Abstract
We present a tableau-based proof procedure forvariable domain-minimal entailment, a nonmonotonic entailment relation closely related to McCarthy's domain circumscription. By using a modified tableau rule for existential formulas, an idea first suggested by Hintikka, we construct partial and in a certain sense domainminimal models, represented by a particular selection of complete open branches. A nonmonotonic consequence relation is defined by adding domain-closure axioms to these minimal branches and refuting a goal formula wrt. each extended minimal branch. For theories with certain properties, this consequence relation can be proven sound and complete wrt. variable domain-minimal entailment.
The proof procedure has been implemented in a free-variable, order-sorted tableau theorem prover calledMiniTab. Some implementation issues are discussed at the end of the article.
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Lorenz, S. A tableau prover for domain minimization. J Autom Reasoning 13, 375–390 (1994). https://doi.org/10.1007/BF00881950
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DOI: https://doi.org/10.1007/BF00881950