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)

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)

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)

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)

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)

Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation’ and ‘information processing’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are (...) the same thing. In this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism on the other. We defend the relevance to cognitive science of both computation, in a generic sense that we fully articulate for the first time, and information processing, in three important senses of the term. Our account advances some foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debates’ empirical aspects. (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 book is intended to explain the larger and intuitive concept of randomness by means of computation, particularly through algorithmic complexity and recursion theory. It also includes the transcriptions (by A. German) of two panel discussion on the topics: Is The Universe Random?, held at the University of Vermont in 2007; and What is Computation? (How) Does Nature Compute?, held at the University of Indiana Bloomington in 2008. The book is intended to the general public, undergraduate and graduate (...) students in math, computer science, physics and other sciences, but also to philosophers of science and researchers. (shrink)

Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation. The theory of domains has proved to be a useful tool for programming languages and other areas of computer science, and for applications in mathematics. Included in this proceedings volume are selected papers of original research presented at the 2nd International Symposium on Domain Theory in Chengdu, China. With authors from France, Germany, Great (...) Britain, Ireland, Mexico, and China, the papers cover the latest research in these sub-areas: domains and computation, topology and convergence, domains, lattices, and continuity, and representations of domains as event and logical structures. Researchers and students in theoretical computer science should find this a valuable source of reference. The survey papers at the beginning should be of particular interest to those who wish to gain an understanding of some general ideas and techniques in this area. (shrink)

A quantum algorithm succeeds not because the superposition principle allows ‘the computation of all values of a function at once’ via ‘quantum parallelism’, but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information‐processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than any classical algorithm. (...) I also introduce the notion of ‘pseudotelepathic’ games and show how the difference between classical and quantum correlations plays a similar role here for games that can be won by quantum players exploiting entanglement, but not by classical players whose only allowed common resource consists of shared strings of random numbers (common causes of the players’ correlated responses in a game). *Received October 2008. †To contact the author, please write to: Department of Philosophy, University of Maryland, College Park, MD 20742; e‐mail: jbub@umd.edu. (shrink)

Discussions about the achievements and limitations of the various approaches to the development of intelligent systems can have an essential impact on empirically based research, and with that also on the future development of computer technologies. However, such discussions are often based on vague concepts and assumptions. In this context, we claim that the proposed `three-world ontology'' offers the most appropriate conceptual framework in which the basic problems concerned with cognition and computation can be suitably expressed and discussed, although (...) the solutions of some of these problems seem to lie beyond the horizon of our current understanding. We stress the necessity to differentiate between authentic and functional cognitive abilities; although computation is not a plausible way towards authentic intelligence, we claim that computational systems do offer virtually unlimited possibilities to replicate and surpass human cognitive abilities on the functional level. (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)

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)

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)

Multiple realizability (MR) is traditionally conceived of as the feature of computational systems, and has been used to argue for irreducibility of higher-level theories. I will show that there are several ways a computational system may be seen to display MR. These ways correspond to (at least) five ways one can conceive of the function of the physical computational system. However, they do not match common intuitions about MR. I show that MR is deeply interest-related, and for this reason, difficult (...) to pin down exactly. I claim that MR is of little importance for defending computationalism, and argue that it should rather appeal to organizational invariance or substrate neutrality of computation, which are much more intuitive but cannot support strong antireductionist arguments. (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)

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.

The contribution of the body to cognition and control in natural and artificial agents is increasingly described as “off-loading computation from the brain to the body”, where the body is said to perform “morphological computation”. Our investigation of four characteristic cases of morphological computation in animals and robots shows that the ‘off-loading’ perspective is misleading. Actually, the contribution of body morphology to cognition and control is rarely computational, in any useful sense of the word. We thus distinguish (...) (1) morphology that facilitates control, (2) morphology that facilitates perception and the rare cases of (3) morphological computation proper, such as ‘reservoir computing.’ where the body is actually used for computation. This result contributes to the understanding of the relation between embodiment and computation: The question for robot design and cognitive science is not whether computation is offloaded to the body, but to what extent the body facilitates cognition and control – how it contributes to the overall ‘orchestration’ of intelligent behaviour. (shrink)

Social kinds are heterogeneous. As a consequence of this diversity, some authors have sought to identify and analyse different kinds of social kinds. One distinct kind of social kinds, however, has not yet received sufficient attention. I propose that there exists a class of social-computation-supporting kinds, or SCS-kinds for short. These SCS-kinds are united by the function of enabling computations implemented by social groups. Examples of such SCS-kinds arereimbursement form,US dollar bill,chair of the board. I will analyse SCS-kinds, contrast (...) my analysis with theories of institutional kinds, and discuss the benefits of investigating SCS-kinds. (shrink)

Structured argumentation systems, and their implementation, represent an important research subject in the area of Knowledge Representation and Reasoning. Structured argumentation advances over abstract argumentation frameworks by providing the internal construction of the arguments that are usually defined by a set of (strict and defeasible) rules. By considering the structure of arguments, it becomes possible to analyze reasons for and against a conclusion, and the warrant status of such a claim in the context of a knowledge base represents the main (...) output of a dialectical process. Computing such statuses is a costly process, and any update to the knowledge base could potentially have a huge impact if done naively. In this work, we investigate the case of updates consisting of both additions and removals of pieces of knowledge in the Defeasible Logic Programming (DeLP) framework, first analyzing the complexity of the problem and then identifying conditions under which we can avoid unnecessary computations—central to this is the development of structures (e.g. graphs) to keep track of which results can potentially be affected by a given update. We introduce a technique for the incremental computation of the warrant statuses of conclusions in DeLP knowledge bases that evolve due to the application of (sets of) updates. We present the results of a thorough experimental evaluation showing that our incremental approach yields significantly faster running times in practice, as well as overall fewer recomputations, even in the case of sets of updates performed simultaneously. (shrink)

Proposals for quantum computation rely on superposed states implementing multiple computations simultaneously, in parallel, according to quantum linear superposition (e.g., Benioff, 1982; Feynman, 1986; Deutsch, 1985, Deutsch and Josza, 1992). In principle, quantum computation is capable of specific applications beyond the reach of classical computing (e.g., Shor, 1994). A number of technological systems aimed at realizing these proposals have been suggested and are being evaluated as possible substrates for quantum computers (e.g. trapped ions, electron spins, quantum dots, nuclear (...) spins, etc., see Table 1; Bennett, 1995; and Barenco, 1995). The main obstacle to realization of quantum computation is the problem of interfacing to the system (input, output) while also protecting the quantum state from environmental decoherence. If this problem can be overcome, then present day classical computers may evolve to quantum computers. (shrink)

Which notion of computation (if any) is essential for explaining cognition? Five answers to this question are discussed in the paper. (1) The classicist answer: symbolic (digital) computation is required for explaining cognition; (2) The broad digital computationalist answer: digital computation broadly construed is required for explaining cognition; (3) The connectionist answer: sub-symbolic computation is required for explaining cognition; (4) The computational neuroscientist answer: neural computation (that, strictly, is neither digital nor analogue) is required for (...) explaining cognition; (5) The extreme dynamicist answer: computation is not required for explaining cognition. The first four answers are only accurate to a first approximation. But the “devil” is in the details. The last answer cashes in on the parenthetical “if any” in the question above. The classicist argues that cognition is symbolic computation. But digital computationalism need not be equated with classicism. Indeed, computationalism can, in principle, range from digital (and analogue) computationalism through (the weaker thesis of) generic computationalism to (the even weaker thesis of) digital (or analogue) pancomputationalism. Connectionism, which has traditionally been criticised by classicists for being non-computational, can be plausibly construed as being either analogue or digital computationalism (depending on the type of connectionist networks used). Computational neuroscience invokes the notion of neural computation that may (possibly) be interpreted as a sui generis type of computation. The extreme dynamicist argues that the time has come for a post-computational cognitive science. This paper is an attempt to shed some light on this debate by examining various conceptions and misconceptions of (particularly digital) computation. (shrink)

We consider processes of emergence within the conceptual framework of the Information Loss principle and the concepts of systems conserving information; systems compressing information; and systems amplifying information. We deal with the supposed incompatibility between emergence and computability tout-court. We distinguish between computational emergence, when computation acquires properties, and emergent computation, when computation emerges as a property. The focus is on emergence processes occurring within computational processes. Violations of Turing-computability such as non-explicitness and incompleteness are intended to (...) represent partially the properties of phenomenological emergence, such as logical openness, given by the observer’s cognitive role; structural dynamics where change regards rules rather than only values; and multi-modelling where multiple non-equivalent models are required to model such structural dynamics. In this way, we validate, from an epistemological viewpoint, models and simulations of phenomenological emergence where the sequence of events constitutes the natural, analogical non-Turing computation which a cognitive complex system can reproduce through learning. Reproducibility through learning is different from Turing-like computational iteration. This paper aims to open a new, non-reductionist understanding of the conceptual relationship between emergence and computability. (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)

The emerging contemporary natural philosophy provides a common ground for the integrative view of the natural, the artificial, and the human-social knowledge and practices. Learning process is central for acquiring, maintaining, and managing knowledge, both theoretical and practical. This paper explores the relationships between the present advances in understanding of learning in the sciences of the artificial, natural sciences, and philosophy. The question is, what at this stage of the development the inspiration from nature, specifically its computational models such as (...) info-computation through morphological computing, can contribute to machine learning and artificial intelligence, and how much on the other hand models and experiments in machine learning and robotics can motivate, justify, and inform research in computational cognitive science, neurosciences, and computing nature. We propose that one contribution can be understanding of the mechanisms of ‘learning to learn’, as a step towards deep learning with symbolic layer of computation/information processing in a framework linking connectionism with symbolism. As all natural systems possessing intelligence are cognitive systems, we describe the evolutionary arguments for the necessity of learning to learn for a system to reach humanlevel intelligence through evolution and development. The paper thus presents a contribution to the epistemology of the contemporary philosophy of nature. (shrink)

Chaotic dynamics can be related to analog computation. A possibility of electronically implementing the chaos -driven contracting system in the target article is explored with an analog electronic circuit with inevitable noise from the viewpoint of analog computation with chaotic neurons.

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)

This book explores the application of dynamical theory to cognitive science. Giunti shows how the dynamical approach can illuminate problems of cognition, information processing, consciousness, meaning, and the relation between body and mind.

It is sometimes suggested that the history of computation in cognitive science is one in which the formal apparatus of Turing-equivalent computation, or effective computability, was exported from mathematical logic to ever wider areas of cognitive science and its environs. This paper, however, indicates some respects in which this suggestion is inaccurate. Computability theory has not been focused exclusively on Turing-equivalent computation. Many essential features of Turing-equivalent computation are not captured in definitions of computation as (...) symbol manipulation. Turing-equivalent computation did not play the role in McCulloch and Pitts’s early cybernetic work that is sometimes attributed to it. Finally, various segments of the neuroscientific community invoke a notion of computation that differs from the Turing-equivalent notion.Keywords: Circular causality; Computation; Cortical maps; Neural networks; Symbol manipulation; Turing-equivalent computation. (shrink)

Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from (...) sufficiently close computable approximations. In addition to considering the nature of computability relative to any given physical theory, we can consider the relationship between versions of computability corresponding to different models of physics. Deutsch and Penrose have argued on mathematical grounds that quantum computation and Turing computation have equivalent formal power. We suggest this equivalence is invalid when considered from the physical point of view, by highlighting a quantum computational behaviour that cannot meaningfully be considered feasible in the classical universe. (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)

I describe a pedagogical scheme devised to teach efficiently to computer scientists just enough quantum mechanics to permit them to understand the theoretical developments of the last decade going under the name of “quantum computation.” I then note that my offbeat approach to quantum mechanics, designed to be maximally efficacious for this specific educational purpose, is nothing other than the Copenhagen interpretation.

To compute is to execute an algorithm. More precisely, to say that a device or organ computes is to say that there exists a modelling relationship of a certain kind between it and a formal specification of an algorithm and supporting architecture. The key issue is to delimit the phrase of a certain kind. I call this the problem of distinguishing between standard and nonstandard models of computation. The successful drawing of this distinction guards Turing's 1936 analysis of (...) class='Hi'>computation against a difficulty that has persistently been raised against it, and undercuts various objections that have been made to the computational theory of mind. (shrink)

to small scales. Further, it is often useful to describe motor control and sensorimotor coordination in terms of external elds such as force elds and sensory images. We survey the basic concepts of eld computation, including both feed-forward eld operations and eld dynamics resulting from recurrent connections. Adaptive and learning mechanisms are discussed brie y. The application of eld computation to motor control is illustrated by several examples: external force elds associated with spinal neurons, population coding of direction (...) in motor cortex, continuous transformation of direction elds, and linear gain elds and coordinate transformations in posterior parietal cortex. Next we survey some eld-based representations of motion, including direct, Fourier, Gabor and wavelet or multiresolution representations. Finally we consider brie y the application of these representations to constraint satisfaction, which has many applications in motor control. (shrink)

Ibn al-Bann1321) is the author of one of the four extant of the unfinished zq (fl. Tunis and Marrakesh ca. 1193j accessible for the computation of planetary longitudes. The present paper studies some modifications of the structure of the tables the purpose of which is to make calculations easier. The tables of the planetary and lunar equations of the centre are ' appears as a clever adapter, who displays a clear ingenuity allowing him to introduce formal modifications which give (...) his work an appearance of novelty which does not correspond to reality. (shrink)

The mainstream view in cognitive science is that computation lies at the basis of and explains cognition. Our analysis reveals that there is no compelling evidence or argument for thinking that brains compute. It makes the case for inverting the explanatory order proposed by the computational basis of cognition thesis. We give reasons to reverse the polarity of standard thinking on this topic, and ask how it is possible that computation, natural and artificial, might be based on cognition (...) and not the other way around. (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)