Hykel Hosni

This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events. By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals. Our main result provides a way to regard standard two-place conditional probabilities as one-place probability functions on conditional events. We also consider a logical counterpart of our Boolean algebras of conditionals with links to preferential consequence relations for non-monotonic reasoning. The overall framework of this paper provides a novel perspective on the rich interplay between logic and probability in the representation of conditional knowledge.

KEYWORDS:  Conditional probability; conditional events; Boolean algebras; preferential consequence relations

This paper introduces and investigates Depth-bounded Belief functions, a logic-based representation of quantified uncertainty. Depth-bounded Belief functions are based on the framework of Depth-bounded Boolean logics, which provide a hierarchy of approximations to classical logic. Similarly, Depth-bounded Belief functions give rise to a hierarchy of increasingly tighter lower and upper bounds over classical measures of uncertainty. This has the rather welcome consequence that “higher logical abilities” lead to sharper uncertainty quantification. In particular, our main results identify the conditions under which Dempster-Shafer Belief functions and probability functions can be represented as a limit of a suitable sequence of Depth-bounded Belief functions.

KEYWORDS: Belief functions; Uncertain reasoning; Depth-bounded logics; Probability.

P. Baldi and H. Hosni. (2020). “Depth-bouned Belief Functions” Internatonal Journal of Approximate Reasoning, Volume 123, August 2020, Pages 26-40. doi.org/10.1016/j.ijar.2020.05.001 (Open Access)

Since the seminal work of John Nash, convex combinations of actions are known to guarantee the existence of equilibria in strategic-form games. This paper introduces an alternative notion of randomisation among actions – possibilistic randomisation – and investigates the mathematical consequences of doing so. The framework of possibility theory gives rise to two distinct notions of equilibria both of which are characterised in our main results: a qualitative one based on the Sugeno integral and a quantitative one based on the Choquet integral. Then the two notions of equilibrium are compared against a coordination game with payoff-distinguishable equilibria known as the Weak-link game.

KEYWORDS: Possibilistic randomisation; Mixed strategies; Possibilistic expected utility; Nash equilibria; Weak-link game; Selection of multiple equilibria

Hosni, H and E. Marchioni. (2019). “Possibilistic randomisation in strategic-form games” Internatonal Journal of Approximate Reasoning, 114, 204-225.  https://doi.org/10.1016/j.ijar.2019.08.008

Preprint

We investigate the property of strict coherence in the setting of many-valued logics. Our main results read as follows: (i) a map from an MV-algebra to [0,1] is strictly coherent if and only if it satisfies Carnap’s regularity condition, and (ii) a [0,1]-valued book on a finite set of many-valued events is strictly coherent if and only if it extends to a faithful state of an MV-algebra that contains them. Remarkably this latter result allows us to relax the rather demanding conditions for the Shimony-Kemeny characterisation of strict coherence put forward in the mid 1950s in this Journal.

KEYWORDS: s. Probability logic, strict coherence, MV-algebras, faithful states, many-valued logics.

Flaminio, T., H. Hosni, and F. Montagna. (2018). “Strict Coherence on Many Valued Events” Journal of Symbolic Logic . 83(1), 55-69. DOI:10.1017/jsl.2017.34

Head and neck cancers can be used as a paradigm for exploring “big data” applications in oncology. Computational strategies derived from big data science hold the promise of shedding new light on the molecular mechanisms driving head and neck cancer pathogenesis, identifying new prognostic and predictive factors, and discovering potential therapeutics against this highly complex disease. Big data strategies integrate robust data input, from radiomics, genomics, and clinical-epidemiological data to deeply describe head and neck cancer characteristics. Thus, big data may advance research generating new knowledge and improve head and neck cancer prognosis supporting clinical decision-making and development of treatment recommendations.

KEYWORDS: Big data; Decision support system; Evidence based medicine; Forecasting; Genomics; Guidelines; Head and neck cancer; Machine learning; Oncology; Radiomics; Radiotherapy; Support vector machine; Surgery

Resteghini C, Trama A, Borgonovi E, Hosni H, Corrao G, Orlandi E, Calareso G, De Cecco L, Piazza C, Mainardi L, Licitra L. “Big Data in Head and Neck Cancer”. Current Treatment Options in Oncology 2018 Oct 25;19(12):62. doi: 10.1007/s11864-018-0585-2.

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Datacentric enthusiasm is growing strong across a variety of domains.
Whilst data science asks unquestionably exciting scientific questions, we argue that its
contributions should not be extrapolated from the scientific context in which they originate. In particular we suggest that the simple-minded idea to the effect that data can be seen as a replacement for scientific modelling is not tenable.
By recalling some well-known examples from dynamical systems we conclude that data science performs at its best when coupled with the subtle art of modelling.

KEYWORDS: Big data, Scientific modelling

H. Hosni and A. Vulpiani, “Data science and the art of modelling”,  Lettera Matematica International (May 2018) https://doi.org/10.1007/s40329-018-0225-5

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