The received view is that computational states are individuated at least in part by their semantic properties. I offer an alternative, according to which computational states are individuated by their functional properties. Functional properties are specified by a mechanistic explanation without appealing to any semantic properties. The primary purpose of this paper is to formulate the alternative view of computational individuation, point out that it supports a robust notion of computational explanation, and defend it on the grounds of how computational (...) states are individuated within computability theory and computer science. A secondary purpose is to show that existing arguments for the semantic view are defective. (shrink)

The received view is that computational states are individuated at least in part by their semantic properties. I offer an alternative, according to which computational states are individuated by their functional properties. Functional properties are specified by a mechanistic explanation without appealing to any semantic properties. The primary purpose of this paper is to formulate the alternative view of computational individuation, point out that it supports a robust notion of computational explanation, and defend it on the grounds of how computational (...) states are individuated within computability theory and computer science. A secondary purpose is to show that existing arguments for the semantic view are defective. (shrink)

By the Riesz representation theorem for the dual of C [0; 1], if F: C [0; 1] → ℝ is a continuous linear operator, then there is a function g: [0;1] → ℝ of bounded variation such that F = ∫ f dg . The function g can be normalized such that V = ‖F ‖. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, (...) which allows to define natural computability for a variety of operators. We show that there are a computable operator S mapping g and an upper bound of its variation to F and a computable operator S ′ mapping F and its norm to some appropriate g. (shrink)

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational content (...) is extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing. (shrink)

Society is becoming increasingly reliant upon the dependability of computerbased systems. Achieving and demonstrating the dependability of systems requires the construction and review of valid and coherent arguments. This paper discusses the need for a variety of classes of arguments in dependable systems and reviews existing approaches to the representation of arguments in each of these classes. The issues surrounding the certification of safety critical systems demonstrate the current need for richer representations of dependability arguments which support tools for (...) their construction and review. The paper discusses how a meta-logical framework, informed by aspects of both formal and informal logic, offers a rich and unified means of representing dependability arguments and of thus addressing this need. (shrink)

Advocates of the computational theory of mind claim that the mind is a computer whose operations can be implemented by various computational systems. According to these philosophers, the mind is multiply realisable because—as they claim—thinking involves the manipulation of syntactically structured mental representations. Since syntactically structured representations can be made of different kinds of material while performing the same calculation, mental processes can also be implemented by different kinds of material. From this perspective, consciousness plays a minor role in mental (...) activity. However, contemporary neuroscience provides experimental evidence suggesting that mental representations necessarily involve consciousness. Consciousness does not only enable individuals to become aware of their own thoughts, it also constantly changes the causal properties of these thoughts. In light of these empirical studies, mental representations appear to be intrinsically dependent on consciousness. This discovery represents an obstacle to any attempt to construct an artificial mind. (shrink)

Cognitive representations are typically analysed in terms of content, vehicle and format. While current work on formats appeals to intuitions about external representations, such as words and maps, in this paper we develop a computational view of formats that does not rely on intuitions. In our view, formats are individuated by the computational profiles of vehicles, i.e., the set of constraints that fix the computational transformations vehicles can undergo. The resulting picture is strongly pluralistic, it makes space for a variety (...) of different formats, and is intimately tied to the computational approach to cognition in cognitive science and artificial intelligence. (shrink)

Turing computation over a non-linguistic domain presupposes a notation for the domain. Accordingly, computability theory studies notations for various non-linguistic domains. It illuminates how different ways of representing a domain support different finite mechanical procedures over that domain. Formal definitions and theorems yield a principled classification of notations based upon their computational properties. To understand computability theory, we must recognize that representation is a key target of mathematical inquiry. We must also recognize that computability theory is an intensional (...) enterprise: it studies entities as represented in certain ways, rather than entities detached from any means of representing them. (shrink)

Although Clark & Thornton's “trading spaces” hypothesis is supposed to require trading internal representation for computation, it is not used consistently in that fashion. Not only do some of the offered computation-saving strategies turn out to be nonrepresentational, others (e.g., cultural artifacts) are external representations. Hence, C&T's hypothesis is consistent with antirepresentationalism.

This paper discusses essential motivational representations necessary for a comprehensive computational cognitive architecture. It hypothesizes the need for implicit drive representations, as well as explicit goal representations. Drive representations consist of primary drives — both low-level primary drives (concerned mostly with basic physiological needs) and high-level primary drives (concerned more with social needs), as well as derived (secondary) drives. On the basis of drives, explicit goals may be generated on the fly during an agent’s interaction with various situations. These motivational (...) representations help to make cognitive architectural models more comprehensive and provide deeper explanations of psychological processes. This work represents a step forward in making computational cognitive architectures better reflections of the human mind and all its motivational complexity and intricacy. (shrink)

The modelling of concepts, besides involving disciplines like philosophy of mind and psychology, is a fundamental and lively research problem in several artificial intelligence (AI) areas, such as knowledge representation, machine learning, and natural language processing. In this scenario, the most prominent proposed solutions adopt different (often incompatible) assumptions about the nature of such a notion. Each of these solutions has been developed to capture some specific features of concepts and support some specific (artificial) cognitive operations. This paper critically (...) reviews the most notable computational approaches to the representation of concepts. The main goals are (i) to provide a shared terminology for the desiderata of concepts and their computational representation; (ii) to classify and assess the heterogeneous computational approaches according to the provided terminology; (iii) to provide a reader who may not be very familiar with theories of concepts with an introduction to major themes in this research and with pointers to different research projects, and (iv) to offer philosophers, and potentially AI practitioners, a well-informed guide for selecting among various (and possibly competing) computational representations of concepts. (shrink)

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may (...) give rise to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems. (shrink)

An influential view in cognitive science is that computation in cognitive systems is semantic, conceptually depending on representation: to compute is to manipulate representations. I argue that accepting the non-semantic teleomechanistic view of computation lays the ground for a promising alternative strategy, in which computation helps to explain and naturalise representation, rather than the other way around. I show that this computation-based approach to representation presents six decisive advantages over the semantic view. I (...) claim that it can improve the two most influential current theories of representation, teleosemantics and structural representation, by providing them with precious tools to tackle some of their main shortcomings. In addition, the computation-based approach opens up interesting new theoretical paths for the project of naturalising representation, in which teleology plays a role in individuating computations, but not representations. (shrink)

In this paper we consider persuasion in the context of practical reasoning, and discuss the problems associated with construing reasoning about actions in a manner similar to reasoning about beliefs. We propose a perspective on practical reasoning as presumptive justification of a course of action, along with critical questions of this justification, building on the account of Walton. From this perspective, we articulate an interaction protocol, which we call PARMA, for dialogues over proposed actions based on this theory. We outline (...) an axiomatic semantics for the PARMA Protocol, and discuss two implementations which use this protocol to mediate a discussion between humans. We then show how our proposal can be made computational within the framework of agents based on the Belief-Desire-Intention model, and illustrate this proposal with an example debate within a multi agent system. (shrink)

Expected utility theory seeks to define rational choice behavior. Given a collection of acts available to some decision maker, expected utility theorists commonly identify the “rational” act as the act which _maximizes expected utility_ (where the expectation is taken with respect to some probability measure). The mathematical core of expected utility theory is a representation theorem. These theorems link expected utility maximization to a qualitative description of an agent’s choice behavior, captured in a preference relation. We say that an (...) agent’s preferences are _represented_ by a utility function and/or probability measure which is derived from the representation theorem. Representation theorems only prove that such a function exists, but do not show how to find it. Thus one may ask: given an agent’s preference relation, when can we compute a representing utility function? In this paper I prove a computable version of the von Neumann-Morgenstern representation theorem, answering this question in the affirmative. (shrink)

Recently, Horsman et al. have proposed a new framework, Abstraction/Representation theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a novel account of what is means to be a computer. After expounding on this account, I compare it with other accounts of concrete computation, finding that it does not quite fit in the standard categorization: while it is most similar to some semantic accounts, it is not (...) itself a semantic account. Then I evaluate it according to the six desiderata for accounts of concrete computation proposed by Piccinini. Finding that it does not clearly satisfy some of them, I propose a modification, which I call Agential AR theory, that does, yielding an account that could be a serious competitor to other leading account of concrete computation. (shrink)

Lattice representations are an important tool for computability theorists when they embed nondistributive lattices into degree-theoretic structures. In this expository paper, we present the basic definitions and results about lattice representations needed by computability theorists. We define lattice representations both from the lattice-theoretic and computability-theoretic points of view, give examples and show the connection between the two types of representations, discuss some of the known theorems on the existence of lattice representations that are of interest to computability theorists, and give (...) a simple example of the use of lattice representations in an embedding result. (shrink)

To explain why, in scientific problem solving, a diagram can be “worth ten thousand words,” Jill Larkin and Herbert Simon (1987) relied on a computer model: two representations can be “informationally” equivalent but differ “computationally,” just as the same data can be encoded in a computer in multiple ways, more or less suited to different kinds of processing. The roots of this proposal lay in cognitive psychology, more precisely in the “imagery debate” of the 1970s on whether there are image-like (...) mental representations. Simon (1972, 1978) hoped to solve this debate by thoroughly reducing the differences between forms of mental representations (e.g., between images and sentences) to differences in computational efficiency; to carry out this reduction, he borrowed from computer science the concepts of data type and of data structure. I argue that, in the end, his account amounted to nothing more than characterizing representations by the fast operations on them. This analysis then allows me to assess what Simon’s approach actually achieves when transported from psychology to the study of scientific representations, as in Larkin and Simon (1987): it allows comparing, not representations in and of themselves, but rather the computational roles they play in particular problem-solving processes—that is, representations together with a particular way of using them. (shrink)

I argue that there are no plausible non-representational explanations of episodes of hallucination. To make the discussion more specific, I focus on visual hallucinations in Charles Bonnet syndrome. I claim that the character of such hallucinatory experiences cannot be explained away non-representationally, for they cannot be taken as simple failures of cognizing or as failures of contact with external reality—such failures being the only genuinely non-representational explanations of hallucinations and cognitive errors in general. I briefly introduce a recent computational model (...) of hallucination, which relies on generative models in the brain, and argue that the model is a prime example of a representational explanation referring to representational mechanisms. The notion of the representational mechanism is elucidated, and it is argued that hallucinations—and other kinds of representations—cannot be exorcised from the cognitive sciences. (shrink)

Reformers urge that representation no longer earns its explanatory keep in cognitive science, and that it is time to discard this troublesome concept. In contrast, we hold that without representation cognitive science is utterly bereft of tools for explaining natural intelligence. In order to defend the latter position, we focus on the explanatory role of representation in computation. We examine how the methods of digital and analog computation are used to model a relatively simple target (...) system, and show that representation plays an in-eliminable explanatory role in both cases. We conclude that, to the extent that biologic systems engage in computation, representation is destined to play an explanatory role in cognitive science. (shrink)

Some modifications are suggested to recent (1985) generalised phrase-structure grammar which make the formalism more suitable to computational use, and at the same time provide a clear and elegant redefinition for parts of the formalism which are standardly complex and ill-defined. It is shown how the feature-instantiation principles can be represented as explicit rules in a format similar to metarules, and how a grammar of four parts, immediate-dominance rules, linear-precedence rules, metarules, and these new propagation rules, can be used to (...) produce the ordinary GPSG analyses of English. Methods of computational implementation are discussed, in particular it is suggested that the parts of the grammar are most conveniently interpreted as instructions as to how to produce a set of context-free phrase-structure rules which can be used with a simple left-corner parser. (shrink)

This research aims to clarify, by constructing and testing a computer simulation, the use of multiple representations in problem solving, focusing on their role in visual reasoning. The model is motivated by extensive experimental evidence in the literature for the features it incorporates, but this article focuses on the system's structure. We illustrate the model's behavior by simulating the cognitive and perceptual processes of an economics expert as he teaches some well‐learned economics principles while drawing a graph on a blackboard. (...) Data in the experimental literature and concurrent verbal protocols were used to guide construction of a linked production system and parallel network, CaMeRa (Computation with Multiple Representations), that employs a “Mind's Eye” representation for pictorial information, consisting of a bitmap and associated node‐link structures. Propositional list structures are used to represent verbal information and reasoning. Small individual pieces from the different representations are linked on a sequential and temporary basis to form a reasoning and inferencing chain, using visually encoded information recalled to the Mind's Eye from long‐term memory and from cues recognized on an external display. CaMeRa, like the expert, uses the diagrammatic and verbal representations to complement one another, thus exploiting the unique advantages of each. (shrink)

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: extending the representation to the process of setting the problem, relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, (...) where the problem solver is completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution. Completing the physical representation shows that the number of computation steps required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution. (shrink)

The Epistemology Of Computer Simulation has developed as an epistemological and methodological analysis of simulative sciences using quantitative computational models to represent and predict empirical phenomena of interest. In this paper, Executable Cell Biology and Agent-Based Modelling are examined to show how one may take advantage of qualitative computational models to evaluate reachability properties of reactive systems. In contrast to the thesis, advanced by EOCS, that computational models are not adequate representations of the simulated empirical systems, it is shown how (...) the representational adequacy of qualitative models is essential to evaluate reachability properties. Justification theory, if not playing an essential role in EOCS, is exhibited to be involved in the process of advancing and corroborating model-based hypotheses about empirical systems in ECB and ABM. Finally, the practice of evaluating model-based hypothesis by testing the simulated systems is shown to constitute an argument in favour of the thesis that computer simulations in ECB and ABM can be put on a par with scientific experiments. (shrink)

I argue that there are no plausible non-representational explanations of episodes of hallucination. To make the discussion more specific, I focus on visual hallucinations in Charles Bonnet syndrome. I claim that the character of such hallucinatory experiences cannot be explained away non-representationally, for they cannot be taken as simple failures of cognizing or as failures of contact with external reality—such failures being the only genuinely non-representational explanations of hallucinations and cognitive errors in general. I briefly introduce a recent computational model (...) of hallucination, which relies on generative models in the brain, and argue that the model is a prime example of a representational explanation referring to representational mechanisms. The notion of the representational mechanism is elucidated, and it is argued that hallucinations—and other kinds of representations—cannot be exorcised from the cognitive sciences. (shrink)

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery, are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a theoretical analysis of the cognitive roles such representations play, based on an ethnographic study of the building of computational models in a systems biology laboratory. Specifically, we focus on a case of model-building by an engineer that (...) led to a remarkable discovery in basic bioscience. Accounting for such discoveries requires a distributed cognition analysis, as DC focuses on the roles played by external representations in cognitive processes. However, DC analyses by and large have not examined scientific discovery, and they mostly focus on memory offloading, particularly how the use of existing external representations changes the nature of cognitive tasks. In contrast, we study discovery processes and argue that discoveries emerge from the processes of building the computational representation. The building process integrates manipulations in imagination and in the representation, creating a coupled cognitive system of model and modeler, where the model is incorporated into the modeler's imagination. This account extends DC significantly, and we present some of the theoretical and application implications of this extended account. (shrink)

Abstract Mental representations, Swiatczak (Minds Mach 21:19–32, 2011) argues, are fundamentally biochemical and their operations depend on consciousness; hence the computational theory of mind, based as it is on multiple realisability and purely syntactic operations, must be wrong. Swiatczak, however, is mistaken. Computation, properly understood, can afford descriptions/explanations of any physical process, and since Swiatczak accepts that consciousness has a physical basis, his argument against computationalism must fail. Of course, we may not have much idea how consciousness (itself a (...) rather unclear plurality of notions) might be implemented, but we do have a hypothesis—that all of our mental life, including consciousness, is the result of computational processes and so not tied to a biochemical substrate. Like it or not, the computational theory of mind remains the only game in town. Content Type Journal Article Pages 1-8 DOI 10.1007/s11023-012-9271-5 Authors David Davenport, Computer Engineering Department, Bilkent University, 06800 Ankara, Turkey Journal Minds and Machines Online ISSN 1572-8641 Print ISSN 0924-6495. (shrink)

In philosophical logic and metaphysics there is a long-standing debate around the most appropriate structures to represent indeterministic scenarios concerning the future. We reconstruct here such a debate in a computational setting, focusing on the fundamental difference between moment-based and history-based structures. Our presentation is centered around two versions of an indeterministic scenario in which a programmer wants a machine to perform a given task at some point after a specified time. One of the two versions includes an assumption about (...) the future behaviour of the machine that cannot be encoded in any programming instruction; such version has models over history-based structures but no model over a moment-based structure. Therefore, our work adds a new stance to the debate: moment-based structures can be said to rule out certain indeterministic scenarios that are computationally unfeasible. (shrink)

Khalidi identifies cognition with Marrian computation. He further argues that Marrian levels of inquiry should be interpreted ontologically as corresponding to distinct semi‐closed causal domains. But this counterintuitively places the causal domain of representations outside of cognition proper. A closer look at Khalidi's account of concepts shows that these allegedly separate Marrian domains are more tightly integrated than he allows. Theories of concepts converge on algorithmic‐representational models rather than computational ones. This suggests that we should reject the wholesale identification (...) of cognition with computation. (shrink)

Gualtiero Piccinini articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. Physical Computation discusses previous accounts of computation and argues that the mechanistic account is better. Many kinds of computation are explicated, such as digital (...) vs. analog, serial vs. parallel, neural network computation, program-controlled computation, and more. Piccinini argues that computation does not entail representation or information processing although information processing entails computation. Pancomputationalism, according to which every physical system is computational, is rejected. A modest version of the physical Church-Turing thesis, according to which any function that is physically computable is computable by Turing machines, is defended. (shrink)

Following the concept of internal representations, signal processing in a neuronal system has to be evaluated exclusively on the basis of internal system characteristics. Thus, this approach omits the external observer as a control function for sensory integration. Instead, the configuration of the system and its computational performance are the effects of endogeneous factors. Such self-referential operation is due to a strictly local computation in a network. Thereby, computations follow a set of rules that constitutes the emergent behaviour of (...) the system. Because these rules can be demonstrated to correspond to a "logic" intrinsic to the system, it can be shown that the concept of internal representation provides the basis for neurosemantics. (shrink)

Cognition can often be modeled as the transformation of a set of variables into another. At least two kinds of entities are needed in this process: signals and coders. Representations are usually taken to be signals, but sometimes they are the coders: sometimes the computational complexity of variable transformations can be strikingly reduced by relying on a structure that mirrors that of some task-relevant entity. These kinds of coders are what philosophers call structural representations.

According to logical theories of meaning, a meaning of an expression can be formalized and encoded in truth conditions. Vagueness of the language and individual differences between people are a challenge to incorporate into the meaning representations. In this paper, we propose a new approach to study truth-conditional representations of vague concepts. For a case study, we selected two natural language quantifiers most and more than half. We conducted two online experiments, each with 90 native English speakers. In the first (...) experiment, we tested between-subjects variability in meaning representations. In the second experiment, we tested the stability of meaning representations over time by testing the same group of participants in two experimental sessions. In both experiments, participants performed the verification task. They verified a sentence with a quantifier (e.g., “Most of the gleerbs are feezda.”) based on the numerical information provided in the second sentence, (e.g., “60% of the gleerbs are feezda”). To investigate between-subject and within-subject differences in meaning representations, we proposed an extended version of the Diffusion Decision Model with two parameters capturing truth conditions and vagueness. We fit the model to responses and reaction times data. In the first experiment, we found substantial between-subject differences in representations of most as reflected by the variability in the truth conditions. Moreover, we found that the verification of most is proportion-dependent as reflected in the reaction time effect and model parameter. In the second experiment, we showed that quantifier representations are stable over time as reflected in stable model parameters across two experimental sessions. These findings challenge semantic theories that assume the truth-conditional equivalence of most and more than half and contribute to the representational theory of vague concepts. The current study presents a promising approach to study semantic representations, which can have a wide application in experimental linguistics. (shrink)

This paper deals with the question: how is computation best individuated? -/- 1. The semantic view of computation: computation is best individuated by its semantic properties. 2. The causal view of computation: computation is best individuated by its causal properties. 3. The functional view of computation: computation is best individuated by its functional properties. -/- Some scientific theories explain the capacities of brains by appealing to computations that they supposedly perform. The reason for (...) that is usually that computation is individuated semantically. I criticize the reasons in support of this view and its presupposition of representation and semantics. Furthermore, I argue that the only justified appeal to a representational individuation of computation might be that it is partly individuated by implicit intrinsic representations. (shrink)

The concept of representation has become almost inextricably bound to the concept of symbol systems. the concepts is nowhere more prevalent than in descriptions of "internal representations." These representations are thought to occur in an internal symbol system that allows the brain to store and use information. In this paper we explore a different approach to understanding psychological processes, one that retains a commitment to representations and computations but that is not based on the idea that information must be (...) stored and manipulated in symbol systems. In particular, we suggest that the notion of a symbol system as currently understood construes psychological processes in terms of a specific type of computational system, in which a control function "reads," "interprets," and manipulates discrete entities called "symbols." We argue that other types of computational systems may provide a more appropriate characterization of psychological processes. One implication of our argument is the need to consider the constraints placed on computational theories in psychology by the nature of the computing device itself, the human brain. Perhaps surprisingly, this implication leads us to the conclusion that a "functionalist" conception of psychological processes (discussed below) does not entail that physiology is irrelevant to psychology, as has been maintained by prominent adherents of the symbol-systems approach. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, the (...) definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

I articulate and defend a new theory of what it is for a physical system to implement an abstract computational model. According to my descriptivist theory, a physical system implements a computational model just in case the model accurately describes the system. Specifically, the system must reliably transit between computational states in accord with mechanical instructions encoded by the model. I contrast my theory with an influential approach to computational implementation espoused by Chalmers, Putnam, and others. I deploy my theory (...) to illuminate the relation between computation and representation. I also rebut arguments, propounded by Putnam and Searle, that computational implementation is trivial. (shrink)

ABSTRACT Shagrir and Sprevak explore the apparent necessity of representation for the individuation of digits in computational systems.1 1 I will first offer a response to Sprevak’s argument that does not mention Shagrir’s original formulation, which was more complex. I then extend my initial response to cover Shagrir’s argument, thus demonstrating that it is possible to individuate digits in non-representational computing mechanisms. I also consider the implications that the non-representational individuation of digits would have for the broader theory of (...) computing mechanisms. 1 The Received View: No Computation without Representation 2 Computing Mechanisms and Functional Individuation 3 Against Computational Externalism 4 Implications for the Mechanistic Account. (shrink)

In this paper we review some problems with traditional approaches for acquiring and representing knowledge in the context of developing user interfaces. Methodological implications for knowledge engineering and for human-computer interaction are studied. It turns out that in order to achieve the goal of developing human-oriented (in contrast to technology-oriented) human-computer interfaces developers have to develop sound knowledge of the structure and the representational dynamics of the cognitive system which is interacting with the computer.We show that in a first step (...) it is necessary to study and investigate the different levels and forms of representation that are involved in the interaction processes between computers and human cognitive systems. Only if designers have achieved some understanding about these representational mechanisms, user interfaces enabling individual experiences and skill development can be designed. In this paper we review mechanisms and processes for knowledge representation on a conceptual, epistemological, and methodologieal level, and sketch some ways out of the identified dilemmas for cognitive modeling in the domain of human-computer interaction. (shrink)

Cognition is commonly taken to be computational manipulation of representations. These representations are assumed to be digital, but it is not usually specified what that means and what relevance it has for the theory. I propose a specification for being a digital state in a digital system, especially a digital computational system. The specification shows that identification of digital states requires functional directedness, either for someone or for the system of which it is a part. In the case or digital (...) representations, to be a token of a representational type, where the function of the type is to represent. [An earlier version of this paper was discussed in the web-conference "Interdisciplines" https://web.archive.org/web/20100221125700/http://www.interdisciplines.org/adaptation/papers/7 ]. (shrink)