$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...

Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this fr...

BACKGROUND Effective and safe glycemic control in critically ill patients requires accurate glucose sensors and adequate insulin dosage calculators. The LOGIC-Insulin calculator for glycemic control has recently been validated in the LOGIC-1 randomized controlled trial. In this study, we aimed to determine the allowable error for intermittent and continuous glucose sensors, on the basis of the ...

Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic. We relax the problem so that if the verification process cannot succeed at the prescribed precision, it outputs an inconclusive result. The problem is solved ...

Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this fr...

In this paper, a new method, applying the fuzzy logic system, is proposed to discretize the continuous-time controller in computer-controlled systems. All the continuous-time controllers can be reconstructed by the proposed method under the Sampling Theorem. That is, the fuzzy logic systems are used to add nonlinearity and to approximate smooth functions. Hence, the proposed controller is a new...

Pratt [22] defines action algebras as Kleene algebras with residuals and action logic as the equational theory of action algebras. In opposition to Kleene algebras, action algebras form a (finitely based) variety. Jipsen [9] proposes a Gentzen-style sequent system for action logic but leaves it as an open question if this system admits cut-elimination and if action logic is decidable. We show t...

In this paper we introduce a variant of temporal logic tailored for specifying desired properties of continuous signals. The logic is based on a bounded subset of the real-time logic MITL, augmented with a static mapping from continuous domains into propositions. From formulae in this logic we create automatically property monitors that can check whether a given signal of bounded length and fin...