Lógicas epistémica y doxástica con restricciones

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.