ) b or b ) c; on the other hand, a ) c has a verifying model, a ^ b ^ c, which does not falsify either; this explains why a) c is an ME-consequence of (for any strength assignment). What this shows is that, under the ME approach, and in isolation, defaults do chain transitively. A similar observation is made by Kern-Isberner (1997). Obviously, other defaults which deal with the same propositions or formulæ, may cause interference which prevents this from happening, but, other things being equal, transitivity is to be expected. 5.2. Conflicting inheritance and specificity 82 What this means for Reiter and Criscuolo’s example is that, by choosing not to accept the transitive conclusion that “typically high school dropouts are employed”, they are imposing an extra constraint which implies an exceptional circumstance—that they wish to remain agnostic about a particular situation—and clearly this will need to be encoded when attempting to represent the problem using defaults. Since transitive behaviour is normal in unexceptional circumstances, it is not surprising that it is a property which has been isolated and considered important. This simple example also demonstrates that, if it is accepted that ME-entailment represents the least biased consequence relation, it can be used to discover the hidden biases which exist in one’s knowledge. Any unusual conclusions or side effects reflect differences in the problem as it has been encoded and the implicit constraints which the user has failed to encode. An example of this process is given in chapter 7.