Deductive Algorithmic Knowledge
Abstract
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 NPcomplete in general, no harder than propositional logic. It remains NPcomplete when we fix a deductive system that is decidable in nondeterministic polynomial time. These results extend in a straightforward way to multiple agents.
 Publication:

arXiv eprints
 Pub Date:
 May 2004
 arXiv:
 arXiv:cs/0405038
 Bibcode:
 2004cs........5038P
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Logic in Computer Science;
 I.2.4;
 F.4.1
 EPrint:
 28 pages. A preliminary version of this paper appeared in the Proceedings of the 8th International Symposium on Artificial Intelligence and Mathematics, AI&