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• W169484759 abstract "We study the trade-off between the expressive abili- ties and the complexity of reasoning in propositional nonmonotonic knowledge bases. We first analyze, in an expressive epistemi c modal framework, the most popular forms of nonmonotonic mechanisms used in knowledge representation: in particular, we prove t hat epis- temic queries and epistemic integrity constraints are natu rally ex- pressed through the notion of negation as failure. Based on t he above analysis, we then characterize the complexity of reasoning with dif- ferent subsets of such nonmonotonic constructs. This characteriza- tion induces a complexity based classification of the variou s forms of nonmonotonic reasoning considered: in particular, we prove that negation as failure is computationally harder than epistem ic disjunc- tion, which apparently contradicts previous complexity re sults ob- tained in the logic programming setting. 1 MOTIVATION Research in nonmonotonic logics has extensively studied the prob- lem of establishing the complexity of various forms of common- sense reasoning (see e.g. (2, 7)). In particular, the comple xity of rea- soning in several propositional nonmonotonic formalisms has been established. The results obtained show that the problem of reason- ing in propositional nonmonotonic logics lies typically at the second level of the polynomial hierarchy (e.g. in default logic, au toepistemic logic, propositional circumscription, disjunctive logic programming, McDermott and Doyle's modal logics, and the modal logic of only knowing). Hence, it is harder (unless the polynomial hierarchy col- lapses) than reasoning in standard propositional logic. However, despite the amount of results obtained, a systematic study of the relationship between the expressive abilities of a non- monotonic formalism and the complexity of reasoning in the pres- ence of such abilities has not been fully analyzed, which has been partly due to the lack of a common formal framework in which the different forms of nonmonotonic reasoning could be compared and studied. In particular, a careful analysis of the most used n onmono- tonic mechanisms for representing commonsense knowledge, with the aim of identifying the contribution of each single featu re to the complexity of reasoning, has not been pursued so far. Such an analy- sis would allow for precisely identifying the complexity of reasoning with a given set of nonmonotonic abilities, thus enabling for design- ing optimized inference methods for nonmonotonic knowledge rep- resentation systems. The present work is a first step towards a principled analysis of the relationship between the expressive abilities and the complexity of" @default.
• W169484759 created "2016-06-24" @default.
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• W169484759 date "1998-01-01" @default.
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• W169484759 title "Expressiveness vs. complexity in nonmonotonic knowledge bases: propositional case" @default.
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