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

Finite Gödel algebras with modal operators

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In a joint paper with Lluis Godo and Ricardo O. Rodriguez we recently studied a modal expansion of finite Gödel algebras (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.

The paper has been published in the proceedings of WoLLIC2019 which have been held in Utrecht (Netherlands) on July 2019. Further details are available in Springer webpage: LNCS11541

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

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.

Brazil and mangoes

IMG_20180203_143956_261.jpgFirst week in Campinas (São Paulo, Brazil) for a one month visit to the Centre for Logic, Epistemology and History of Science. The work here is focusing on determining a term-equivalent (unary and easier to interpret) fragments of Lukasiewicz finite-valued logics which could capture paraconsistent properties. It’s funny, some arithmetic, prime numbers, and little bit of algebra at work. When we do not work, I use to have a walk. It’s summer here and wherever I look, I see mangoes.

Ramón y Cajal

On January 16, I started my Ramón y Cajal research grant at the Artificial Intelligence Research Institute of the Spanish National Research Council placed in UAB campus in Bellaterra, Barcelona. My research activity will be mainly concerned with the development of logics for AI and in particular with logical foundations of uncertainty (the usual thing).

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That’s the good news. The bad one is: I need to find a house in Barcelona, and it ain’t easy.

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.