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)

Most cognitive scientists believe that cognitive processing (e.g., thought, speech, perception, and sensori‐motor processing) is the hallmark of intelligent systems. Aside from modeling such processes, cognitive science is in the business of mechanistically explaining how minds and other intelligent systems work. As one might expect, mechanistic explanations appeal to the causal‐functional interactions among a system's component structures. Good explanations are the ones that get the causal story right. But getting the causal story right requires positing structures that are really in (...) the system. After all, within the context of a mechanistic explanation, to posit X is to claim not only that X exists but that X is doing some causal labor. Because most cognitive scientists believe that cognitive processing requires the use, manipulation, and storage of internal representations, they characteristically posit internal representations to explain how intelligent systems work. (shrink)

I analyse the double function of models (representing the phenomena, and being a tool for calculating and predicting them) from a cognitive point of view. Taking the same approach as Ronald Giere, I nevertheless argue that he is to much committed to an abstract conception of theories and that one should give more attention to the particular formats in which models are expressed and grasped. By taking the example of Classical Mechanics, I show that a model, as an abstract entity, (...) doesn't represent anything if not presented in some particular format, be it linguistic, diagrammatic, or pictorial. This format is crucial to the relation between the two main functions of models. (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)

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)

This paper analyses the impact of representation and search operators on Computational Complexity. A model of computation is introduced based on a directed graph, and representation and search are defined to be the vertices and edges of this graph respectively. Changing either the representation or the search algorithm leads to different possible complexity classes. The final section explores the role of representation in reducing time complexity in Artificial Intelligence.

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)

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)

Peter Godfrey-Smith recently introduced the idea of representational ‘organization’. When a collection of representations form an organized family, similar representational vehicles carry similar contents. For example, where neural firing rate represents numerosity (an analogue magnitude representation), similar firing rates represent similar numbers of items. Organization has been elided with structural representation, but the two are in fact distinct. An under-appreciated merit of representational organization is the way it facilitates computational processing. Representations from different organized families can interact, for (...) example to perform addition. Their being organized allows them to implement a useful computation. Many of the cases where organization has seemed significant, but which fall short of structural representation, are cases where representational organization underpins a computationally useful processing structure. (shrink)

Relative to digital computation, analogue computation has been neglected in the philosophical literature. To the extent that attention has been paid to analogue computation, it has been misunderstood. The received view—that analogue computation has to do essentially with continuity—is simply wrong, as shown by careful attention to historical examples of discontinuous, discrete analogue computers. Instead of the received view, I develop an account of analogue computation in terms of a particular type of analogue representation that allows for discontinuity. This (...) account thus characterizes all types of analogue computation, whether continuous or discrete. Furthermore, the structure of this account can be generalized to other types of computation: analogue computation essentially involves analogue representation, whereas digital computation essentially involves digital representation. Besides being a necessary component of a complete philosophical understanding of computation in general, understanding analogue computation is important for computational explanation in contemporary neuroscience and cognitive science. (shrink)

The ‘received view’ about computation is that all computations must involve representational content. Egan and Piccinini argue against the received view. In this paper, I focus on Egan’s arguments, claiming that they fall short of establishing that computations do not involve representational content. I provide positive arguments explaining why computation has to involve representational content, and how that representational content may be of any type. I also argue that there is no need for computational psychology to be individualistic. Finally, I (...) draw out a number of consequences for computational individuation, proposing necessary conditions on computational identity and necessary and sufficient conditions on computational I/O equivalence of physical systems.Keywords: Computation; Representation; Computational identity; Explanation; Narrow content; Physical computation. (shrink)

A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored. The problem of completeness of mathematics is linked to its counterpart in quantum mechanics. That model includes two Peano arithmetics or Turing machines independent of each other. The complex Hilbert space underlying quantum mechanics as the base of its mathematical formalism is interpreted as a generalization of Peano arithmetic: It is a doubled infinite set of doubled Peano arithmetics having a (...) remarkable symmetry to the axiom of choice. The quantity of information is interpreted as the number of elementary choices (bits). Quantum information is seen as the generalization of information to infinite sets or series. The equivalence of that model to a quantum computer is demonstrated. The condition for the Turing machines to be independent of each other is reduced to the state of Nash equilibrium between them. Two relative models of language as game in the sense of game theory and as ontology of metaphors (all mappings, which are not one-to-one, i.e. not representations of reality in a formal sense) are deduced. (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)

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)

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)

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 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)

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)

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)

The computability of reals was introduced by Alan Turing [20] by means of decimal representations. But the equivalent notion can also be introduced accordingly if the binary expansion, Dedekind cut or Cauchy sequence representations are considered instead. In other words, the computability of reals is independent of their representations. However, as it is shown by Specker [19] and Ko [9], the primitive recursiveness and polynomial time computability of the reals do depend on the representation. In this paper, we explore (...) how the weak computability of reals depends on the representation. To this end, we introduce three notions of weak computability in a way similar to the Ershov's hierarchy of Δ02-sets of natural numbers based on the binary expansion, Dedekind cut and Cauchy sequence, respectively. This leads to a series of classes of reals with different levels of computability. We investigate systematically questions as on which level these notions are equivalent. We also compare them with other known classes of reals like c. e. and d-c. e. reals. (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)

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.

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)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large type-2 problems. they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding (...) biases so as to reduce specific type-2 problems to (tractable) type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general (not task-specific) strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy representational redescription language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

The generation of route descriptions is a fundamental task of navigation systems. A particular problem in this context is to identify routes that can easily be described and processed by users. In this work, we present a framework for representing route networks with the qualitative information necessary to evaluate and optimize route descriptions with regard to ambiguities in them. We identify different agent models that differ in how agents are assumed to process route descriptions while navigating through route networks and (...) discuss which agent models can be translated into PDL programs. Further, we analyze the computational complexity of matching route descriptions and paths in route networks in dependency of the agent model. Finally, we empirically evaluate the influence of the agent model on the optimization and the processing of route instructions. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” Type-1 problems, by (...) contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

The purpose of this paper is to explore three alternative frameworks for understanding the nature of language and mentality, which accent syntactical, semantical, and pragmatical aspects of the phenomena with which they are concerned, respectively. Although the computational conception currently exerts considerable appeal, its defensibility appears to hinge upon an extremely implausible theory of the relation of form to content. Similarly, while the representational approach has much to recommend it, its range is essentially restricted to those units of language that (...) can be understood in terms of undefined units. Thus, the only alternative among these three that can account for the meaning of primitive units of language is one emphasizing the basic role of skills, habits, and tendencies in relating signs and dispositions. (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)

I examine the abstraction/representation theory of computation put forward by Horsman et al., connecting it to the broader notion of modeling, and in particular, model-based explanation, as considered by Rosen. I argue that the ‘representational entities’ it depends on cannot themselves be computational, and that, in particular, their representational capacities cannot be realized by computational means, and must remain explanatorily opaque to them. I then propose that representation might be realized by subjective experience (qualia), through being the bearer (...) of the structure of abstract objects that are represented. (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)

We show how Kreisel's representation theorem for sets in the analytical hierarchy can be generalized to sets defined by positive induction and use this to estimate the complexity of constructions in the theory of domains with totality.

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)

Implicit and explicit filling-in phenomena should be distinguished. Blind spot phenomena and mechanisms of boundary completion can be accounted for by implicit filling-in. Surface regions are “painted” with perceptual quantities, such as brightness, by explicit filling-in. “Filling-in” and “finding-out” relate to different computational tasks. Mechanisms of purposive computation (e.g., for navigation) evaluate local measurements, thus “finding out”; whereas mechanisms for grasping might require passive reconstruction, thus “filling in.”.

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)

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)

The book examines one of the most contested topics in linguistics and cognitive science: the role of recursion in language. It offers a precise account of what recursion is, what role it should play in cognitive theories of human knowledge, and how it manifests itself in the mental representations of language and other cognitive domains.

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)

Cooper (1983) pioneered underspecified scope representation in formal and computational semantics through his introduction of quantifier storage into Montague semantics as an alternative to the syntactic operation of quantifying-in. In this paper we address an important issue in the development of an adequate formal theory of underspecified semantics. The tension between expressive power and computational tractability poses an acute problem for any such theory. Ebert (2005) shows that any reasonable current treatment of underspecified semantic representation either suffers from (...) expressive incompleteness or produces a combinatorial explosion that is equivalent to generating the full set of possible scope readings in the course of disambiguation. In previous work we have presented an account of underspecified scope representations within Property Theory with Curry Typing (PTCT), an intensional first-order theory for natural language semantics. Here we show how filters applied to the underspecified-scope terms of PTCT permit both expressive completeness and the reduction of computational complexity in a significant class of non-worst case scenarios. (shrink)

The tension between expressive power and computational tractability poses an acute problem for theories of underspecified semantic representation. In previous work we have presented an account of underspecified scope representations within Property Theory with Curry Typing, an intensional first-order theory for natural language semantics. Here we show how filters applied to the underspecified-scope terms of PTCT permit both expressive completeness and the reduction of computational complexity in a significant class of non-worst case scenarios.

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)

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)

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)

A long tradition, which starts with the metaphor of the wax tablet presented in the Theaetetus of Plato, leads us to think that the relationship between mental representation and the represented reality is in a certain way mechanical or automatic. But the truth is that the conventional aspects of signification make it impossible to understand it as a physical- mechanical process. The computer sciences, contrary to a superficial vision, do not support but rather disprove this mechanistic conception of rationality, (...) confirming that semiosis can only occur in free subjects, that is to say, not completely subject to the laws of matter. (shrink)

It is proposed to conceive of representation as an emergent phenomenon that is supervenient on patterns of activity of coarsely tuned and highly redundant feature detectors. The computational underpinnings of the outlined concept of representation are (1) the properties of collections of overlapping graded receptive fields, as in the biological perceptual systems that exhibit hyperacuity-level performance, and (2) the sufficiency of a set of proximal distances between stimulus representations for the recovery of the corresponding distal contrasts between stimuli, (...) as in multidimensional scaling. The present preliminary study appears to indicate that this concept of representation is computationally viable, and is compatible with psychological and neurobiological data. (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.

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)