@conference {5612,
title = {On Boolean Algebras of Conditionals and Their Logical Counterpart},
booktitle = {Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 14th European Conference, ECSQARU 2017},
volume = {10369},
year = {2017},
pages = {246-256},
abstract = {This paper sheds a novel light on the longstanding problem of investigating the logic of conditional events. Building on the framework of Boolean algebras of conditionals previously introduced by the authors, we make two main new contributions. First, we fully characterise the atomic structure of these algebras of conditionals. Second, we introduce the logic of Boolean conditionals (LBC) and prove its completeness with respect to the natural semantics induced by the structural properties of the atoms in a conditional algebra as described in the first part. In addition we outline the close connection of LBC with preferential consequence relations, arguably one of the most appreciated systems of non-monotonic reasoning.},
url = {https://link.springer.com/chapter/10.1007/978-3-319-61581-3_23}
}
@article {5291,
title = {Coherence in the aggregate: a betting method for belief functions on many-valued events},
journal = {International Journal of Approximate Reasoning},
volume = {58},
year = {2015},
pages = {71-86},
publisher = {Elsevier},
abstract = {Betting methods, of which de Finetti{\textquoteright}s Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a two-fold aim. Whilst providing an (operational) 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 the classical Dutch Book method.},
keywords = {Belief functions, De Finetti, Many-valued events, Subjective probability},
url = {http://www.sciencedirect.com/science/article/pii/S0888613X1500002X},
author = {Tommaso Flaminio and Llu{\'\i}s Godo and Hykel Hosni}
}
@conference {5408,
title = {On the algebraic structure of conditional events},
booktitle = {ECSQARU 2015},
volume = {9161},
year = {2015},
month = {15/07/2015},
pages = {106-116},
publisher = {Springer},
organization = {Springer},
edition = {S. Destercke and T. Denoeux},
address = {Compi{\`e}gne, France},
abstract = {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.},
author = {Tommaso Flaminio and Llu{\'\i}s Godo and Hykel Hosni}
}
@article {5170,
title = {On the logical structure of de Finetti{\textquoteright}s notion of event},
journal = {Journal of Applied Logic},
volume = {12},
year = {2014},
pages = {279-301},
publisher = {Elsevier},
abstract = {This paper sheds new light on the subtle relation between probability and logic by (i) providing a logical development of Bruno de Finetti{\textquoteright}s conception of events and (ii) suggesting that the subjective nature of de Finetti{\textquoteright}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{\textquoteright}t hold: some probability values don{\textquoteright}t represent decision-relevant quantifications of uncertainty.},
keywords = {Choice-based probability, De Finetti{\textquoteright}s coherence criterion, Events, Informations frames},
url = {http://www.sciencedirect.com/science/article/pii/S1570868314000214},
author = {Tommaso Flaminio and Llu{\'\i}s Godo and Hykel Hosni}
}
@conference {4923,
title = {Zero-probability and coherent betting: A logical point of view},
booktitle = {12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2013},
volume = {7958},
year = {2013},
month = {07/07/2013},
pages = {206-217},
publisher = {Springer},
organization = {Springer},
edition = {Linda C. van der Gaag},
address = {Utrecht, The Netherlands},
abstract = {The investigation reported in this paper aims at clarifying an important yet subtle distinction between (i) the logical objects on which measure theoretic probability can be defined, and (ii) the interpretation of the resulting values as rational degrees of belief. Our central result can be stated informally as follows. Whilst all subjective degrees of belief can be expressed in terms of a probability measure, the converse does not hold: probability measures can be defined over linguistic objects which do not admit of a meaningful betting interpretation. The logical framework capable of expressing this will allow us to put forward a precise formalisation of de Finetti{\textquoteright}s notion of event which lies at the heart of the Bayesian approach to uncertain reasoning.},
url = {http://link.springer.com/chapter/10.1007\%2F978-3-642-39091-3_18},
author = {Tommaso Flaminio and Llu{\'\i}s Godo and Hykel Hosni}
}
@conference {4657,
title = {De Finetti{\textquoteright}s bets on partially evaluated Kripke frames},
booktitle = {Computability in Europe - Turing{\textquoteright}s Centenary},
year = {2012},
month = {19/6/2012},
address = {Cambridge, UK},
abstract = {De Finetti{\textquoteright}s conception of events is one of the most distinctive aspects of his theory of probability, yet it appears to be somewhat elusive. The purpose of this note is to set up a formal framework in which a rigorous characterisation of this notion, and its cognate modelling assumptions, gives rise to a detailed formalisation of the betting problem which underlies the celebrated Dutch Book Argument. In particular, we introduce partially evaluated Kripke frames, relational structures which put the implicit modal semantics of events on a rigorous footing and allow us to refine the notion of coherence originally put forward by de Finetti. As our main result shows, this refinement captures an intuitive condition which de Finetti imposed on the betting problem, namely that it is irrational to bet on an event which may be true, but whose truth will never be ascertained by the players.},
url = {http://www.mathcomp.leeds.ac.uk/turing2012/WScie12/},
author = {Tommaso Flaminio and Hykel Hosni}
}
@conference {4646,
title = {The epistemic structure of de Finetti{\textquoteright}s betting problem},
booktitle = {9th Italian Convention on Computational Logic (CILC 2012)},
volume = {857},
year = {2012},
month = {6/06/2012},
pages = {241{\textendash}245},
address = {Rome},
abstract = {De Finetti{\textquoteright}s conception of events is one of the most distinctive aspects of his theory of probability, yet it appears to be somewhat elusive. The purpose of this note is to set up a formal framework in which a rigorous characterisation of this notion, and its cognate modelling assumptions, gives rise to a detailed formalisation of the betting problem which underlies the celebrated Dutch Book Argument. As our main result shows, this re?nement captures an intuitive condition which de Finetti imposed on the betting problem, namely that it is irrational to bet on an event which may be true, but whose truth will never be ascertained by the players.},
url = {http://ceur-ws.org/Vol-857/},
author = {Tommaso Flaminio and Hykel Hosni},
editor = {Francesca A. Lisi}
}
@conference {4157,
title = {On Conditional Many-valued Events Alegbras},
booktitle = {Algebra and Probability in Many Valued Logics},
year = {2009},
address = {Darmstadt, Germany},
author = {Tommaso Flaminio and Hykel Hosni}
}
@conference {4160,
title = {Towards an algebraic framework for many-valued conditional probability},
booktitle = {Progic 2009: 4th Workshop on Combining Probability and Logic},
year = {2009},
address = {Groningen, The Netherlands},
author = {Tommaso Flaminio and Hykel Hosni}
}