We consider an interpretation of monadic second-order logic of order in the continuous time structure of finitely variable signals. We provide a characterization of the expressive power of monadic logic. As a by-product of our characterization we show that many fundamental theorems which hold in the discrete time interpretation of monadic logic are still valid in the continuous time interpretat...

We generalise the correspondence between -categorical theories and their automorphism groups to arbitrary complete in classical logic, some (including, particular, all ones) continuous logic.

The aim of this paper is to present a new algebraic approach from computer algebra to a discretized continuous logic. It makes use of a previous model of p-valued logic (where p is a prime number) based on the use of Gröbner bases of polynomial ideals. A five-valued logic (i.e., p = 5) with some modal operators has been considered as a compromise between precision and complexity of the polynomi...

We consider an interpretation of monadic second-order logic of order in the continuous time structure of nitely variable signals and show the decidability of monadic logic in this structure. The expressive power of monadic logic is illustrated by providing a straightforward meaning preserving translation into monadic logic of three typical continuous time speciication formalism: Temporal Logic ...

Continuous stochastic logic (CSL) deals with the verification of systems operating in continuous time, it may be traced to the well known tree logic CTL. The present logic contains a nextas well as an until-operator, and it permits expressing steady-state probabilities. We propose in this paper a probabilistic interpretation of this logic that is based on stochastic relations without making spe...

Mining large datasets using machine learning approaches often leads to models that are hard to interpret and not amenable to the generation of hypotheses that can be experimentally tested. We present 'Logic Optimization for Binary Input to Continuous Output' (LOBICO), a computational approach that infers small and easily interpretable logic models of binary input features that explain a continu...

We develop a multi-modal/temporal logic for the analysis of a general class of continuous dynamical systems over arbitrary time-lines. Our frames consist of a topological space together with a flow (or group action), which is a function from the product of space and time into space that satisfies the two flow laws; we further require this function to be continuous. Over Euclidean space and real...

In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of Lukasiewicz logic) and continuous logic, and prove effective versions of some related theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncount...

Mining large datasets using machine learning approaches often leads to models that are hard to interpret and not amenable to the generation of hypotheses that can be experimentally tested. Finding ‘actionable knowledge’ is becoming more important, but also more challenging as datasets grow in size and complexity. We present ‘Logic Optimization for Binary Input to Continuous Output’ (LOBICO), a ...