Four probability-preserving properties of inferences
- Ernest W. Adams
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Different inferences in probabilistic logics of conditionals ‘preserve’ the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability 1 when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case conclusions must have positive probability when premisses do, and in the last case conclusions must be at least as probable as their least probable premisses. Precise definitions and well known examples are given for each of these properties, characteristic principles are shown to be valid and complete for deriving conclusions of each of these kinds, and simple trivalent truthtable ‘tests’ are described for determining which properties are possessed by any given inference. Brief comments are made on the application of these results to certain modal inferences such as “Jones may own a car, and if he does he will have a driver's license. Therefore, he may have a driver's license.”
- Adams, E.W., 1966. “Probability and the logic of conditionals”, in J. Hintikka and P. Suppes (eds), Aspects of Inductive Logic, North-Holland, Amsterdam, 265–316.
- Adams, E.W., 1975. The Logic of Conditionals; an Application of Probability to Deductive Logic, D. Reidel, Dordrecht.
- Adams, E.W., 1986. “On the logic of high probability”, Journal of Philosophical Logic 15, 255–279.
- Adams, E.W., 1993. “On the rightness of certain counterfactuals”, Pacific Philosophical Quarterly 74, (1), 1–10.
- Adams, E.W., 1995, “Remarks on a theorem of McGee”, Journal of Philosophical Logic 24, 343–348.
- Adams, E.W. and Levine, H.P., 1975. “On the uncertainties transmitted from premises to conclusions in deductive inferences”, Synthese 30, nos. 3/4, 429–460.
- Calabrese, P., 1990. “Reasoning with uncertainty using conditional logic and probability”, in I.R. Goodman, M.M. Gupta, H.T. Nguyen and G.S. Rogers (eds), Conditional Logic in Expert Systems, North-Holland, Amsterdam, 71–100.
- Dubois, D. and Prade, H., 1993. “Conditional objects: a three-valued scmantics for nonmontonic inference”, in Conditionals in Knowledge Representation, a workshop held in conjunction with IJCAI-93, C. Boutelier and J. Delgrande, organizers, IJCAI-93, 81–87.
- Gilio, Angelo, to appear. “On the logic of conditionals and coherence principles”.
- Goodman, I.R., Nguyen, H.T. and Walker, E.A., 1991. Conditional Inference and Logic for Intelligent Systems. North-Holland, Amsterdam.
- Kyburg, H., 1990. “Probability, rationality, and the rule of detachment”, in Y. Bar-Hillel (ed.), Logic, Methodology, and Philosophy of Science, North-Holland, Amsterdam, 301–310.
- Lewis, D., 1974. Counterfactuals, Harvard University Press.
- McGee, V., 1981. “Finite Matrices and the Logic of Conditionals”, Journal of Philosophical Logic 10, 349–351.
- McGee, V., 1994. “Learning the impossible”, in B. Skyrms and E. Eells (eds), Probability and Conditionals, Belief Revision and Rational Decision, Cambridge University Press, Cambridge, 179–199.
- Popper, K.R., 1959. The Logic of Scientific Discovery, Hutchinson of London, London.
- Stalnaker, R.C., 1969. “A theory of conditionals”, in N. Rescher (ed.), Studies in Logical Theory, Blackwell.
- Suppes, P., 1966. “Probabilistic inference and the principle of total evidence”, in J. Hintikka and P. Suppes (eds), Aspects of Inductive Logic, North-Holland, Amsterdam, 49–65.
- Four probability-preserving properties of inferences
Journal of Philosophical Logic
Volume 25, Issue 1 , pp 1-24
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Ernest W. Adams (1)
- Author Affiliations
- 1. University of California, Berkeley, USA