16 found
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  1. On the logical structure of de Finetti's notion of event.Tommaso Flaminio, Lluis Godo & Hykel Hosni - 2014 - Journal of Applied Logic 12 (3):279-301.
    This paper sheds new light on the subtle relation between probability and logic by (i) providing a logical development of Bruno de Finetti's conception of events and (ii) suggesting that the subjective nature of de Finetti's interpretation of probability emerges in a clearer form against such a logical background. By making explicit the epistemic structure which underlies what we call Choice-based probability we show that whilst all rational degrees of belief must be probabilities, the converse doesn't hold: some probability values (...)
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  2. On the expressive power of Łukasiewicz square operator.Marcelo E. Coniglio, Francesc Esteva, Tommaso Flaminio & Lluis Godo - forthcoming - Journal of Logic and Computation.
    The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...)
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  3. How to Believe Long Conjunctions of Beliefs: Probability, Quasi-Dogmatism and Contextualism.Stefano Bonzio, Gustavo Cevolani & Tommaso Flaminio - 2021 - Erkenntnis 88 (3):965-990.
    According to the so-called Lockean thesis, a rational agent believes a proposition just in case its probability is sufficiently high, i.e., greater than some suitably fixed threshold. The Preface paradox is usually taken to show that the Lockean thesis is untenable, if one also assumes that rational agents should believe the conjunction of their own beliefs: high probability and rational belief are in a sense incompatible. In this paper, we show that this is not the case in general. More precisely, (...)
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  4. Coherence in the aggregate: a betting method for belief functions on many-valued events.Tommaso Flaminio, Lluis Godo & Hykel Hosni - unknown
    Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises (...)
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  5.  24
    Boolean algebras of conditionals, probability and logic.Tommaso Flaminio, Lluis Godo & Hykel Hosni - 2020 - Artificial Intelligence 286 (C):103347.
  6.  18
    Three characterizations of strict coherence on infinite-valued events.Tommaso Flaminio - 2020 - Review of Symbolic Logic 13 (3):593-610.
    This article builds on a recent paper coauthored by the present author, H. Hosni and F. Montagna. It is meant to contribute to the logical foundations of probability theory on many-valued events and, specifically, to a deeper understanding of the notion of strict coherence. In particular, we will make use of geometrical, measure-theoretical and logical methods to provide three characterizations of strict coherence on formulas of infinite-valued Łukasiewicz logic.
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  7.  20
    Strict coherence on many-valued events.Tommaso Flaminio, Hykel Hosni & Franco Montagna - 2018 - Journal of Symbolic Logic 83 (1):55-69.
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  8.  52
    Counterfactuals as modal conditionals, and their probability.Giuliano Rosella, Tommaso Flaminio & Stefano Bonzio - 2023 - Artificial Intelligence 323 (C):103970.
    In this paper we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be reconstructed in (...)
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  9.  50
    A logical and algebraic treatment of conditional probability.Tommaso Flaminio & Franco Montagna - 2005 - Archive for Mathematical Logic 44 (2):245-262.
    Abstract.This paper is devoted to a logical and algebraic treatment of conditional probability. The main ideas are the use of non-standard probabilities and of some kind of standard part function in order to deal with the case where the conditioning event has probability zero, and the use of a many-valued modal logic in order to deal probability of an event φ as the truth value of the sentence φ is probable, along the lines of Hájek’s book [H98] and of [EGH96]. (...)
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  10.  18
    A logico-geometric comparison of coherence for non-additive uncertainty measures.Esther Anna Corsi, Tommaso Flaminio & Hykel Hosni - 2024 - Annals of Pure and Applied Logic 175 (9):103342.
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  11. Sure-wins under coherence: a geometrical perspective.Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi - 2019 - In Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science.
    In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...)
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  12.  13
    Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras.Tommaso Flaminio & Sara Ugolini - 2024 - Annals of Pure and Applied Logic 175 (9):103337.
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  13.  47
    Franco Montagna’s Work on Provability Logic and Many-valued Logic.Lev Beklemishev & Tommaso Flaminio - 2016 - Studia Logica 104 (1):1-46.
    Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic.
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  14. Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science.Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi (eds.) - 2019
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  15.  55
    NP-containment for the coherence test of assessments of conditional probability: a fuzzy logical approach. [REVIEW]Tommaso Flaminio - 2007 - Archive for Mathematical Logic 46 (3-4):301-319.
    In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be characterized by means of the logical consistency of a suitable theory T χ defined on the modal-fuzzy logic FP k (RŁΔ) built up over the many-valued logic RŁΔ. Such modal-fuzzy logic was previously introduced in Flaminio (Lecture Notes in Computer Science, vol. (...)
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  16.  54
    On the algebraic structure of conditional events: 13th European conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015. [REVIEW]Tommaso Flaminio, Lluis Godo & Hykel Hosni - unknown
    This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts.
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