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- W95968475 abstract "In our 2007 paper David and I studied consequence relations that correspond to conditional probability functions above thresholds, the probabilistic consequence relations. We showed that system O is a probabilistically sound system of Horn rules for the probabilistic consequence, and we conjectured that O might also provide a complete axiomatization of the set of finite premised Horn rules for probabilistic consequence relations. In a 2009 paper Paris and Simmonds provided a mathematically complex way to characterize all of the sound finite-premised Horn rules for the probabilistic consequence relations, and they established that the rules derivable from system O are insufficient. In this paper I provide a brief accounts of system O and the probabilistic consequence relations. I then show that O together with the probabilistically sound (Non-Horn) rule known as Negation Rationality implies an additional systematic collection of sound Horn rules for probabilistic consequence relations. I call O together with these new Horn rules ‘O+’. Whether O+ is enough to capture all probabilistically sound finite premised Horn rules remains an open question." @default.
- W95968475 created "2016-06-24" @default.
- W95968475 creator A5048228585 @default.
- W95968475 date "2013-12-21" @default.
- W95968475 modified "2023-10-16" @default.
- W95968475 title "New Horn Rules for Probabilistic Consequence: Is $$mathrm{O}{+}$$ Enough?" @default.
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- W95968475 doi "https://doi.org/10.1007/978-94-007-7759-0_9" @default.
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