We introduce a first-order dynamic logic for reasoning about systems with discrete and continuous state transitions, and we present a sequent calculus for this logic. As a uniform model, our logic supports hybrid programs with discrete and differential actions. For handling real arithmetic during proofs, we lift quantifier elimination to dynamic logic. To obtain a modular combination, we use si...

Real-time systems usually encompass parts that are best described by a continuous-time model, such as physical processes under control, together with other components that are more naturally formalized by a discrete-time model, such as digital computing modules. Describing such systems in a unified framework based on metric temporal logic requires to integrate formulas which are interpreted ove...

Inference in classical logic is monotonic: if a conclusion can be derived from a set of premises, then no additional premises will ever invalidate this conclusion. However, commonsense reasoning has a nonmonotonic component. Human beings draw sensible conclusions from what they know, making default assumptions where needed. And if there is new information, we might reconsider previous conclusio...

The paper proposes the realization of a Fuzzy Logic Temperature Controller. In this paper an analysis of Fuzzy Logic Controller is made and a temperature controller using MATLAB is developed. Here we used Fuzzy Logic Toolbox which is very useful software for development and testing of Fuzzy Logic system. It can be very quickly implemented and its visual impact is very encouraging. In this contr...

Intelligent techniques are versatile in signal classification and estimation. Prominent techniques like fuzzy logic, artificial neural networks, genetic algorithms plays a significant role in signal classification and are helpful in developing various continuous control schemes. This chapter presents the effectiveness of fuzzy logic concept in classifying the vibration signals based on their fr...

We propose a first-order dynamic logic for reasoning about hybrid systems. As a uniform model for discrete and continuous evolutions in hybrid systems, we introduce hybrid programs with differential actions. Our logic can be used to specify and verify correctness statements about hybrid programs, which are suitable for symbolic processing by calculus rules. Using first-order variables, our logi...

Continuity and Logical Completeness. An application of sheaf theory and topoi. section: Category theory The notion of a continuously variable quantity can be regarded as a generalization of that of a particular (constant) quantity, and the properties of such quantities are then akin to, and derived from, the properties of constants. For example, the continuous, real-valued functions on a topolo...

p. 1 Knowledge Without Modality: A Simplified Framework for Chronological Ignorance p. 25 Design Complete Sequential Calculus for Continuous Fixpoint Temporal Logic p. 36 Logical Omniscience and Classical Logic p. 52 Weak Implication: Theory and Applications p. 65 Deriving Inference Rules for Terminological Logics p. 84 Linear Proofs and Linear Logic p. 106 Relevance and Revision About Generali...

The concentration of molecules can be changed by chemical reactions and thereby offer a continuous readout. Yet computer architecture is cast in textbooks in terms of binary valued, Boolean variables. To enable reactive chemical systems to compute we show how, using the Cox interpretation of probability theory, one can transcribe the equations of chemical kinetics as a sequence of coupled logic...