Knowing Minimum/Maximum n Formulae

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 resourcebounded 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 1, . . . , n', are definable using min(n). We introduce several syntactic epistemic logics with min(n) operators, and prove completeness and decidability results for those logics.

• Type: Conference
• Year: 2006
• Where: ECAI
• Authors: Thomas Ågotnes, Natasha Alechina
• Keywords: Artificial Intelligence, ECAI 2006, Nullary Operators, Reasoner, Syntactic Epistemic Logics