Nonmonotonic Reasoning Is Sometimes Simpler! 1
نویسنده
چکیده
We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4-expansion for a given set A of premises is P 2-complete. Similarly, we show that for a given formula ' and a set A of premises, it is P 2-complete to decide whether ' belongs to at least one S4-expansion for A, and it is P 2-complete to decide whether ' belongs to all S4-expansions for A. This refutes a conjecture of Gottlob that these problems are PSPACE-complete. An interesting aspect of these results is that reasoning (testing satissability and provability) in the monotonic modal logic S4 is PSPACE-complete. To the best of our knowledge, the nonmonotonic logic S4 is the rst example of a nonmonotonic formalism which is computationally easier than the monotonic logic that underlies it (assuming PSPACE does not collapse to P 2).
منابع مشابه
Is Intractability of Non-Monotonic Reasoning a Real Drawback?
Several studies about computational complexity of nonmonotonic reasoning (NMR) showed that nonmonotonic inference is significantly harder than classical, monotonic inference. This contrasts with the general idea that NMR can be used to make knowledge representation and reasoning simpler, not harder. In this paper we show that, to some extent, NMR fulfills the representation goal. In particular,...
متن کاملA Unified View of Consequence Relation, Belief Revision and Conditional Logic
The notion of minimality is widely used in three different areas of Artificial Intelligence: non-monotonic reasoning, belief revision, and conditional reasoning. However, it is difficult for the readers of the literature in these areas to perceive the similarities clearly, because each formalization in those areas uses its own language sometimes without referring to other for-malizations. We de...
متن کاملLogic in Nonmonotonic Reasoning
We present a conceptual description of nonmonotonic formalisms as essentially two-layered reasoning systems consisting of a monotonic logical system, coupled with a mechanism of a reasoned choice of default assumptions. On this ‘surgery’, the main features of a nonmonotonic formalism are determined by the interplay between its logical basis and the nonmonotonic overhead. Furthermore, it allows ...
متن کاملAgainst Nonmonotonic Logic (DRAFT)
The monotonicity property of inference in conventional formal systems of logic (S ` A and S ⊆ T implies T ` A) appears to prohibit certain crucial steps in practical intuitive reasoning. For example, reasoning by default (using assertions that are assumed to hold until explicitly contradicted) appears to be impossible in monotonic systems. Many crucial steps in practical reasoning certainly req...
متن کاملTowards First-Order Nonmonotonic Reasoning
We investigate the problem of reasoning in nonmonotonic extensions of rst-order logic. In particular, we study reasoning in rst-order MKNF, the modal logic of minimal knowledge and negation as failure introduced by Lifschitz. MKNF can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, and logic programming. B...
متن کامل