Modal logics between propositional and first-order
Prof Melvin Fitting
Department of Mathematics and Computer Science,
One can add the machinery of relation symbols and terms to a
propositional modal logic without adding quantifiers. Ordinarily this
is no extension beyond the propositional. But if terms are allowed to
be non-rigid, a scoping mechanism (usually written using lambda
abstraction) must also be introduced to avoid ambiguity. Since
quantifiers are not present, this is not really a first-order logic,
but it is not exactly propositional either. I will show that for
propositional logics such as K, T and D, adding such machinery
produces a decidable logic, but adding it to logics between K4 and S5
produces an undecidable one. (Transitivity is the villain here.) The
proof of undecidability consists of showing that classical first-order
logic can be embedded.
Place: Information technology, Uppsala University
Room 1510 is in Building 1, Floor 5, room 10
(in the southern part of the building).
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Updated 08-Jan-2001 15:16 by Roland Grönroos
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