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.

Gilio, A., Pfeifer, N., & Sanfilippo, G. (2016). Transitivity in coherence-based probability logic. JOURNAL OF APPLIED LOGIC, 14, 46-64 [10.1016/j.jal.2015.09.012].

Transitivity in coherence-based probability logic

SANFILIPPO, Giuseppe
2016

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.
Settore MAT/06 - Probabilita' E Statistica Matematica
Settore M-FIL/02 - Logica E Filosofia Della Scienza
Settore MAT/01 - Logica Matematica
Gilio, A., Pfeifer, N., & Sanfilippo, G. (2016). Transitivity in coherence-based probability logic. JOURNAL OF APPLIED LOGIC, 14, 46-64 [10.1016/j.jal.2015.09.012].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/157810
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