First order Gödel logic G∞, enriched with the projection operator 4—in contrast to other important t-norm based fuzzy logics, like Lukasiewicz and Product logic—is well known to be recursively axiomatizable. However, unlike in classical logic, testing (1-)unsatisfiability, i.e., checking whether a formula has no interpretation that assigns the designated truth value 1 to it, cannot be straightf...

This paper is devoted to construction of fuzzy preference relations and to showing how this construction is connected with Lukasiewicz filters and TL-evaluators. We will study also extensions of Lukasiewicz filters on subsets of some X 6= ∅ to TL-evaluators on the system (lattice) of fuzzy functions f : X → [0, 1].

The paper deals with infinite block matrices having compact off diagonal parts. Bounds for the spectrum are established and estimates for the norm of the resolvent are proposed. Applications to matrix integral operators are also discussed. The main tool is the π-triangular operators defined in the paper.

We connect Lukasiewicz logic, a well-established many-valued logic, with weighted logics, recently introduced by Droste and Gastin. We use this connection to show that for formal series with coefficients in semirings derived from MValgebras, recognizability and definability in a fragment of second order Lukasiewicz logic coincide.

Abstract: Efficient conditioning and error estimates are presented for the numerical solution of matrix Riccati equations in the continuous-time and discrete-time LQG design. The estimates implemented involve the solution of triangular Lyapunov equations along with usage of the LAPACK norm estimator.

Fuzzy formal logics were introduced in order to handle graded truth values instead of only ‘true’ and ‘false’. A wide range of such logics were introduced successfully, like Monoidal T-norm based Logic, Basic Logic, Gödel Logic, Lukasiewicz Logic etc. However, in general, fuzzy set theory is not only concerned with vagueness, but also with uncertainty. A possible solution is to use intervals in...

Following the guidelines proposed by Hájek in [1], some proposals of research on Fuzzy Description Logics (FDLs) were given in [2]. One of them consists in the definition and development of a family of description languages, each one having as underlying fuzzy logic the expansion with an involutive negation and truth constants of the logic defined by a divisible finite t-norm. A general framewo...

The paper deals with infinite block matrices having compact off diagonal parts. Bounds for the spectrum are established and estimates for the norm of the resolvent are proposed. Applications to matrix integral operators are also discussed. The main tool is the π-triangular operators defined in the paper.