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Gianluca Paolini
University of Amsterdam
  1.  36
    Quantum Team Logic and Bell’s Inequalities.Tapani Hyttinen, Gianluca Paolini & Jouko Väänänen - 2015 - Review of Symbolic Logic 8 (4):722-742.
    A logical approach to Bell's Inequalities of quantum mechanics has been introduced by Abramsky and Hardy [2]. We point out that the logical Bell's Inequalities of [2] are provable in the probability logic of Fagin, Halpern and Megiddo [4]. Since it is now considered empirically established that quantum mechanics violates Bell's Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell's Inequalities are not provable, and prove a Completeness Theorem for this logic. For this (...)
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  2.  18
    Strongly minimal Steiner systems I: Existence.John Baldwin & Gianluca Paolini - 2021 - Journal of Symbolic Logic 86 (4):1486-1507.
    A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner k-system is a linear space such that each line has size exactly k. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a vocabulary $\tau $ with a single ternary relation R. We prove that for every integer k there exist $2^{\aleph _0}$ -many integer valued functions $\mu $ such that (...)
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  3.  27
    Beyond abstract elementary classes: On the model theory of geometric lattices.Tapani Hyttinen & Gianluca Paolini - 2018 - Annals of Pure and Applied Logic 169 (2):117-145.
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  4.  10
    Computable scott sentences for quasi–Hopfian finitely presented structures.Gianluca Paolini - 2023 - Archive for Mathematical Logic 62 (1):55-65.
    We prove that every quasi-Hopfian finitely presented structure _A_ has a _d_- \(\Sigma _2\) Scott sentence, and that if in addition _A_ is computable and _Aut_(_A_) satisfies a natural computable condition, then _A_ has a computable _d_- \(\Sigma _2\) Scott sentence. This unifies several known results on Scott sentences of finitely presented structures and it is used to prove that other not previously considered algebraic structures of interest have computable _d_- \(\Sigma _2\) Scott sentences. In particular, we show that every (...)
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  5.  19
    A logic for arguing about probabilities in measure teams.Tapani Hyttinen, Gianluca Paolini & Jouko Väänänen - 2017 - Archive for Mathematical Logic 56 (5-6):475-489.
    We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our axiomatisation. We use the Hardy–Weinberg Principle of biology and the Bell’s Inequalities of quantum physics as examples.
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  6.  20
    Dependence logic in pregeometries and ω-stable theories.Gianluca Paolini & Jouko Väänänen - 2016 - Journal of Symbolic Logic 81 (1):32-55.
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  7.  39
    Independence logic and abstract independence relations.Gianluca Paolini - 2015 - Mathematical Logic Quarterly 61 (3):202-216.
    We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics and statistics.
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  8.  10
    Computable Scott sentences and the weak Whitehead problem for finitely presented groups.Gianluca Paolini - 2024 - Annals of Pure and Applied Logic 175 (7):103441.
  9.  9
    Reduction of database independence to dividing in atomless Boolean algebras.Tapani Hyttinen & Gianluca Paolini - 2016 - Archive for Mathematical Logic 55 (3-4):505-518.
    We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections between independence in database theory and stochastic independence. As indeed, in light of the aforementioned reduction and recent work of Ben-Yaacov :957–1012, 2013), the former case of independence can be seen as the discrete version of the latter.
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  10.  10
    Coxeter Groups and Abstract Elementary Classes: The Right-Angled Case.Tapani Hyttinen & Gianluca Paolini - 2019 - Notre Dame Journal of Formal Logic 60 (4):707-731.
    We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes (AECs), for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results translates (...)
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  11.  14
    First-order model theory of free projective planes.Tapani Hyttinen & Gianluca Paolini - 2021 - Annals of Pure and Applied Logic 172 (2):102888.
  12.  14
    A Finite Axiomatization of G-Dependence.Gianluca Paolini - 2017 - Journal of Logic, Language and Information 26 (3):293-302.
    We show that a form of dependence known as G-dependence admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.
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  13.  18
    Independence in Model Theory and Team Semantics.Gianluca Paolini - 2018 - Bulletin of Symbolic Logic 24 (4):461-462.
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