Abstract
We consider the monodic formulas of common knowledge predicate logic, which allow applications of epistemic operators to formulas with at most one free variable. We provide finite axiomatizations of the monodic fragment of the most important common knowledge predicate logics (the full logics are known to be not recursively enumerable) and single out a number of their decidable fragments. On the other hand, it is proved that the addition of the equality symbol to the monodic fragment makes it not recursively enumerable.
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Sturm, H., Wolter, F., Zakharyaschev, M. (2000). Monodic Epistemic Predicate Logic. In: Ojeda-Aciego, M., de Guzmán, I.P., Brewka, G., Moniz Pereira, L. (eds) Logics in Artificial Intelligence. JELIA 2000. Lecture Notes in Computer Science(), vol 1919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40006-0_23
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DOI: https://doi.org/10.1007/3-540-40006-0_23
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