Gödel ≡ Bell ≡ Kochen–Specker — Gödel's Quantum Shadow Is Contextuality and Non-Locality; Bell's Logical Shadow Is Self-Reference — An Equivalence Revealing Einstein's Nemesis 95 Years Overdue

Authors: Franchi Viceré, Christian

Subject Terms: Bohrification, Lawvere fixed-point theorem, Born rule, categorical logic, Kolmogorov probability, Heyting algebra, kernel verification, intuitionistic logic, Boolean algebra, coherent conditional probability, Bohr topos, daseinisation, Penrose objective reduction, first incompleteness theorem, Gödel incompleteness, Joyal arithmetic universe, Einstein vindication, contextuality, Tsirelson bound, spectral presheaf, Bell theorem, quantum probability, Kochen-Specker theorem, machine-checked proof, topos theory, Lean 4, CHSH inequality, non-contextuality, Coletti-Scozzafava, wave function collapse, Bell inequality, de Finetti coherence, EPR completeness, quantum non-locality, arithmetic universe, diagonal lemma, Wolfram Mathematica certificate, EPR paradox

Optimizing de Finetti’s Coherence: A Complexity Analysis

Authors: Lapenta, Serafina^Aff13, Napolitano, Sebastiano^{Aff13, Aff14}

Contributors: Li, Gang, Series Editor^Aff1, Filipe, Joaquim, Series Editor^Aff2, Xu, Zhiwei, Series Editor^Aff3, Vantaggi, Barbara, editor^Aff4, Coletti, Giulianella, editor^Aff5, Denoeux, Thierry, editor^Aff6, Laurent, Anne, editor^Aff7, Petturiti, Davide, editor^Aff8, Miranda, Enrique, editor^Aff9, Medina, Jesús, editor^Aff10, Bouchon-Meunier, Bernadette, editor^Aff11, Yager, Ronald R., editor^Aff12

Source: Information Processing and Management of Uncertainty in Knowledge-Based Systems : 21st International Conference, IPMU 2026, Rome, Italy, June 15–19, 2026, Proceedings, Part II. 3020:219-232

Unimodular triangulations in Łukasiewicz logic: Complexity bounds of probabilistic coherence

Authors: Flaminio, Tommaso ^a, Lapenta, Serafina ^{b, ⁎}, Napolitano, Sebastiano ^{b, c}

Source: In International Journal of Approximate Reasoning December 2025 187

De Finetti theorem and Borel states in [0,1]-valued algebraic logic: De Finetti theorem and Borel states in \([0, 1]\)-valued algebraic logic

Authors: MUNDICI, DANIELE, KUHR J.

Source: International Journal of Approximate Reasoning. 46:605-616

Subject Terms: De Finetti coherence criterion, MV-algebras, Applied Mathematics, 02 engineering and technology, de Finetti coherence criterion, Probability and inductive logic, 01 natural sciences, Subjective probability, Other algebras related to logic, Borel state, Theoretical Computer Science, Dutch book, Artificial Intelligence, Many-valued logic, subjective probability, Finitely additive measure, 0202 electrical engineering, electronic engineering, information engineering, Dutch Book, 0101 mathematics, finitely additive measure, Software

File Description: application/xml

Bookmaking over infinite-valued events

Authors: MUNDICI, DANIELE

Source: International Journal of Approximate Reasoning. 43:223-240

Subject Terms: MV-algebras, De Finetti coherence criterion, Applied Mathematics, many-valued logic, MV-algebra, 02 engineering and technology, Probability and inductive logic, 01 natural sciences, Axioms, other general questions in probability, Łukasiewicz logic, Subjective probability, Theoretical Computer Science, state, Dutch book, Artificial Intelligence, Many-valued logic, subjective probability, Finitely additive measure, 0202 electrical engineering, electronic engineering, information engineering, Łukasiewicz logic, De Finetti coherence criterion, Dutch Book, Finitely additive measure, Many-valued logic, MV-algebra, State, Subjective probability, Dutch Book, 0101 mathematics, State, finitely additive measure, Software

File Description: application/xml

Faithful and Invariant Conditional Probability in Łukasiewicz Logic

Authors: Mundici, Daniele^Aff1

Contributors: Wójcicki, Ryszard, editor^Aff21, Hendricks, Vincent F., editor^Aff22, Mundici, Daniele, editor^Aff23, Orłowska, Ewa, editor^Aff24, Segerberg, Krister, editor^Aff25, Wansing, Heinrich, editor^{Aff26, Aff13}, Makinson, David, editor^Aff11, Malinowski, Jacek, editor^Aff12

Source: Towards Mathematical Philosophy : Papers from the Studia Logica conference Trends in Logic IV. 28:213-232

Łukasiewicz logic and Riesz spaces: Łukasiewicz logic and Riesz spaces.

Authors: DI NOLA, Antonio, Ioana Leustean

Source: Soft Computing. 18:2349-2363

Subject Terms: MV-algebras, 06D35, 03B50, Mathematics - Logic, \(\Gamma\)-equivalence, de Finetti coherence criterion, Riesz MV-algebra, Ordered abelian groups, Riesz groups, ordered linear spaces, 01 natural sciences, Riesz MV-algebras, General theory of \(C^*\)-algebras, Many-valued logic, \(\Gamma\)-functor, FOS: Mathematics, 0101 mathematics, Logic (math.LO), Ordered topological linear spaces, vector lattices

File Description: application/xml

Access URL: http://arxiv.org/pdf/1309.1575
http://arxiv.org/abs/1309.1575

Measures, states and de Finetti maps on pseudo-BCK algebras

Authors: Lavinia Corina Ciungu, Anatolij Dvurecenskij

Source: Fuzzy Sets and Systems. 161:2870-2896

Subject Terms: MV-algebras, Bosbach state, MV-algebra, lattice-ordered group, Mathematics - Logic, 02 engineering and technology, de Finetti coherence, 01 natural sciences, Borel state, BCK-algebras, BCI-algebras, BCK-algebra, extremal state, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Logic (math.LO)

File Description: application/xml

Access URL: http://arxiv.org/pdf/0905.4789
http://arxiv.org/abs/0905.4789

On varieties of MV-algebras with internal states

Authors: DI NOLA, Antonio, DVURECENSKIJ A, LETTIERI, Ada

Source: International Journal of Approximate Reasoning. 51:680-694

Subject Terms: MV-algebras, Subdirectly irreducible state MV-algebra, State-morphism-operator, Applied Mathematics, State-morphism MV-algebra, 02 engineering and technology, de Finetti coherence, 01 natural sciences, Theoretical Computer Science, state-morphism MV-algebras, State MV-algebra, MV-algebraic state, Artificial Intelligence, Internal state, Many-valued logic, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Software

File Description: application/xml; application/pdf

Access URL: http://hdl.handle.net/11588/367794
https://hdl.handle.net/11386/2600060
https://hdl.handle.net/11588/367794
https://doi.org/10.1016/j.ijar.2010.01.017

Interpretation of De Finetti coherence criterion in Łukasiewicz Logic: Interpretation of De Finetti coherence criterion in Łukasiewicz logic

Authors: MUNDICI, DANIELE

Source: Annals of Pure and Applied Logic. 161:235-245

Subject Terms: MV-algebras, De Finetti coherence criterion, Logic, MV-algebra, 02 engineering and technology, Probability and inductive logic, 01 natural sciences, Axioms, other general questions in probability, Łukasiewicz logic, Borel probability measure, Dutch book, many-valued logics, Many-valued logic, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics

File Description: application/xml; application/pdf

Access URL: https://hdl.handle.net/2158/372455

Sandwich-type theorems and applications to invariant measures

Authors: BOCCUTO, Antonio, CANDELORO, Domenico

Subject Terms: Riesz space, sandwich theorem, invariant measure, de Finetti coherence, asymptotic density

Access URL: https://hdl.handle.net/11391/156842

Comments on Reasoning about Uncertainty of Fuzzy Events: An Overview by Tommaso Flaminio, Lluıs Godo, and Enrico Marchioni

Authors: Kroupa, T. (Tomáš)

Subject Terms: fuzzy measure, fuzzy event, de Finetti coherence criterion

Relation: https://hdl.handle.net/11104/0208813

Availability: https://hdl.handle.net/11104/0208813