| Abstract | Numerous logics have been developed for reason-ing about inconsistency which differ in (i) the logic
to which they apply, and (ii) the criteria used to
draw inferences. In this paper, we propose a gen-
eral framework for reasoning about inconsistency
in a wide variety of logics including ones for which
inconsistency resolution methods have not yet been
studied (e.g. various temporal and epistemic log-
ics). We start with Tarski and Scott’s axiomatiza-
tion of logics, but drop their monotonicity require-
ments that we believe are too strong for AI. For
such a logic L, we define the concept of an option.
Options are sets of formulas in L that are closed and
consistent according to the notion of consequence
and consistency in L. We show that by defining an
appropriate preference relation on options, we can
capture several existing works such as Brewka’s
subtheories. We also provide algorithms to com-
pute most preferred options.
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