Knowing Minimum/Maximum n Formulae

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 φ 1, …, φ 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.

Authors

• Thomas Ågotnes
• Natasha Alechina

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