Abstract
In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be characterized by means of the logical consistency of a suitable theory Tχ defined on the modal-fuzzy logic FPk(RŁΔ) built up over the many-valued logic RŁΔ. Such modal-fuzzy logic was previously introduced in Flaminio (Lecture Notes in Computer Science, vol. 3571, 2005) in order to treat conditional probability by means of a list of simple probabilities following the well known (smart) ideas exposed by Halpern (Proceedings of the eighth conference on theoretical aspects of rationality and knowledge, pp 17–30, 2001) and by Coletti and Scozzafava (Trends Logic 15, 2002). Roughly speaking, such logic is obtained by adding to the language of RŁΔ a list of k modalities for “probably” and axioms reflecting the properties of simple probability measures. Moreover we prove that the satisfiability problem for modal formulas of FPk(RŁΔ) is NP-complete. Finally, as main result of this paper, we prove FPk(RŁΔ) in order to prove that the problem of establishing the coherence of rational assessments of conditional probability is NP-complete.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
