Notre Dame Journal of Formal Logic 51 (1):119-126 (2010)
1 Choice conjecture In axiomatizing nonclassical extensions of classical sentential logic one tries to make do, if one can, with adding to classical sentential logic a finite number of axiom schemes of the simplest kind and a finite number of inference rules of the simplest kind. The simplest kind of axiom scheme in effect states of a particular formula P that for any substitution of formulas for atoms the result of its application to P is to count as an axiom. The simplest kind of onepremise inference rule in effect states of a particular pair of formulas P and Q that for any substitution of formulas for atoms, if the result of its application to P is a theorem, then the result of its application to Q is to count as a theorem; similarly for many-premise rules. Such are the schemes and rules of all the best-known modal and tense logics, for instance. Sometimes it is difficult to find such simple schemes and rules. In that case one may resort to less simple schemes or less simple rules. There is no generally recognized rigorous definition of "next simplest kind" of scheme. Neither is there any generally recognized definition of "next simplest kind" of rule, and hence there is no fully rigorous enunciation of the choice conjecture, the conjecture that schemes of the next simplest kind can always be avoided in favor of rules of the next simplest kind and vice versa. Nonetheless, there are cases where intuitively one does recognize that the schemes or rules in a given axiomatization are only slightly more complex than the simplest kind, including cases where one does have a choice between adopting slightly-more-complex-than-simplest schemes and adopting slightly-more-complex-than-simplest rules. In tense logic early examples of slightly more complex rules are found in  and  : there is one example of the embarrassed use of such rules in the former, and many examples of the enthusiastic use of such rules in the latter and its sequels. Accordingly the rules in question have come to be called "Gabbay-style" rules.
|Keywords||probability logic qualitative probability axiomatization|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Shifting Frames: From Divided to Distributed Psychologies of Scientific Agents.Peter J. Taylor - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:304-310.
A Novel Interpretation of Plato's Theory of Forms.P. X. Monaghan - 2010 - Metaphysica 11 (1):63-78.
Commodification or Compensation: A Reply to Ketchum.H. M. Malm - 1989 - Hypatia 4 (3):128-135.
Added to index2009-05-01
Total downloads32 ( #160,408 of 2,169,136 )
Recent downloads (6 months)1 ( #345,573 of 2,169,136 )
How can I increase my downloads?