We define a notion of reasoning using world-rank-functions, independently of any symbolic
language. We then show that every symmetric neural network (like Hopfield networks or …

The paper presents a connectionist framework that is capable of representing and learning
propositional knowledge. An extended version of propositional calculus is developed and is …

In recent years, there has been considerable interest in nonmonotonic reasoning systems.
Unfortunately, formal rigor has not always kept pace with the enthusiastic propagation of …

The purpose of this paper is to argue that nonmonotonic reasoning in general can be
viewed as monotonic inferences constrained by a simple notion of priority constraint. More …

This paper considers the problem of expressing predicate calculus in con (cid: 173)
nectionist networks that are based on energy minimization. Given a first (cid: 173) order …

There is a gap between two different modes of computation: the symbolic mode and the
subsymbolic (neuron-like) mode. The aim of this paper is to overcome this gap by viewing …

Connectionist networks with symmetric weights (like Hopfield networks and Boltzmann
Machines) use gradient descent to find a minimum for quadratic energy functions. We show …

The paper consists of two parts. The first part describes a class of networks called inference
networks. An inference network is a directed graph with'primitive','OR','AND'and'NOT'nodes.' …

One facet of the question of integration of Logic and Connectionist Systems, and how these
can complement each other, concerns the points of contact, in terms of semantics, between …

Publisher Summary Classic logic is monotonic in the following sense: whenever a sentence
A is a logical consequence of a set of sentences T, A is also a consequence of an arbitrary …