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Journal of Logic and Computation 2006 16(2):287-309; doi:10.1093/logcom/exi078
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Vol. 16 No. 2, © The Author, 2006. Published by Oxford University Press. All rights reserved.

Original Articles

Deductive Algorithmic Knowledge

Riccardo Pucella

Northeastern University, Boston, MA 02115 USA. Email: riccardo{at}ccs.neu.edu

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.

Keywords: Epistemic logic, algorithmic knowledge, explicit knowledge, deductive systems, axiomatizations

Received 20 June 2005.


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