On the syntactico-semantical completeness of first-order fuzzy logic. II. Main results

On the syntactico-semantical completeness of first-order fuzzy logic. I. Syntax and semantics

Axiomatizations of Fuzzy Attribute Logic

We study fuzzy attribute logic, i.e. a logic for reasoning about formulas of the form A ⇒ B where A and B are fuzzy sets (non-sharp collections) of attributes. A formula A ⇒ B is true in a data table with fuzzy attributes iff each object having all attributes from A has also all attributes from B, membership degrees of A and B playing a role of thresholds. We present a set of axioms and prove s...

Equality propositional logic and its extensions

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

First-Order Classical Modal Logic

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness...

Optimal intelligent control for glucose regulation

This paper introduces a novel control methodology based on fuzzy controller for a glucose-insulin regulatory system of type I diabetes patient. First, in order to incorporate knowledge about patient treatment, a fuzzy logic controller is employed for regulating the gains of the basis Proportional-Integral (PI) as a self-tuning controller. Then, to overcome the key drawback of fuzzy logic contro...