Two-layered logics for uncertainty
Section outline
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We will look at a specific format of a logic - two-layered (modal) logics - where two layers of reasoning (which can be two different logics) are separated syntactically and semantically: the inner layer of reasoning about events or evidence, and the outer layer of reasoning about (un)certainty about the events or evidence (or belief or likelihood). The two layers are connected with a modality interpreted via a chosen uncertainty measure defined on the formulas of the inner logic. We will first look at classical propositional logic-based two-layered logics for probability introduced in 90's, and then at some paraconsistent BD-based generalizations.