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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
Logic Journal of the IGPL, Vol. 8, No. 4
, 2000
"... Algebraic Logic. In preparation. Manuscript. ..."
unknown title
"... Abstract We shall describe the set of strongly meet irreducible logics in the lattice ELin:t of normal tense logics (in the bimodal propositional language) of weak orderings. Based on this description it is shown that all logics in ELin:t are independently axiomatizable. Then the description is used ..."
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Abstract We shall describe the set of strongly meet irreducible logics in the lattice ELin:t of normal tense logics (in the bimodal propositional language) of weak orderings. Based on this description it is shown that all logics in ELin:t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. Mathematics Subject Classification: 03B45, 03B25 Keywords: Modal Logic, Tense Logic, independent axiomatizability, decidability, Kripke semantics
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...
epage MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION
"... ... there is no one fundamental logical notion of necessity, nor consequently of possibility. If this conclusion is valid, the subject of modality ought to be banished from logic, since propositions are simply true or false... [Russell, 1905] 1 ..."
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... there is no one fundamental logical notion of necessity, nor consequently of possibility. If this conclusion is valid, the subject of modality ought to be banished from logic, since propositions are simply true or false... [Russell, 1905] 1