Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
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
Relations between the logic of theory change and nonmonotonic logic
Proceedings of the Workshop on The Logic of Theory Change
On a Linear Representation Theory for Quantitative Belief Change
AI '02 Proceedings of the 15th Australian Joint Conference on Artificial Intelligence: Advances in Artificial Intelligence
On a linear framework for belief dynamics in multi-agent environments
CLIMA VII'06 Proceedings of the 7th international conference on Computational logic in multi-agent systems
On a linear framework for belief dynamics in multi-agent environments
CLIMA VII'06 Proceedings of the 7th international conference on Computational logic in multi-agent systems
Connectives in cumulative logics
Pillars of computer science
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Our starting point is the observation that with a given Hilbert space H we may, in a way to be made precise, associate a class of non-monotonic consequence relations in such a way that there exists a one-to-one correspondence between the rays of H and these consequence relations. The projectors in Hilbert space may then be viewed as a sort of revision operators. The lattice of closed subspaces appears as a natural generalisation of the concept of a Lindenbaum algebra in classical logic. The logics presentable by Hilbert spaces are investigated and characterised. Moreover, the individual consequence relations are studied. A key concept in this context is that of a consequence relation having a pointer to itself. It is proved that such consequence relations have certain remarkable properties in that they reflect their metatheory at the object level to a surprising extent. The tools used in the investigation stem from two different areas of research, namely from the disciplines of non-monotonic logic on the one hand and from Hilbert space theory on the other. There exist surprising connections between these two fields of research the investigation of which constitutes the purpose of this pape