A reduction of the theory of confirmation to the notions of distance and measure
We present an analysis and formalization of confirmation of a theory through observation. The basic ideas are, first, to carry the results of single observations over to neighbouring cases by analogy, using an abstract distance relation as in the Stalnaker/Lewis semantics for counterfactual conditionals. A theory is then, in a second step, considered confirmed iff we have thus concluded positively for a “large” part of the universe — where “large” is interpreted by a weak filter. Formal semantics as well as sound and complete axiomatizations for the (trivial) first order and the propositional case are given.
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- N.Goodman, “Fact, Fiction, and Forecast”, Harvard Univ. Press, 1955Google Scholar
- D.Lewis, “Counterfactuals”, Harvard, Cambridge, Mass., USA, 1973Google Scholar
- D.Makinson, “General patterns in nonmonotonic reasoning”, in D.Gabbay, C.Hogger, Robinson (eds.), “Handbook of Logic in Artificial Intelligence and Logic Programming”, vol. III: “Nonmonotonic and Uncertain Reasoning”, Oxford University Press, 1994, p. 35–110Google Scholar
- K.Schlechta: “Defaults as Generalized Quantifiers”, to appear in: Journal of Logic and Computation, Oxford (1994/95), also as Research Report RR 16, 05/94, Laboratoire d'Informatique de Marseille, URA CNRS 1787, Université de Provence, 3 pl., Victor Hugo, F-13331 Marseille Cedex 3, FranceGoogle Scholar
- K.Schlechta: “Some Results on Classical Preferential Models”, Journal of Logic and Computation, Oxford, Vol.2, No.6 (1992), p. 675–686Google Scholar
- K.Schlechta: “Logic, Topology, and Integration”, to appear in: Journal of Automated Reasoning, D.Reidel Publ. Company (1994/95)Google Scholar
- K.Schlechta: “A Reduction of the Theory of Confirmation to the Notions of Distance and Measure” Research Report RR 64, 12/94, Laboratoire d'Informatique de Marseille, URA CNRS 1787, Université de Provence, 3 pl. Victor Hugo, F-13331 Marseille Cedex 3, FranceGoogle Scholar
- K.Schlechta, D.Makinson: “Local and Global Metrics for the Semantics of Counterfactual Conditionals”, Journal of Applied Non-Classical Logics, Hermes, Paris (1994)Google Scholar
- Stalnaker, “A theory of conditionals”, in N.Rescher (ed.), “Studies in Logical Theory”, Blackwell, Oxford, p. 98–112Google Scholar