Checking Strong Equivalence with Duplication-Free Tableaux
نویسندگان
چکیده
In Answer Set Programming, Lifschitz, Pearce and Valverde have defined Strong equivalence as follows: Π1 and Π2 are strongly equivalent if for every program Π, Π1 ∪ Π and Π2 ∪ Π are equivalent, i.e., have the same answer sets. A logical characterization of Strong Equivalence is provided by the same authors via i) translation of programs into a classical signature (creating, say, c(Π1) and c(Π2)) and checking equivalence of so-obtained formulae w.r.t. to the Logic of Here-andThere. Here-and-There is an intermediate logic only minimally weaker than classical logic. Indeed Strong Equivalence can be checked with classical logic model checkers but only at the cost of introducing extra atoms. We remain within Lifschitz et al. logical framework and describe an optimal tableaux system for Here-and-There. Such Tableau is derived from a similar, but weaker system introduced by some of the authors for modal intuitionistic logic. Checking strong equivalence can therefore be done in a very concise form without introducing extra atoms and without duplications in proofs.
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