17/04 - Juan Carlos

Restricted normal modal logics and levelled possible worlds semantics

Restricted normal modal logics are defined by imposing conditions on the modal axioms and rules of normal modal systems. The conditions are defined in terms of a depth (associated with the modal connective) and a complexity function. It is proven that the logics obtained are characterized by a subtle adaptation of the  possible worlds semantics in which levels are associated with the worlds. Restricted normal modal logics constitute a general framework allowing the definition of a huge variety of modal systems, which can have different applications. For instance, they are useful to define epistemic logics where the logical omniscience problem is partially controlled.

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