A Logic For Ignorance

We introduce and motivate a non-standard multi-modal logic to represent and reason about ignorance in Multi-Agent Systems. We argue that in Multi-agent systems being able to reason about what agents ignore is just as important as being able to reason about what agents know. We show a sound and complete axiomatisation for the logic. We investigate its applicability by restating the feasibility condition for the FIPA communication primitive of inform. As we know, there are known knowns; there are things we know that we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns — the ones we don’t know we don’t know. Donald Rumsfeld (US Secretary of State for Defence)

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