
12 July 2017

05:00PM  07:00PM

Room: Catalana

Chairs: Brunella Gerla, Diego Valota and Pietro Codara
Recent trends in manyvalued logic and fuzziness
Abstract  We study commutative idempotent semirings in general, and some examples in particular. We show that the class Red of semiring reducts of MValgebras, although axiomatized by a first order theory, is not axiomatized by a geometric theory (in the topostheoretic sense) or a universalexistential first order theory. Then we perform comparisons between the class Red, the class of all semirings, and some socalled exotic semirings.
Abstract  Fuzzy relational compositions based on fuzzy quantifiers naturally do not preserve all the properties that are preserved for "standard" fuzzy relational compositions and, in many cases, the property is preserved only in a weaker form. For example, the associativity, that is preserved in the standard case derived from the universal and the existential quantifiers, generally does not hold for the case of compositions based on fuzzy quantifiers. However, is it the case that only the standard quantifiers lead to the preservation of such properties? Without any restriction on the shape of the fuzzy relations, the answer is positive.
Abstract  A structural description of absorbentcontinuous grouplike commutative residuated lattices over complete, orderdense chains will be presented. The theorem is sharp, no further generalization is possible. Grouplike commutative residuated lattices will be characterized as Abelian latticeordered groups deprived of their cancellative property only. The so called partiallexicographic product constructions (two of them) will be introduced, which construct grouplike commutative residuated lattices. As a sideeffect, it gives rise to the socalled involutive ordinal sum construction, which constructs grouplike commutative residuated lattices from a family of grouplike commutative residuated lattices. Via two decomposition theorems, corresponding to the partiallexicographic product constructions, it will be shown that any orderdense grouplike commutative residuated chain, which has only a finite number of idempotents can be built by iterating finitely many times the partiallexicographic product constructions using solely totally ordered Abelian groups, as building blocks. The result extends the famous structural description of totally ordered Abelian groups by Hahn, to orderdense grouplike commutative residuated chains with finitely many idempotents.
Abstract  A twofold general approach to the theory of formal concept analysis is introduced by considering intuitionistic fuzzy sets valued on a residuated lattice as underlying structure for the construction.
Abstract  In this paper we study Moisil logic, a manyvalued system based on the idea of nuancing. We prove a completeness theorem for graded deduction and make a first attempt towards a game semantics for this logic.
Abstract  We provide a standard completeness proof which uniformly applies to a large class of axiomatic extensions of Involutive Monoidal Tnorm Logic (IMTL). In particular, we identify sufficient conditions on the proof calculi which ensure density elimination and then standard completeness. Our argument contrasts with all previous approaches for involutive logics which are logicspecific.
Abstract  In a previous paper, it was shown that the (minimal) modal logic \${$\backslash$}MLn\$ with fuzzy accessibility relations over the finitevalued \{{$\backslash$}L\}ukasiewicz logic {$\backslash$}L\$\_n\$ and a corresponding multimodal logic \${$\backslash$}mMLn\$ (with a modality \${$\backslash$}Box\_a\$ for each value \$a\$ in the \$n\$valued {$\backslash$}L\$\_n\$chain) had the same expressive power when the language is extended with truthconstants. In this paper we partially extend these results partially when replacing the underlying logic {$\backslash$}L\$\_n\$ by the infinitevalued \{{$\backslash$}L\}ukasiewicz logic (with rational truth constants in the language). We prove that the (standard) tautologies of the modal logic \${$\backslash$}ML\$ (resp. \${$\backslash$}mML\$) are in fact the common tautologies of all the logics \${$\backslash$}MLn\$ (resp. all the logics \${$\backslash$}mMLn\$) when letting \$n\$ vary over \${$\backslash$}mathbb\{N\}\$. This fact opens the door to show an alternative proof of the finite model property for these logics and hence their decidability.
Abstract  We give a [0,1]functional representation of the finitely generated free algebras in the variety generated by Chang's MValgebra C, and in the variety generated by the left continuous tnorm arising as Jenei's rotation JPi of the product tnorm. We generalise the construction of JPi from C by building a family T\_n of involutive tnorm algebras such that the MValgebras in the variety generated by T\_n form the variety generated by S\_n\^{}{$\backslash$}omega and L\_\{n+1\}.