Introduction Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks) has reached a critical mass which enables the community to strive for applicable implementations and use cases. Recent work has covered a great variety of logics used in artificial intelligence and provides a multitude of techniques for dealing with them within the context of artificial neural networks. Already in the pioneering days of computational models of neural cognition, the question was raised how symbolic knowledge can be represented and dealt with within neural networks. The landmark paper [McCulloch and Pitts, 1943] provides fundamental insights how propositional logic can be processed using simple artificial neural networks. Within the following decades, however, the topic did not receive much attention as research in arti

A novel theoretical framework is delineated for supervised and unsupervised learning. It is called framework of fuzzy lattices, or FLframework for short, and it suggests mathematically sound tools for dealing separately and/or jointly with disparate types of data including vectors of numbers, fuzzy sets, symbols, etc. Specific schemes are proposed for clustering and classification having the capacity to deal with both missing and don't care data values; the schemes in question can be implemented as neural networks. The proposed learning schemes are employed here for pattern recognition on seven data sets including benchmark data sets, and the results are compared with those ones by various learning techniques from the literature. Finally, aiming at a mutual cross-fertilization, the FL-framework is associated with established theories for learning and/or decision-making including probability theory, fuzzy set theory, Bayesian decision-making, theory of evidence, and adaptive resonance t...

this article are of varying nature: position summaries, individual research summaries, historical accounts, discussion of controversial issues, etc. We have not attempted to connect the various pieces together, or to organize them within a coherent framework. Despite this, we think, the reader will find this collection useful.

this article are of varying nature: position summaries, individual research summaries, historical accounts, discussion of controversial issues, etc. No attempt was made to connect up the various pieces, nor to organize them in a coherent order. Despite this, we think the reader will find this collection useful.

ABSTRACT. We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with an operation on the hierarchy that expresses the formation of complex theories from simple theories that express first principles. Another operation forms abstractions expressing the shared concepts in an array of theories. The use of categorical model theory makes possible the incremental analysis of possible worlds, or instances, for the theories, and the mapping of instances of a theory to instances of its more abstract parts. We describe the theoretical approach by applying it to the semantics of neural networks.