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Quantum probability and Hilbert's sixth problem.
Accardi L. Accardi L. Philos Trans A Math Phys Eng Sci. 2018 Apr 28;376(2118):20180030. doi: 10.1098/rsta.2018.0030. Philos Trans A Math Phys Eng Sci. 2018. PMID: 29555809 Review.
With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entangled and a new probabilistic model arose in addition to the classical one. ...
With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entan …
A Logical Modeling of Severe Ignorance.
Bonzio S, Fano V, Graziani P, Pra Baldi M. Bonzio S, et al. J Philos Logic. 2023 Apr 11:1-28. doi: 10.1007/s10992-022-09697-x. Online ahead of print. J Philos Logic. 2023. PMID: 37362804 Free PMC article.
As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it severe ignorance. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued …
As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditio …
Rényi Entropy, Signed Probabilities, and the Qubit.
Brandenburger A, La Mura P, Zoble S. Brandenburger A, et al. Entropy (Basel). 2022 Oct 3;24(10):1412. doi: 10.3390/e24101412. Entropy (Basel). 2022. PMID: 37420432 Free PMC article.
The states of the qubit, the basic unit of quantum information, are 2 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formula …
The states of the qubit, the basic unit of quantum information, are 2 2 positive semi-definite Hermitian matrices with trace 1. We contribut …
The logic induced by effect algebras.
Chajda I, Halaš R, Länger H. Chajda I, et al. Soft comput. 2020;24(19):14275-14286. doi: 10.1007/s00500-020-05188-w. Epub 2020 Jul 26. Soft comput. 2020. PMID: 32968356 Free PMC article.
Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effect algebras which need not be lattice-ordered, we introduce a certain kind of implication which is everywhere defined but whose result need …
Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effe …
A Topological Approach to Full Belief.
Baltag A, Bezhanishvili N, Özgün A, Smets S. Baltag A, et al. J Philos Logic. 2019;48(2):205-244. doi: 10.1007/s10992-018-9463-4. Epub 2018 May 23. J Philos Logic. 2019. PMID: 30956353 Free PMC article.
We then propose a solution consisting in interpreting belief in a similar way based on hereditarily extremally disconnected spaces, and axiomatize the belief logic of hereditarily extremally disconnected spaces. ...
We then propose a solution consisting in interpreting belief in a similar way based on hereditarily extremally disconnected spaces, and a …
Suppes predicate for genetics and natural selection.
Magalhães JC, Krause D. Magalhães JC, et al. J Theor Biol. 2001 Mar 21;209(2):141-53. doi: 10.1006/jtbi.2000.2243. J Theor Biol. 2001. PMID: 11401456
Patrick Suppes' slogan that "to axiomatize a theory is to present a set-theoretical predicate" was used in the synthetic theory of evolution. ...
Patrick Suppes' slogan that "to axiomatize a theory is to present a set-theoretical predicate" was used in the synthetic theory of ev …
Self-Testing of Physical Theories, or, Is Quantum Theory Optimal with Respect to Some Information-Processing Task?
Weilenmann M, Colbeck R. Weilenmann M, et al. Phys Rev Lett. 2020 Aug 7;125(6):060406. doi: 10.1103/PhysRevLett.125.060406. Phys Rev Lett. 2020. PMID: 32845669
A generalization of our results showing that all nonquantum GPTs are strictly inferior to quantum mechanics for this task would point to a new way to axiomatize quantum theory, and enable an experimental test that simultaneously rules out such GPTs....
A generalization of our results showing that all nonquantum GPTs are strictly inferior to quantum mechanics for this task would point to a n …