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. (shrink)

In their provocative 1988 paper, Fodor and Pylyshyn issued a formidable challenge to connectionists, i.e. to provide a non‐classical explanation of the empirical phenomenon of systematicity in cognitive agents. Since the appearance of F&P's challenge, a number of connectionist systems have emerged which prima facie meet this challenge. However, Fodor and McLaughlin (1990) advance an argument, based upon a general principle of nomological necessity, to show that one of these systems (Smolensky's) could not satisfy the Fodor‐Pylyshyn challenge. Yet, if Fodor (...) and McLaughlin's analysis is correct, it is doubtful whether any existing connectionist system would fare better than Smolensky's. In the view of Fodor and McLaughlin, humans and classical architectures display systematicity as a matter of nomological necessity (necessity by virtue of natural law), but connectionist architectures do not. However, I argue that the Fodor‐Pylyshyn‐McLaughlin appeal to nomological necessity is untenable. There is a sense in which neither classical nor connectionist architectures possess nomological (or‘nomic’) necessity. However, the sense in which classical architectures do possess nomic necessity applies equally well to at least some connectionist architectures. Representational constituents can have causal efficacy within both classical and connectionist architectures. (shrink)

Fodor's and Pylyshyn's stand on systematicity in thought and language has been debated and criticized. Van Gelder and Niklasson, among others, have argued that Fodor and Pylyshyn offer no precise definition of systematicity. However, our concern here is with a learning based formulation of that concept. In particular, Hadley has proposed that a network exhibits strong semantic systematicity when, as a result of training, it can assign appropriate meaning representations to novel sentences (both simple and embedded) which contain words in (...) syntactic positions they did not occupy during training. The experience of researchers indicates that strong systematicity in any form is difficult to achieve in connectionist systems.Herein we describe a network which displays strong semantic systematicity in response to Hebbian, connectionist training. During training, two-thirds of all nouns are presented only in a single syntactic position (either as grammatical subject or object). Yet, during testing, the network correctly interprets thousands of sentences containing those nouns in novel positions. In addition, the network generalizes to novel levels of embedding. Successful training requires a, corpus of about 1000 sentences, and network training is quite rapid. The architecture and learning algorithms are purely connectionist, but classical insights are discernible in one respect, viz, that complex semantic representations spatially contain their semantic constituents. However, in other important respects, the architecture is distinctly non-classical. (shrink)

In their provocative 1988 paper, Fodor and Pylyshyn issued a formidable challenge to connectionists, i.e. to provide a non‐classical explanation of the empirical phenomenon of systematicity in cognitive agents. Since the appearance of F&P's challenge, a number of connectionist systems have emerged which prima facie meet this challenge. However, Fodor and McLaughlin (1990) advance an argument, based upon a general principle of nomological necessity, to show that one of these systems (Smolensky's) could not satisfy the Fodor‐Pylyshyn challenge. Yet, if Fodor (...) and McLaughlin's analysis is correct, it is doubtful whether any existing connectionist system would fare better than Smolensky's. In the view of Fodor and McLaughlin, humans and classical architectures display systematicity as a matter of nomological necessity (necessity by virtue of natural law), but connectionist architectures do not. However, I argue that the Fodor‐Pylyshyn‐McLaughlin appeal to nomological necessity is untenable. There is a sense in which neither classical nor connectionist architectures possess nomological (or‘nomic’) necessity. However, the sense in which classical architectures do possess nomic necessity applies equally well to at least some connectionist architectures. Representational constituents can have causal efficacy within both classical and connectionist architectures. (shrink)

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. (shrink)

Fodor's and Pylyshyn's stand on systematicity in thought and language has been debated and criticized. Van Gelder and Niklasson, among others, have argued that Fodor and Pylyshyn offer no precise definition of systematicity. However, our concern here is with a learning based formulation of that concept. In particular, Hadley has proposed that a network exhibits strong semantic systematicity when, as a result of training, it can assign appropriate meaning representations to novel sentences (both simple and embedded) which contain words in (...) syntactic positions they did not occupy during training. The experience of researchers indicates that strong systematicity in any form is difficult to achieve in connectionist systems.Herein we describe a network which displays strong semantic systematicity in response to Hebbian, connectionist training. During training, two-thirds of all nouns are presented only in a single syntactic position (either as grammatical subject or object). Yet, during testing, the network correctly interprets thousands of sentences containing those nouns in novel positions. In addition, the network generalizes to novel levels of embedding. Successful training requires a, corpus of about 1000 sentences, and network training is quite rapid. The architecture and learning algorithms are purely connectionist, but ‘classical’ insights are discernible in one respect, viz, that complex semantic representations spatially contain their semantic constituents. However, in other important respects, the architecture is distinctly non-classical. (shrink)

The past decade has witnessed the emergence of a novel stance on semantic representation, and its relationship to context sensitivity. Connectionist-minded philosophers, including Clark and van Gelder, have espoused the merits of viewing hidden-layer, context-sensitive representations as possessing semantic content, where this content is partially revealed via the representations'' position in vector space. In recent work, Bodén and Niklasson have incorporated a variant of this view of semantics within their conception of semantic systematicity. Moreover, Bodén and Niklasson contend that they (...) have produced experimental results which not only satisfy a kind of context-based, semantic systematicity, but which, to the degree that reality permits, effectively deals with challenges posed by Fodor and Pylyshyn (1988), and Hadley (1994a). The latter challenge involved well-defined criteria for strong semantic systematicity. This paper examines the relevant claims and experiments of Bodén and Niklasson. It is argued that their case fatally involves two fallacies of equivocation; one concerning ''semantic content'' and the other concerning ''novel test sentences''. In addition, it is argued that their ultimate construal of context sensitive semantics contains serious confusions. These confusions are also found in certain publications dealing with "latent semantic analysis". Thus, criticisms presented here have relevance beyond the work of Bodén and Niklasson. (shrink)

A process-oriented model of belief is presented which permits the representation of nested propositional attitudes within first-order logic. The model (NIM, for nested intensional model) is axiomatized, sense-based (via intensions), and sanctions inferences involving nested epistemic attitudes, with different agents and different times. Because NIM is grounded upon senses, it provides a framework in which agents may reason about the beliefs of another agent while remaining neutral with respect to the syntactic forms used to express the latter agent's beliefs. Moreover, (...) NIM provides agents with a conceptual map, interrelating the concepts of knowledge, belief, truth, and a number of cognate concepts, such as infers, retracts, and questions. The broad scope of NIM arises in part from the fact that its axioms are represented in a novel extension of first-order logic, -FOL (presented herein). -FOL simultaneously permits the representation of truth ascriptions, implicit self-reference, and arbitrarily embedded sentences within a first-order setting. Through the combined use of principles derived from Frege, Montague, and Kripke, together with context-sensitive semantic conventions, -FOL captures the logic of truth inferences, while avoiding the inconsistencies exhibited by Tarski. Applications of -FOL and NIM to interagent reasoning are described and the soundness and completeness of -FOL are established herein. (shrink)

In his discussion of results which I (with Michael Hayward) recently reported in this journal, Kenneth Aizawa takes issue with two of our conclusions, which are: (a) that our connectionist model provides a basis for explaining systematicity “within the realm of sentence comprehension, and subject to a limited range of syntax” (b) that the model does not employ structure-sensitive processing, and that this is clearly true in the early stages of the network's training. Ultimately, Aizawa rejects both (a) and (b) (...) for reasons which I think are ill-founded. In what follows, I offer a defense of our position. In particular, I argue (1) that Aizawa adopts a standard of explanation that many accepted scientific explanations could not meet, and (2) that Aizawa misconstrues the relevant meaning of ‘structure-sensitive process’. (shrink)

Within AI and the cognitively related disciplines, there exist a multiplicity of uses of belief. On the face of it, these differing uses reflect differing views about the nature of an objective phenomenon called belief. In this paper I distinguish six distinct ways in which belief is used in AI. I shall argue that not all these uses reflect a difference of opinion about an objective feature of reality. Rather, in some cases, the differing uses reflect differing concerns with special (...) AI applications. In other cases, however, genuine differences exist about the nature of what we pre-theoretically call belief. To an extent the multiplicity of opinions about, and uses of belief, echoes the discrepant motivations of AI researchers. The relevance of this discussion for cognitive scientists and philosophers arises from the fact that (a) many regard theoretical research within AI as a branch of cognitive science, and (b) even if theoretical AI is not cognitive science, trends within AI influence theories developed within cognitive science. It should be beneficial, therefore, to unravel the distinct uses and motivations surrounding belief, in order to discover which usages merely reflect differing pragmatic concerns, and which usages genuinely reflect divergent views about reality. (shrink)

It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s (...) results and accepted theorems of recursion theory, does provide the basis for an apparent paradox. The difficulty arises when such an algorithm is embedded within a computer program of sufficient arithmetic power. The required computer program (an AI system) is described herein, and the paradox is derived. A solution to the paradox is proposed, which, it is argued, illuminates the truth status of axioms in formal models of programs and Turing machines. (shrink)

It is argued that van der Velde and de Kamps employ binding circuitry that effectively constitutes a form of conjunctive binding. Analogies with prior systems are discussed and hypothetical origins of binding circuitry are examined for credibility.

An earlier article by the author, "quine and strawson on logical theory" ("analysis" volume 34, pages 207-208), is expanded and defended against criticisms made by charles sayward in "the province of logic" ("analysis" volume 36, pages 47-48). it is shown that quine's definition of logical truth presupposes an understanding of "possibility," even if the term 'sentence' is used set-theoretically, and that if quine is allowed the concept of "possibility," then strawson must be allowed modal concepts for his purposes. the traditional (...) claim that an argument is valid if and only if the corresponding conditional is necessary is also defended. (shrink)

In his most comprehensive book on the subject , Roger Penrose provides arguments to demonstrate that there are aspects of human understanding which could not, in principle, be attained by any purely computational system. His central argument relies crucially on oft-cited theorems proven by Gödel and Turing. However, that key argument has been the subject of numerous trenchant critiques, which is unfortunate if one believes Penrose's conclusions to be plausible. In the present article, alternative arguments are offered in support of (...) Penrose-like conclusions . It is argued here that a purely computational agent, which lacked conscious awareness, would be incapable of possessing crucial concepts and of understanding certain kinds of geometrically-based proofs. Specifically, it is argued that the acquisition of human-like concepts of countable and non-denumerable infinities, and human-like comprehension of a particular geometrically motivated proof does require conscious apprehension of the subject matter involved. This does not preclude the possibility that a computational agent might come to possess the requisite consciousness, but it is argued that if this consciousness does arise within the agent, it does so, at best, as an emergent, contingent side-effect of the underlying processes involved. (shrink)

Marcus et al.’s experiment (1999) concerning infant ability to distinguish between differing syntactic structures has prompted connectionists to strive to show that certain types of neural networks can mimic the infants’ results. In this paper we take a closer look at two such attempts: Shultz and Bale [Shultz, T.R. and Bale, A.C. (2001), Infancy 2, pp. 501–536] Altmann and Dienes [Altmann, G.T.M. and Dienes, Z. (1999) Science 248, p. 875a]. We were not only interested in how well these two models (...) matched the infants’ results, but also whether they were genuinely learning the grammars involved in this process. After performing an extensive set of experiments, we found that, at first blush, Shultz and Bale’s model (2001) replicated the infant’s known data, but the model largely failed to learn the grammars. We also found serious problems with Altmann and Dienes’ model (1999), which fell short of matching any of the infant’s results and of learning the syntactic structure of the input patterns. (shrink)

In the late 1980s, there were many who heralded the emergence of connectionism as a new paradigm – one which would eventually displace the classically symbolic methods then dominant in AI and Cognitive Science. At present, there remain influential connectionists who continue to defend connectionism as a more realistic paradigm for modeling cognition, at all levels of abstraction, than the classical methods of AI. Not infrequently, one encounters arguments along these lines: given what we know about neurophysiology, it is just (...) not plausible to suppose that our brains are digital computers. Thus, they could not support a classical architecture. I argue here for a middle ground between connectionism and classicism. I assume, for argument's sake, that some form(s) of connectionism can provide reasonably approximate models – at least for lower-level cognitive processes. Given this assumption, I argue on theoretical and empirical grounds that most human mental skills must reside in separate connectionist modules or sub-networks. Ultimately, it is argued that the basic tenets of connectionism, in conjunction with the fact that humans often employ novel combinations of skill modules in rule following and problem solving, lead to the plausible conclusion that, in certain domains, high level cognition requires some form of classical architecture. During the course of argument, it emerges that only an architecture with classical structure could support the novel patterns of information flow and interaction that would exist among the relevant set of modules. Such a classical architecture might very well reside in the abstract levels of a hybrid system whose lower-level modules are purely connectionist. (shrink)

In his discussion of results which I (with Michael Hayward) recently reported in this journal, Kenneth Aizawa takes issue with two of our conclusions, which are: (a) that our connectionist model provides a basis for explaining systematicity within the realm of sentence comprehension, and subject to a limited range of syntax (b) that the model does not employ structure-sensitive processing, and that this is clearly true in the early stages of the network''s training. Ultimately, Aizawa rejects both (a) and (b) (...) for reasons which I think are ill-founded. In what follows, I offer a defense of our position. In particular, I argue (1) that Aizawa adopts a standard of explanation that many accepted scientific explanations could not meet, and (2) that Aizawa misconstrues the relevant meaning of structure-sensitive process. (shrink)