Now the impossible proposition that A ∧ ¬A just is the inconsistent set {{w1, w2}, {w3, w4, w5}}, whereas the impossible proposition that B ∧ ¬B just is the inconsistent set {{w2, w3, w4}, {w1, w5}}; and these are distinct inconsistent sets of sets of worlds (they are sets of mutually disjoint sets of genuine worlds).
To achieve this, we employ an abstract consequence operation to "look beneath the water level", generalising the minimal inconsistent set concept and the related free formula notion.
Though the issue is too technical to be addressed here, and more appropriately dealt with in the entries on paraconsistent logic and inconsistent mathematics, the reader can consult Routley, 1979, Brady, 1989, for classical inconsistent set theories, and Weber, 2010b, 2012, for important recent results in the field.
On the other hand, a "might -counterfactual is true in a world w iff not every way of adding as might -counterfactuale antecedent as consistruey allows reaches a point where adding the consequent world result in an inconsistent set".
Finally, we show how inconsistency measures based on hitting sets of minimal inconsistent sets can be extended using hitting sets of DMUSes.
Minimal inconsistent sets have been the main tool to localise inconsistency, but we argue that they are like the exposed part of an iceberg, failing to capture contradictions hidden under the water.
Shouldn't there be a single set of rules for describing it, rather than two inconsistent sets?
However, environmental groups claim the move would water down protections, create a complex, inconsistent set of laws across the country and do little to aid business.
Neither black nor white in the Jim Crow South, the Chinese navigated a confusing, sometimes inconsistent set of laws and social mores.
The N.B.A.-inspired format consisted of four 18-minute quarters, complete with timeouts and land-, pier- and water-bound coaches shouting instructions and warning when an inconsistent set of waves rolled forth from the glassy water.
