Strong equivalence for causal theories

Strong equivalence is an important property for nonmonotonic formalisms, allowing safe local changes to a nonmonotonic theory. This paper considers strong equivalence for nonmonotonic causal theories of the kind introduced by McCain and Turner. Causal theories T-1 and T-2 are strongly equivalent if, for every causal theory T, T-1 boolean OR T and T-2 boolean OR T are equivalent (that is, have the same causal models). The paper introduces a convenient characterization of this property in terms of so-called SE-models, much as was done previously for answer set programs and default theories. A similar result is provided for the nonmonotonic modal logic UCL. The paper also introduces a reduction from the problem of deciding strong equivalence of two causal theories to the problem of deciding equivalence of two sets of propositional formulas.