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Some philosophical problems from the standpoint of artificial intelligence
 AI, IN MACHINE INTELLIGENCE 4, MELTZER AND MICHIE (EDS
, 1969
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Algebraic Polymodal Logic: A Survey
 LOGIC JOURNAL OF THE IGPL
, 2000
"... This is a review of those aspects of the theory of varieties of Boolean algebras with operators (BAO's) that emphasise connections with modal logic and structural properties that are related to natural properties of logical systems. It begins with ..."
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This is a review of those aspects of the theory of varieties of Boolean algebras with operators (BAO's) that emphasise connections with modal logic and structural properties that are related to natural properties of logical systems. It begins with
Modal Logics that Need Very Large Frames
"... . The Kuznetsov{Index of a modal logic is the least cardinal such that any consistent formula has a Kripke{model of size if it has a Kripke{model at all. The Kuznetsov{Spectrum is the set of all Kuznetsov{Indices of modal logics with countably many operators. It has been shown by Thomason that th ..."
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. The Kuznetsov{Index of a modal logic is the least cardinal such that any consistent formula has a Kripke{model of size if it has a Kripke{model at all. The Kuznetsov{Spectrum is the set of all Kuznetsov{Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov{Index i!+! . Futhermore, Chagrov has constructed an extension of K4 with Kuznetsov{Index i! . We will show here that for each countable ordinal there are logics with Kuznetsov{Index i . Furthermore, we show that the Kuznetsov{Spectrum is identical to the spectrum of indices for 1 1 {theories, which is likewise dened. A particular consequence is the following. If inaccessible (weakly compact, measurable) cardinals exist, then the least inaccessible (weakly compact, measurable) cardinal is also a Kuznetsov{Index. 1. Introduction Suppose ' is an elementary formula and that ' is consistent with an elementary theory T in a countable language. Then t...
Logic Journal of the IGPL, Vol. 8, No. 4
, 2000
"... Algebraic Logic. In preparation. Manuscript. ..."