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.

By applying the concept of Lukasiewicz fuzzy set to BE-algebras, notions BE-algebra and BE-filter are introduced, their properties investigated. Characterizations discussed, relationship between (resp., BE-filter) is established. The conditions for ∈-set, q-set O-set be BE-subalgebras explored. created by using BE-filter.

Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic and, specifically, knowledge base satisfiability is an undecidable problem for Product Logic. We complete here the analy...

Three-valued logics belong to a family of nonclassical logics that started to flourish in the 1920s and 1930s, following the work of ( Lukasiewicz, 1920), and earlier insights coming from Frege and Peirce (see (Frege, 1879), (Frege, 1892), (Fisch and Turquette, 1966)). All of them were moved by the idea that not all sentences need be True or False, but that some sentences can be indeterminate i...

Rule-driven processing is a proven way of achieving high-speed in fuzzy processing. Up to now, ruledriven architectures where designed to work with minimum or product as T-norm. Nevertheless, a Lukasiewicz T-norm is typically used with the compositional rule of inference in expert systems applications that are based on a fuzzy inference engine. This paper presents a rule-driven processing archi...

We present some model theoretic results for Lukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the Lukasiewicz BL-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Mo...