  The framework of algorithmic knowledge assumes that agents use algorithms to
compute the facts they explicitly know. In many cases of interest, a deductive
system, rather than a particular algorithm, captures the formal reasoning used
by the agents to compute what they explicitly know. We introduce a logic for
reasoning about both implicit and explicit knowledge with the latter defined
with respect to a deductive system formalizing a logical theory for agents. The
highly structured nature of deductive systems leads to very natural
axiomatizations of the resulting logic when interpreted over any fixed
deductive system. The decision problem for the logic, in the presence of a
single agent, is NP-complete in general, no harder than propositional logic. It
remains NP-complete when we fix a deductive system that is decidable in
nondeterministic polynomial time. These results extend in a straightforward way
to multiple agents.
