MV-algebras, multiple bets and subjective states

De Finetti’s No-Dutch-Book Criterion for Gödel logic

“…In fact, de Finetti defined coherence [4, loc. cit.] using (1), and not (5). When (non-classical) events are described by formulae of a [0, 1]-valued logic, they formally behave as bounded real random variables -truthvalues range in [0, 1].…”

“…To the best of our knowledge, no such result is available. It turns out that the stronger notion of coherence corresponding to(5) does not characterise conv Wn -see Example 3.10 8. The height of an element t ∈ Fn is the cardinality of ↓ t.…”

Gradational Accuracy and Nonclassical Semantics

“…This result applies directly to many of the settings set out earlier: Classical, Kleene Gaps, LP gluts, Fuzzy Gaps, and Intuitionistic frameworks all satisfy Paris's axioms. 41 Drawing on the work of Gerla (2000) and Di Nola et al (1999), Paris argues that a similar result holds for finite fuzzy (Łukasiewicz) setting-and Mundici (2006) later extended this to the continuum valued fuzzy setting. As in the classical case, (P2) turns out to be redundant.…”

“…41 Drawing on the work of Gerla (2000) and Di Nola et al (1999), Paris argues that a similar result holds for finite fuzzy (Łukasiewicz) setting-and Mundici (2006) later extended this to the continuum valued fuzzy setting. 41 Drawing on the work of Gerla (2000) and Di Nola et al (1999), Paris argues that a similar result holds for finite fuzzy (Łukasiewicz) setting-and Mundici (2006) later extended this to the continuum valued fuzzy setting.…”

Nonclassical Probability and Convex Hulls

“…There is an alternative approach to a related result that makes appeal to the structure of MV algebras [11,10,7]. This framework is more general in the sense that the logical algebraic structure may fail to be a lattice, but it is more restricted in the sense that an MV algebra requires a negation that behaves classically.…”