A short survey of main historical developments of systems of fuzzy logic in narrow sense, today under the umbrella of the discipline called Mathematical Fuzzy Logic, arising from teducation-teaching-fuzzy_math-fuzzy_mathematics-fuzzy_set_theory-mathematicians-math_teacher-rmon4614_low.jpghe birth of Zadeh’s fuzzy sets in 1965. Particular attention is devoted to show how the tools of mathematical logic have allowed to define logical systems which form the core of Mathematical Fuzzy Logic and allow for a formalization of some topics included in Zadeh’s agenda spanning from fuzzy sets to approximate reasoning and probability theory of fuzzy events.

The full issue can be downloaded for free here

Strict coherence for infinite-valued events

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My paper “Three characterization of strict coherence for infinite-valued events” has been published online on the Review of Symbolic Logic.  If you are interest, please follow this link

Hyperstates of involutive MTL-algebras and states of prelinear semihoop

The paper coauthored by Sara Ugolini and myself on hyperreal-valued probability measures (hyperstates) of involutive MTL-algebras and real-valued states of prelinear semihoop will be available soon in the proceedings of the 8th International Workshop on Logic and Cognition (WOLC2016) and it will be published by Springer (Logic in Asia).

The aim of that contribution is to provide a preliminary investigation for states of prelinear semihoops and hyperstates of algebras in the variety generated by perfect and involutive MTL-algebras (IBP0-algebras for short). Grounding on a recent result showing that IBP0- algebras can be constructed from a Boolean algebra, a prelinear semihoop and a suitably defined operator between them, our first investigation on states of prelinear semihoops will support and justify the notion of hyperstate for IBP0- algebras and will actually show that each such map can be represented by a probability measure on its Boolean skeleton, and a state on a suitably defined abelian l-group.

ECSQARU 2019

The 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019) will be held in Belgrade (Serbia), on September 18-20, 2019, at the Serbian Academy of Sciences and Arts in Belgrade.

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The biennial ECSQARU conferences constitute a major forum for advances in the theory and practice of reasoning under uncertainty, with a focus on bringing symbolic and quantitative aspects together. Contributions come from researchers interested in advancing the scientific knowledge and from practitioners using uncertainty techniques in real-world applications. The scope of the ECSQARU conferences encompasses fundamental issues, representation, inference, learning, and decision making in qualitative and numeric uncertainty paradigms.

Submission infos are here available

Probability theory on product logic

Our paper (coauthored by Lluis Godo, Sara Ugolini and myself) titled “Towards a probability theory for product logic: states, integral representation and reasoning” has been accepted to be published in the International Journal of Approximate Reasoning. There, among other things, we extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique regular Borel probability measure. 

Layers of zero probability and stable coherence over Łukasiewicz events

Tommaso Flaminio, Lluis Godo

The notion of stable coherence has been recently introduced to characterize coherent assignments to conditional many-valued events by means of hyperreal-valued states. In a nutshell, an assignment, or book, β on a finite set of conditional events is stably coherent if there exists a coherent variant β of β such that β maps all antecedents of conditional events to a strictly positive hyperreal number, and such that β and β differ by an infinitesimal. In this paper, we provide a characterization of stable coherence in terms of layers of zero probability for books on Łukasiewicz logic events.

Keywords: Layers of zero probability, Conditional probability, Stable coherence MV-algebras. 

Volume 21, Issue 1, pp. 113–123.