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- Robert F. Hadley (1993). Connectionism, Explicit Rules, and Symbolic Manipulation. Minds and Machines 3 (2):183-200.At present, the prevailing Connectionist methodology forrepresenting rules is toimplicitly embody rules in neurally-wired networks. That is, the methodology adopts the stance that rules must either be hard-wired or trained into neural structures, rather than represented via explicit symbolic structures. Even recent attempts to implementproduction systems within connectionist networks have assumed that condition-action rules (or rule schema) are to be embodied in thestructure of individual networks. Such networks must be grown or trained over a significant span of time. However, arguments are presented herein that humanssometimes follow rules which arevery rapidly assignedexplicit internal representations, and that humans possessgeneral mechanisms capable of interpreting and following such rules. In particular, arguments are presented that thespeed with which humans are able to follow rules ofnovel structure demonstrates the existence of general-purpose rule following mechanisms. It is further argued that the existence of general-purpose rule following mechanisms strongly indicates that explicit rule following is not anisolated phenomenon, but may well be a common and important aspect of cognition. The relationship of the foregoing conclusions to Smolensky''s view of explicit rule following is also explored. The arguments presented here are pragmatic in nature, and are contrasted with thekind of arguments developed by Fodor and Pylyshyn in their recent, influential paper.
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The introduction of connectionist or parallel distributed processing (PDP) systems to model cognitive functions has raised the question of the possible relations between these models and traditional information processing models which employ rules to manipulate representations. After presenting a brief account of PDP models and two ways in which they are commonly interpreted by those seeking to use them to explain cognitive functions, I present two ways one might relate these models to traditional information processing models and so not totally repudiate the tradition of modelling cognition through systems of rules and representations. The proposal that seems most promising is that PDP-type structures might provide the underlying framework in which a rule and representation model might be implemented. To show how one might pursue such a strategy, I discuss recent research by Barsalou on the instability of concepts and show how that might be accounted for in a system whose microstructure had a PDP architecture. I also outline how adopting a multi-leveled view of the mind, where on one level the mind employed a PDP-type system and at another level constituted a rule processing system, would allow researchers to relocate some problems which seemed difficult to explain at one level, such as the capacity for concept learning, to another level where it could be handled in a straightforward manner.
Much of traditional AI exemplifies the explicit representation paradigm, and during the late 1980''s a heated debate arose between the classical and connectionist camps as to whether beliefs and rules receive an explicit or implicit representation in human cognition. In a recent paper, Kirsh (1990) questions the coherence of the fundamental distinction underlying this debate. He argues that our basic intuitions concerning explicit and implicit representations are not only confused but inconsistent. Ultimately, Kirsh proposes a new formulation of the distinction, based upon the criterion ofconstant time processing.The present paper examines Kirsh''s claims. It is argued that Kirsh fails to demonstrate that our usage of explicit and implicit is seriously confused or inconsistent. Furthermore, it is argued that Kirsh''s new formulation of the explicit-implicit distinction is excessively stringent, in that it banishes virtually all sentences of natural language from the realm of explicit representation. By contrast, the present paper proposes definitions for explicit and implicit which preserve most of our strong intuitions concerning straightforward uses of these terms. It is also argued that the distinction delineated here sustains the meaningfulness of the abovementioned debate between classicists and connectionists.
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Connectionism was explicitly put forward as an alternative to classical cognitive science. The questions arise: how exactly does connectionism differ from classical cognitive science, and how is it potentially better? The classical “rules and representations” conception of cognition is that cognitive transitions are determined by exceptionless rules that apply to the syntactic structure of symbols. Many philosophers have seen connectionism as a basis for denying structured symbols. We, on the other hand, argue that cognition is too rich and flexible to be simulable by the exceptionless representation-level rules that classicism requires. However, this very richness of cognition requires syntactically structured representations—what philosophers call a language of thought. The natural mathematical characterization of neural networks comes from the theory of dynamical systems. We propose that the mathematics of dynamical systems, not the mathematics of algorithms, holds the key to how cognitive structure and cognitive processes can be realized in the physical structure and processes of a network.
Terry Horgan and John Tienson have suggested that connectionism might provide a framework within which to articulate a theory of cognition according to which there are mental representations without rules (RWR) (Horgan and Tienson 1988, 1989, 1991, 1992). In essence, RWR states that cognition involves representations in a language of thought, but that these representations are not manipulated by the sort of rules that have traditionally been posited. In the development of RWR, Horgan and Tienson attempt to forestall a particular line of criticism, theSyntactic Argument, which would show RWR to be inconsistent with connectionism. In essence, the argument claims that the node-level rules of connectionist networks, along with the semantic interpretations assigned to patterns of activation, serve to determine a set of representation-level rules incompatible with the RWR conception of cognition. The present paper argues that the Syntactic Argument can be made to show that RWR is inconsistent with connectionism.
In "Representations without Rules, Connectionism and the Syntactic Argument'', Kenneth Aizawa argues against the view that connectionist nets can be understood as processing representations without the use of representation-level rules, and he provides a positive characterization of how to interpret connectionist nets as following representation-level rules. He takes Terry Horgan and John Tienson to be the targets of his critique. The present paper marshals functional and methodological considerations, gleaned from the practice of cognitive modelling, to argue against Aizawa's characterization of how connectionist nets may be understood as making use of representation-level rules.
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