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Klein, Dominik; Gratzl, Norbert; Roy, Olivier (2015): Introspection, Normality and Agglomeration. In: Hoek, Wiebe van der; Holliday, H. Wesley; Wang, Wen-fang (eds.) : Logic, Rationality, and Interaction. Lecture Notes in Computer Science, Vol. 9394. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 195-206
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This paper explores a non-normal logic of beliefs for boundedly rational agents. The logic we study stems from the epistemic-doxastic system developed by Stalnaker. In that system, if knowledge is not positively introspective then beliefs are not closed under conjunction. They are, however, required to be pairwise consistent, a requirement that has been called agglomerativity elsewhere. While bounded agglomerativity requirements, i.e., joint consistency for every n-tuple of beliefs up to a fixed n, are expressible in that logic, unbounded agglomerativity is not. We study an extension of this logic of beliefs with such an unbounded agglomerativity operator, provide a sound and complete axiomatization for it, show that it has a sequent calculus that enjoys the admissibility of cut, that it has the finite model property, and that it is decidable.