Abstract

SIERRA-A, Manuel. Epistemic and doxastic logic with restrictions. ing.cienc. [online]. 2010, vol.6, n.12, pp.81-115. ISSN 1794-9165.

Are presented as extensions of classical propositional calculus hierarchies of deductive systems LDR-n and LER-n with n ≥ 1. LER-n is the epistemic logic with restrictions, LDR-n is the doxastic logic with restrictions. The systems LER-1 and LDR-1 are the classical propositional calculus. System LER-(n + 1) can be seen as the result of applying the rule: if X is theorem of LER-n then +X is theorem of LER-(n + 1). Systems also restricts the validity of the axioms +(X → Y) → (+X → +Y) and +X → X, in terms of depth (complexity with respect to the operator +) of X and Y, and also includes restricted versions of the axioms of positive and negative introspection. LER system results from the union of LER-n systems, and can be seen as the S5 modal logic system with different types of restrictions. Changing +X → X by +X →∼+∼X are built LDR-n and the LDR systems. LDR can be seen as the KD45 modal logic system with different types of restrictions. The systems are characterized with a embedded worlds semantics, with which the ‘omniscience logical problem' is limited.

Keywords : multi-modal logic; possible worlds embedded; epistemic logic; doxastic logic; logical omniscience.

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