De Finetti's no-Dutch-book criterion for Gödel logic

DOI10.1007/s11225-008-9142-5zbMath1165.03008OpenAlexW2038051410MaRDI QIDQ1005945

Vincenzo Marra, Stefano Aguzzoli, Brunella Gerla

Publication date: 17 March 2009

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11225-008-9142-5

zbMATH Keywords

probability theoryGödel logicDutch bookGödel algebrascoherent bettingde Finetti criterion

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Probability and inductive logic (03B48) MV-algebras (06D35) Many-valued logic (03B50) Axioms; other general questions in probability (60A05)

Related Items (18)

Extending possibilistic logic over Gödel logic ⋮ Partially undetermined many-valued events and their conditional probability ⋮ A logical characterization of coherence for imprecise probabilities ⋮ Corrigendum to: ``Towards a probability theory for product logic: states, integral representation and reasoning ⋮ Free algebras, states and duality for the propositional \(\text{Gödel}_{\Delta}\) and drastic product logics ⋮ Towards a probability theory for product logic: states, integral representation and reasoning ⋮ On standard completeness and finite model property for a probabilistic logic on Łukasiewicz events ⋮ Probability over Płonka sums of Boolean algebras: states, metrics and topology ⋮ Probability measures in the logic of nilpotent minimum ⋮ Representing uncertainty on set-valued variables using belief functions ⋮ States of finite GBL-algebras with monoidal sum ⋮ Rota's Fubini lectures: the first problem ⋮ De Finetti's no-Dutch-book criterion for Gödel logic ⋮ Conditionals and Independence in Many-Valued Logics ⋮ Open Partitions and Probability Assignments in Gödel Logic ⋮ Exploring Extensions of Possibilistic Logic over Gödel Logic ⋮ Interpretation of De Finetti coherence criterion in Łukasiewicz logic ⋮ Non-standard probability, coherence and conditional probability on many-valued events

Cites Work

• Bookmaking over infinite-valued events
• De Finetti's no-Dutch-book criterion for Gödel logic
• Metamathematics of fuzzy logic
• MV-algebras, multiple bets and subjective states
• De Finetti theorem and Borel states in \([0, 1\)-valued algebraic logic]
• Computing coproducts of finitely presented Gödel algebras
• Symbolic and Quantitative Approaches to Reasoning with Uncertainty
• Logic with truth values in A linearly ordered heyting algebra
• Free L-algebras

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