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

A representation theorem for finite Gödel algebras with operators

 

T. Flaminio, L. Godo, R. O. Rodriguez

978-3-662-59533-6.jpgIn this paper we introduce and study finite Gödel algebras with operators (GAOs for short) and their dual frames. Taking into account that the category of finite Gödel algebras with homomorphisms is dually equivalent to the category of finite forests with order-preserving open maps, the dual relational frames of GAOs are forest frames: finite forests endowed with two binary (crisp) relations satisfying suitable properties. Our main result is a Jónsson-Tarski like representation theorem for these structures. In particular we show that every finite Gödel algebra with operators determines a unique forest frame whose set of subforests, endowed with suitably defined algebraic and modal operators, is a GAO isomorphic to the original one.

Keywords:Finite Gödel algebras; modal operators; finite forests; representation theorem.

 

In: Iemhoff R., Moortgat M., de Queiroz R. (eds). Logic, Language, Information, and Computation, WoLLIC 2019. LNCS 11541: 223–235, Springer, 2019.

IPMU 2018

 

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My contribute paper titled “Logics for strict coherence and Carnap-regular probability functions” has been recently accepted to be presented at the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems – IPMU 2018.  that will take place in Cádiz, Spain.

Equivalences between subcategories of MTL-algebras via Boolean algebras and prelinear semihoops

Stefano Aguzzoli, Tommaso Flaminio, Sara Ugolini

This article studies the class of strongly perfect MTL-algebras, i.e. MTL-algebras having an involutive co-radical, and the variety they generate, namely SBP0. Once these structures will be introduced, we will first establish categorical equivalences for several of their relevant proper subvarieties by employing a generalized notion of triplets whose main components are a Boolean algebra and a prelinear semihoop. When triplets are further expanded by a suitable operation between their semihoop reducts, we define a category of quadruples that are equivalent to the whole category of SBP0-algebras. Finally, we will provide an explicit representation of SBP0-algebras in terms of (weak) Boolean products.

Keywords: Strongly perfect MTL-algebras, Boolean Algebras, Prelinear Semihoops, Categorical Equivalence

Journal of Logic and Computation, exx014, https://doi.org/10.1093/logcom/exx014