This systematic investigation of computation and mental phenomena by a noted psychologist and computer scientist argues that cognition is a form of computation, that the semantic contents of mental states are encoded in the same general way as computer representations are encoded. It is a rich and sustained investigation of the assumptions underlying the directions cognitive science research is taking. 1 The Explanatory Vocabulary of Cognition 2 The Explanatory Role of Representations 3 The Relevance of Computation 4 (...) The Psychological Reality of Programs: Strong Equivalence 5 Constraining Functional Architecture 6 The Bridge from Physical to Symbolic: Transduction 7 Functional Architecture and Analogue Processes 8 Mental Imagery and Functional Architecture 9 Epilogue: What is Cognitive Science the Science of? (shrink)

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents the state (...) of the art in the area. (shrink)

One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. J. (...) Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. We show that every recursively enumerable random real dominates all other recursively enumerable reals. We conclude that the recursively enumerable random reals are exactly the Ω-numbers [G. J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. Second, we show that the sets in a universal Martin-Lof test for randomness have random measure, and every recursively enumerable random number is the sum of the measures represented in a universal Martin-Lof test. (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)

Computation is central to the foundations of modern cognitive science, but its role is controversial. Questions about computation abound: What is it for a physical system to implement a computation? Is computation sufficient for thought? What is the role of computation in a theory of cognition? What is the relation between different sorts of computational theory, such as connectionism and symbolic computation? In this paper I develop a systematic framework that addresses all of these (...) questions. Justifying the role of computation requires analysis of implementation, the nexus between abstract computations and concrete physical systems. I give such an analysis, based on the idea that a system implements a computation if the causal structure of the system mirrors the formal structure of the computation. This account can be used to justify the central commitments of artificial intelligence and computational cognitive science: the thesis of computational sufficiency, which holds that the right kind of computational structure suffices for the possession of a mind, and the thesis of computational explanation, which holds that computation provides a general framework for the explanation of cognitive processes. The theses are consequences of the facts that computation can specify general patterns of causal organization, and mentality is an organizational invariant, rooted in such patterns. Along the way I answer various challenges to the computationalist position, such as those put forward by Searle. I close by advocating a kind of minimal computationalism, compatible with a very wide variety of empirical approaches to the mind. This allows computation to serve as a true foundation for cognitive science. (shrink)

states are to be understood in terms of their functional relationships to other mental states, not in terms of their material instantiation in any particular kind of hardware. But the argument that material instantiation is irrelevant to functional..

Although the mathematics of interest is very precise, the practice of charging computing and disclosing interest or cost of credit is full of variations and therefore often questionable on ethical grounds. The purpose of this paper is to examine some of the prevalent practices which are incorrect, illogical, unfair or deceptive. Both utilitarian and formalist schools of ethical theory would find these practices to be inappropriate. The paper will specifically look at unfair practices in the areas of estimation of intrayear (...) rates, use of 360 days in a year, the "rule of 78th", interest rate ('APR') advertising, and computation of unpaid balance by credit card issuers to figure interest costs.The current practices are not in the best interest of the average consumer. There is, therefore, an urgent need for new legislation, change in regulatory code and disclosure requirement for eliminating these unethical practices. The author recommends that the Truth in Lending Code of the Federal Reserve should require the disclosure of the effective APR if the periodic rate is determined by dividing the 'APR' by the number of payment period in a year; the use of 360 days in a year methods and the "Rule of 78ths" should be immediately discontinued; Deceptive advertising, which tend to understate the true cost of credit or hides hidden costs and fees should be outlawed; interest should be payable with the same frequency as the frequency of compounding and credit card holders should be provided with a comparative example of various methods of balance computation. (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)

What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. (...) We will point to interesting examples of (ideal) physical machines that fall outside the class of Gandy machines and compute functions that are not Turing-machine computable. (shrink)

The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and (...) sub-symbolic information processing levels. Present account of models of computation highlights several topics of importance for the development of new understanding of computing and its role: natural computation and the relationship between the model and physical implementation, interactivity as fundamental for computational modelling of concurrent information processing systems such as living organisms and their networks, and the new developments in logic needed to support this generalized framework. Computing understood as information processing is closely related to natural sciences; it helps us recognize connections between sciences, and provides a unified approach for modeling and simulating of both living and non-living systems. (shrink)

This Element has three main aims. First, it aims to help the reader understand the concept of computation that Turing developed, his corresponding results, and what those results indicate about the limits of computational possibility. Second, it aims to bring the reader up to speed on analyses of computation in physical systems which provide the most general characterizations of what it takes for a physical system to be a computational system. Third, it aims to introduce the reader to (...) some different kinds of quantum computers, describe quantum speedup, and present some explanation sketches of quantum speedup. If successful, this Element will equip the reader with a basic knowledge necessary for pursuing these topics in more detail. (shrink)

The Local Computation Framework has been used to improve the efficiency of computation in various uncertainty formalisms. This paper shows how the framework can be used for the computation of logical deduction in two different ways; the first way involves embedding model structures in the framework; the second, and more direct, way involves embedding sets of formulae. This work can be applied to many of the logics developed for different kinds of reasoning, including predicate calculus, modal logics, (...) possibilistic logics, probabilistic logics and non-monotonic logics. (shrink)

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory.

This paper connects information with computation and cognition via concept of agents that appear at variety of levels of organization of physical/chemical/cognitive systems – from elementary particles to atoms, molecules, life-like chemical systems, to cognitive systems starting with living cells, up to organisms and ecologies. In order to obtain this generalized framework, concepts of information, computation and cognition are generalized. In this framework, nature can be seen as informational structure with computational dynamics, where an (info-computational) agent is needed (...) for the potential information of the world to actualize. Starting from the definition of information as the difference in one physical system that makes a difference in another physical system – which combines Bateson and Hewitt’s definitions, the argument is advanced for natural computation as a computational model of the dynamics of the physical world, where information processing is constantly going on, on a variety of levels of organization. This setting helps us to elucidate the relationships between computation, information, agency and cognition, within the common conceptual framework, with special relevance for biology and robotics. (shrink)

This paper examines several issues related to information, speed of computation, and simulation of a physical process. It is argued that mental processes proceed at a rate close to the optimal based on thermodynamic considerations. Problems related to the simulation of a quantum mechanical system on a computer are reviewed. Parallels are drawn between biological and adaptive quantum systems.

In a recent paper, Lyngzeidetson [1990] has claimed that a type of parallel computer called the ‘Connection Machine’ instantiates architectural principles which will ‘revolutionize which "functions" of the human mind can and cannot be modelled by (non-human) computational automata.’ In particular, he claims that the Connection Machine architecture shows the anti-mechanist argument from Gödel's theorem to be false for at least one kind of parallel computer. In the first part of this paper, I argue that Lyngzeidetson's claims are not supported (...) by his arguments; in the second part I consider some other aspects of parallel computation which may be of theoretical significance in cognitive science. (shrink)

To clarify the notion of computation and its role in cognitive science, we need an account of implementation, the nexus between abstract computations and physical systems. I provide such an account, based on the idea that a physical system implements a computation if the causal structure of the system mirrors the formal structure of the computation. The account is developed for the class of combinatorial-state automata, but is sufficiently general to cover all other discrete computational formalisms. The (...) implementation relation is non-vacuous, so that criticisms by Searle and others fail. This account of computation can be extended to justify the foundational role of computation in artificial intelligence and cognitive science. (shrink)

In the paper I discuss the importance of relativistic hypercomputation for the philosophy of mathematics, in particular for our understanding of mathematical knowledge. I also discuss the problem of the explanatory role of mathematics in physics and argue that relativistic computation fits very well into the so-called programming account. Relativistic computation reveals an interesting interplay between the empirical realm and the realm of very abstract mathematical principles that even exceed standard mathematics and suggests, that such principles might play (...) an explanatory role. I also argue that relativistic computation does not have some of the weaknesses of other hypercomputational models, thus it is particularly attractive for the philosophy of mathematics. (shrink)

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, (...) computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

The Church-Turing Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare what they mean. (...) We argue for some minimal conditions that must be met if two frameworks are to be compared; if frameworks are radical enough, comparison becomes hopeless. Our aim is to clarify the dialectical situation in this bourgeoning area of research, shedding light on the nature of non-classical logic and the notion of computation alike. (shrink)

This book, a joint publication of the Institute of Physics Publishing and Oxford University Press, is the third in a series of three works that form part of the Oxford/IOP Computational Intelligence Library project. The other two works are the Handbook of Neural Computation and the Handbook of Evolutionary Computation. Each of the three handbooks is available in loose-leaf print form, as well as in an electronic version that combines both CD-ROM and on-line (World Wide Web) access to (...) the contents. In each case, regularly published supplements will be available on a subscription basis. (shrink)

In Contingent Computation, M. Beatrice Fazi offers a new theoretical perspective through which we can engage philosophically with computing. The book proves that aesthetics is a viable mode of investigating contemporary computational systems. It does so by advancing an original conception of computational aesthetics that does not just concern art made by or with computers, but rather the modes of being and becoming of computational processes. Contingent Computation mobilises the philosophies of Gilles Deleuze and Alfred North Whitehead in (...) order to address aesthetics as an ontological study of the generative potential of reality. Through a novel philosophical reading of Gödel’s incompleteness theorems and of Turing’s notion of incomputability, Fazi finds this potential at the formal heart of computational systems, and argues that computation is a process of determining indeterminacy. This indeterminacy, which is central to computational systems, does not contradict their functionality. Instead, it drives their very operation, albeit in a manner that might not always fit with the instrumental, representational and cognitivist purposes that we have assigned to computing. (shrink)

The editors of the Applied Logic Series are happy to present to the reader the fifth volume in the series, a collection of papers on Logic, Language and Computation. One very striking feature of the application of logic to language and to computation is that it requires the combination, the integration and the use of many diverse systems and methodologies - all in the same single application. The papers in this volume will give the reader a glimpse into (...) the problems of this active frontier of logic. The Editors CONTENTS Preface IX 1. S. AKAMA Recent Issues in Logic, Language and Computation 1 2. M. J. CRESSWELL Restricted Quantification 27 3. B. H. SLATER The Epsilon Calculus' Problematic 39 4. K. VON HEUSINGER Definite Descriptions and Choice Functions 61 5. N. ASHER Spatio-Temporal Structure in Text 93 6. Y. NAKAYAMA DRT and Many-Valued Logics 131 7. S. AKAMA On Constructive Modality 143 8. H. W ANSING Displaying as Temporalizing: Sequent Systems for Subintuitionistic Logics 159 9. L. FARINAS DEL CERRO AND V. LUGARDON 179 Quantification and Dependence Logics 10. R. SYLVAN Relevant Conditionals, and Relevant Application Thereof 191 Index 245 Preface This is a collection of papers by distinguished researchers on Logic, Lin guistics, Philosophy and Computer Science. The aim of this book is to address a broad picture of the recent research on related areas. In particular, the contributions focus on natural language semantics and non-classical logics from different viewpoints. (shrink)

A basic deep neural network (DNN) is trained to exhibit a large set of input–output dispositions. While being a good model of the way humans perform some tasks automatically, without deliberative reasoning, more is needed to approach human‐like artificial intelligence. Analysing recent additions brings to light a distinction between two fundamentally different styles of computation: content‐specific and non‐content‐specific computation (as first defined here). For example, deep episodic RL networks draw on both. So does human conceptual reasoning. Combining the (...) two takes advantage of the complementary costs and benefits of each. It also offers a better model of human cognitive competence. (shrink)

Bynum (Putting information first: Luciano Floridi and the philosophy of information. NY: Wiley-Blackwell, 2010) identifies Floridi’s focus in the philosophy of information (PI) on entities both as data structures and as information objects. One suggestion for examining the association between the former and the latter stems from Floridi’s Herbert A. Simon Lecture in Computing and Philosophy given at Carnegie Mellon University in 2001, open problems in the PI: the transduction or transception, and how we gain knowledge about the world as (...) a complex, living, information environment. This paper addresses PI across a model of interoperating levels: perception (P)—intuition (N)—computation (C)—information (I), as factored by cognitive continuity (1), temporality (2), and constitution (3). How might we begin to characterize our experience of an abstract information object across such a matrix? Chudnoff’s rationalist distinctions between perception and intuition serve as a first rung of the ladder. Turing’s brief references to the utility of intuition, in an allied, rationalist-Cartesian sense, provide the next step up to computation. Floridi provides the final link from computation to information. (shrink)

The journal of Cognitive Computation is defined in part by the notion that biologically inspired computational accounts are at the heart of cognitive processes in both natural and artificial systems. Many studies of various important aspects of cognition (memory, observational learning, decision making, reward prediction learning, attention control, etc.) have been made by modelling the various experimental results using ever-more sophisticated computer programs. In this manner progressive inroads have been made into gaining a better understanding of the many components (...) of cognition. Concomitantly in both science and science fiction the hope is periodically re-ignited that a manmade system can be engineered to be fully cognitive and conscious purely in virtue of its execution of an appropriate computer program. However, whilst the usefulness of the computational metaphor in many areas of psychology and neuroscience is clear, it has not gone unchallenged and in this article I will review a group of philosophical arguments that suggest either such unequivocal optimism in computationalism is misplaced—computation is neither necessary nor sufficient for cognition—or panpsychism (the belief that the physical universe is fundamentally composed of elements each of which is conscious) is true. I conclude by highlighting an alternative metaphor for cognitive processes based on communication and interaction. (shrink)