Source: Notre Dame J. Formal Logic Volume 51, Number 1
(2010), 119-126.
Often where an axiomatization of an intensional logic using only finitely many
axioms schemes and rules of the simplest kind is unknown, one has a choice
between an axiomatization involving an infinite family of axiom schemes and one
involving nonstandard "Gabbay-style" rules. The present note adds another
example of this phenomenon, pertaining to the logic comparative probability
("p is no more likely than q"). Peter Gärdenfors
has produced an axiomatization involving an infinite family of schemes, and here
an alternative using a "Gabbay-style" rule is offered. Both axiomatizations
depend on the Kraft-Pratt-Seidenberg theorem from measurement theory.
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References
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Mathematical Reviews (MathSciNet):
MR595112
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Mathematical Reviews (MathSciNet):
MR646465
[4] Gärdenfors, P., "Qualitative probability as an intensional logic", Journal of Philosophical Logic, vol. 4 (1975), pp. 171--85.
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