by Angelo Gilio, Niki Pfeifer, Giuseppe Sanfilippo
Abstract:
Abstract We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults.
Reference:
Angelo Gilio, Niki Pfeifer, Giuseppe Sanfilippo, "Transitivity in coherence-based probability logic", In Journal of Applied Logic, vol. 14, pp. 46-64, 2016. (
[Available on ResearchGate] [Audio slides of the the published paper])
Bibtex Entry:
@Article{2016:JAL,
title = "Transitivity in coherence-based probability logic ",
journal = "Journal of Applied Logic ",
volume = "14",
pages = "46--64",
year = "2016",
issn = "1570-8683",
doi = "10.1016/j.jal.2015.09.012",
scopus="
2-s2.0-84991929159",
wos="WOS:000369550700004",
comment = {
<a href="https://www.researchgate.net/publication/281006026_Transitivity_in_coherence-based_probability_logic">[Available on ResearchGate]</a> <a href="http://audioslides.elsevier.com//ViewerSmall.aspx?source=1&doi=10.1016/j.jal.2015.09.012">[Audio slides of the the published paper]</a>},
url* = "http://www.sciencedirect.com/science/article/pii/S1570868315000816",
url="https://www.researchgate.net/publication/281006026_Transitivity_in_coherence-based_probability_logic",
author = "Angelo Gilio and Niki Pfeifer and Giuseppe Sanfilippo",
abstract = "Abstract We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults. "
}