Epistemic logic for rule-based agents

Abstract
The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, as opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results.
Keywords Epistemic logic  Doxastic logic  Rule-based agents  Resource bounds  Artificial intelligence  Logical omniscience
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References found in this work BETA
Jaakko Hintikka (1962). Knowledge and Belief. Ithaca, N.Y.,Cornell University Press.
D. Kaplan & R. Montague (1960). A Paradox Regained. Notre Dame Journal of Formal Logic 1 (3):79-90.

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Citations of this work BETA
Mark Jago (2012). The Content of Deduction. Journal of Philosophical Logic 42 (2):317-334.
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