AbstractFitting the continuous valid logic of the exclusive OR (XOR) problem requires more than a minimal neural network configuration. This letter shows that the simplest logic to fit the XOR problem involves boundaries that cannot be mapped by a Multi-Layer Perceptron (MLP) with just two hidden nodes. This observation calls into question rule extraction methodologies based on pruning, since t...

Approximate relational Hoare logic (apRHL) is a logic for formal verification of the differential privacy of databases written in the programming language pWHILE. Strictly speaking, however, this logic deals only with discrete random samplings. In this paper, we define the graded relational lifting of the subprobabilistic variant of Giry monad, which described differential privacy. We extend th...

Real-time temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discrete time models are available for analysis. In this paper, we introduce a framework for testing MITL specific...

The conformational energy values of 3-amino-4-nitraminofurazan (C2N4O3H2) molecule changing with two torsion angles were firstly calculated using density functional theory (DFT) with Lee-Young-Parr correlation functional and 6-31 G(d) basis set on Gaussian Program. And then, these obtained discrete data were made continuous by using Fuzzy Logic Modelling (FLM) and Artificial Neural Network (ANN...

The Teleo-Reactive (T-R) paradigm for computing and organizing actions for autonomous agents in dynamic environments can be viewed as having a foundation triplet of durative actions, circuit semantics, and boolean logic. This foundation is intended to enable the construction of semantic circuitry for the continuous computation of parameters and conditions on which agent action is based. Drawing...

Markov-reward models, as extensions of continuous-time Markov chains, have received increased attention for the specification and evaluation of performance and dependability properties of systems. Until now, however, the specification of reward-based performance and dependability measures has been done manually and informally. In this paper, we change this undesirable situation by the introduct...

Fabrication of an integrated circuit with smaller area, besides reducing the cost of manufacturing, usually causes a reduction in the power dissipation and propagation delay. Using the static CMOS technology to fabricate a circuit that realizes a specific logic function and occupies a minimum space, it must be implemented with continuous diffusion runs. Therefore, at the design stage, an Euleri...

Fabrication of an integrated circuit with smaller area, besides reducing the cost of manufacturing, usually causes a reduction in the power dissipation and propagation delay. Using the static CMOS technology to fabricate a circuit that realizes a specific logic function and occupies a minimum space, it must be implemented with continuous diffusion runs. Therefore, at the design stage, an Euleri...

Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-space and continuous-time labelled Markov processes (CMPs). The modalities of CML approximate the rates of the exponentially distributed random variables that characterize the duration of the labeled transitions. In this paper we present a sound and complete Hilbert-style ...

Abstract Following tfhe seminal paper of Offerman et al. (2009), in this study, adaptations constructions continuous-valued logic to prospect theory are presented. Here, we demonstrate that the so-called kappa function and its special cases viable alternatives some elements quadratic scoring rule prospects theory. After, present tau-eta show it may be treated as a generalization prospect. Furth...