The paper presents an analysis of computational processes in neural networks, underlying sequential symbol processing. The main problem addressed in this analysis is that computations in neural networks are massively parallel whereas symbol processing is sequential. It is suggested that the two kinds of processes can be reconciled with each other by the idea of causally constructed representati...

Brains and computers are both dynamical systems that manipulate symbols, but they differ fundamentally in their architectures and operations. Human brains do mathematics; computers do not. Computers manipulate symbols that humans put into them without grounding them in what they represent. Human brains intentionally direct the body to make symbols, and they use the symbols to represent internal...

This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space x and frequency ξ. The symbol smoothness conditions obeyed by many operators in connection to smooth linear partial differential equations allow to write fast-converging, non-asymptotic expansions in adequate systems of rational Che...

The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such representations are compositional and hierarchical, they can be recombined int...

The natural world is infinitely diverse, yet this diversity arises from a relatively small set of coherent properties and rules, such as the laws of physics or chemistry. We conjecture that biological intelligent systems are able to survive within their diverse environments by discovering the regularities that arise from these rules primarily through unsupervised experiences, and representing t...

In an eye movement experiment, we assessed the performance of young (18-30 years) and older (65 + years) adult readers when sentences contained conventional interword spaces, when interword spaces were removed, or when interword spaces were replaced by nonlinguistic symbols. The replacement symbol was either a closed square ([Symbol: see text]) that provided a salient (low-spatial-frequency) cu...

The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such representations are compositional and hierarchical, they can be recombined int...

The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such representations are compositional and hierarchical, they can be recombined int...

Harnad (1994) identifies the symbol grounding problem as central to his distinction between cognition and computation. To Harnad computation is merely the systematically interpretable manipulation of symbols, while cognition requires that these symbols have intrinsic meaning that is acquired through transducers that mediate between a cogitator and the environment. We present a careful analysis ...

We investigate the complexity of a variety of normal-form transformations for transition diagram systems, which are a parsing view of extended context-free grammars. A transition diagram system is a nite collection of nite-state machines each of which is labeled with a unique nonterminal symbol. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the ...