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.

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

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