The Complexity of Theorem Proving in Autoepistemic Logic
نویسنده
چکیده
Autoepistemic logic is one of the most successful formalisms for nonmonotonic reasoning. In this paper we provide a proof-theoretic analysis of sequent calculi for credulous and sceptical reasoning in propositional autoepistemic logic, introduced by Bonatti and Olivetti [5]. We show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen’s system LK . Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK . This contrasts with the situation in sceptical autoepistemic reasoning where we obtain an exponential lower bound to the proof length in Bonatti and Olivetti’s calculus.
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