This paper studies an input-driven one-state differential equation model initially developed for an experimentally demonstrated dynamic molecular switch that switches like synapses in the brain do. The linear-in-the-state and nonlinear-in-the-input model is exactly solvable, and it is shown that it also possesses mathematical properties of convergence and fading memory that enable stable processing of time-varying inputs by nonlinear dynamical systems. Thus, the model exhibits the co-existence of biologically-inspired behavior and desirable mathematical properties for stable learning on sequential data. The results give theoretical support for the use of the dynamic molecular switches as computational units in deep cascaded/layered feedforward and recurrent architectures as well as other more general structures for neuromorphic computing. They could also inspire more general exactly solvable models that can be fitted to emulate arbitrary physical devices which can mimic brain-inspired behaviour and perform stable computation on input signals.

Forgetting as a knowledge management operation has received much less attention than operations like inference, or revision. It was mainly in the area of logic programming that techniques and axiomatic properties have been studied systematically. However, at least from a cognitive view, forgetting plays an important role in restructuring and reorganizing a human's mind, and it is closely related to notions like relevance and independence which are crucial to knowledge representation and reasoning. In this paper, we propose axiomatic properties of (intentional) forgetting for general epistemic frameworks which are inspired by those for logic programming, and we evaluate various forgetting operations which have been proposed recently by Beierle et al. according to them. The general aim of this paper is to advance formal studies of (intentional) forgetting operators while capturing the many facets of forgetting in a unifying framework in which different forgetting operators can be contrasted and distinguished by means of formal properties.