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Restricted normal modal logics and levelled possible worlds semantics
(OXFORD UNIV PRESS, 2014-08-01) Agudelo-Agudelo, Juan C.; Sierra-Aristizabal, Manuel H.; Agudelo-Agudelo, Juan C.; Sierra-Aristizabal, Manuel H.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Restricted normal modal logics are here 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. © 2014 The Author.