This article presents a probabilistic logic whose sen- tences can be interpreted as asserting the acceptabil- ity of gambles described in terms of an underlying logic. This probabilistic logic has a concrete syntax and a complete inference procedure, and it handles conditional as well as unconditional probabilities. It synthesizes Nilsson's original probabilistic logic and Frisch and Haddawy's anytime inference procedure with Wilson and Moral's logic of gambles. Two distinct semantics can be used for our prob- abilistic logic: (1) the measure-theoretic semantics used by the prior logics already mentioned and also by the more expressive logic of Fagin, Halpern, and Meggido and (2) a behavioral semantics. Under the measure-theoretic semantics, sentences of our prob- abilistic logic are interpreted as assertions about a probability distribution over interpretations of the un- derlying logic. Under the behavioral semantics, these sentences are interpreted only as asserting the accept- ability of gambles, and this suggests different direc- tions for generalization.
Keywords. Probabilistic Logic, Anytime Computation, Logic of Gambles, Measure-theoretic and Behavioral Semantics
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Authors addresses:
Peter Gillett
Department of Accounting & Information Systems
School of Business - New Brunswick
RUTGERS: The State University of New Jersey
Jancie H. Levin Building
94 Rockafeller Road
Piscataway
NJ 08854-8054
USA
Richard Scherl
...
Glenn Shafer
Rutgers School of Business - Newark and New Brunswick
Rutgers University
180 University Avenue,
07102, Newark, New Jersey
USA
E-mail addresses:
| Peter Gillett | gillett@business.rutgers.edu |
| Richard Scherl | rscherl@monmouth.edu |
| Glenn Shafer | gshafer@andromeda.rutgers.edu |