Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
What does a conditional knowledge base entail?
Artificial Intelligence
Conditional logics of normality: a modal approach
Artificial Intelligence
Communicating and mobile systems: the &pgr;-calculus
Communicating and mobile systems: the &pgr;-calculus
Modal logic
A logical theory of nonmonotonic inference and belief change
A logical theory of nonmonotonic inference and belief change
Communication and Concurrency
PI-Calculus: A Theory of Mobile Processes
PI-Calculus: A Theory of Mobile Processes
Normal conditions for inference relations and injective models
Theoretical Computer Science
A characterization theorem for injective model classes axiomatized by general rules
Theoretical Computer Science
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The notion of bisimulation is an important concept in process algebra and modern modal logic. This paper explores the notion of B-similarity, which is a kind of bisimulation between preferential models. We characterize the equivalence of preferential models in terms of B-similarity. However, this result is applicable only for preferential models of finite depth. To overcome this defect, we introduce a weak notion of similarity called M-similarity, and obtain a result corresponding to Hennessy-Milner Theorem and Keisler-Shelah's Isomorphism Theorem in modal logic and first-order logic, respectively. As its application, we investigate the expressive power of Boolean combinations of conditional assertions (BCA, for short), and prove that BCAs are the fragments of first-order language preserved under M-similarity. Moreover, we obtain a characterization for elementary classes defined by BCAs. A notion of first-order translation originating from modal logic plays an important role in this paper. In order to illustrate that first-order translation is a powerful tool in the study of nonmonotonic logic, some model-theoretic results about preferential models are proved based on this translation.