Knowing Minimum/Maximum n Formulae

Authors:
Thomas Ågotnes;Natasha Alechina
Affiliations:
University of Bergen, Norway, agotnes@ii.uib.no;University of Nottingham, UK, nza@cs.nott.ac.uk
Venue:
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Year:
2006

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Abstract

We introduce a logical language with nullary operators min(n), for each non-negative integer n, which mean 'the reasoner has at least n different beliefs'. The resulting language allows us to express interesting properties of non-monotonic and resource-bounded reasoners. Other operators, such as 'the reasoner has at most n different beliefs' and the operator introduced in [1, 4]: 'the reasoner knows at most the formulae φ1,…,φn', are definable using min(n). We introduce several syntactic epistemic logics with min(n) operators, and prove completeness and decidability results for those logics.