%0 Journal Article
%T Epistemic and doxastic logic with restrictions
%A Manuel Sierra A.
%J -
%D 2010
%X Are presented as extensions of classical propositional calculus hierarchies of deductive systems LDR每n and LER每n with n > 1. LER每n is the epistemic logic with restrictions, LDR每n is the doxastic logic with restrictions. The systems LER每1 and LDR每1 are the classical propositional calculus. System LER每(n + 1) can be seen as the result of applying the rule: if X is theorem of LER每n then +X is theorem of LER每(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每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每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
%K multi每modal logic
%K possible worlds embedded
%K epistemic logic
%K doxastic logic
%K logical omniscience.
%U http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/335