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)

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)

In this carefully argued critique, Steven Horst pronounces the theory deficient.

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.

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)

Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always (...) fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics. (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)

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 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.

What does it mean to say that an object or system computes? What is it about laptops, smartphones, and nervous systems that they are considered to compute, and why does it seldom occur to us to describe stomachs, hurricanes, rocks, or chairs that way? Though computing systems are everywhere today, it is very difficult to answer these questions. The book aims to shed light on the subject by arguing for the semantic view of computation, which states that computingsystems are (...) always accompanied by representations. This view is presented as an alternative to non-semantic views such as the mechanistic account of computation. (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)

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 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)

The aim of this paper is to present some basic notions of the theory of quantum computing and to compare them with the basic notions of the classical theory of computation. I am convinced, that the results of quantum computation theory (QCT) are not only interesting in themselves, but also should be taken into account in discussions concerning the nature of mathematical knowledge. The philosophical discussion will however be postponed to another paper. QCT seems not to be well-known (...) among philosophers (at least not to the degree it deserves), so the aim of this paper is to provide the necessary technical preliminaries presented in a way accessible to the general philosophical audience. (shrink)

Topological indices are of incredible significance in the field of graph theory. Convex polytopes play a significant role both in various branches of mathematics and also in applied areas, most notably in linear programming. We have calculated some topological indices such as atom-bond connectivity index, geometric arithmetic index, K-Banhatti indices, and K-hyper-Banhatti indices and modified K-Banhatti indices from some families of convex polytopes through M-polynomials. The M-polynomials of the graphs provide us with a great help to calculate the topological indices (...) of different structures. (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)

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)

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)

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)

The book presents investigations into the world of info-computational nature, in which information constitutes the structure, while computational process amounts to its change. Information and computation are inextricably bound: There is no computation without informational structure, and there is no information without computational process. Those two complementary ideas are used to build a conceptual net, which according to Novalis is a theoretical way of capturing reality. We apprehend the reality within a framework known as natural computationalism, the view (...) that the whole universe can be understood as a computational system at many different levels - from quantum mechanical world, to biological organisms including intelligent minds and their societies. Questions about nature of information and computation and their unified view are addressed along with application of info- computational approach to knowledge generation. (shrink)

We discuss robotic art, emotion in robotic art, and compassion in the philosophy of art. We discuss a particular animated artwork, survivor, the walking chair, symbolising survivors of landmine blasts, learning to use crutches, and maimed emotionally as well as physically. Its control incorporates mutual relations between very rudimentary representations of distinct emotions. This artwork is intended for sensitising viewers to the horror experienced by those who survive, and those who don’t. We can only give a small sample, here, of (...) the reactions of viewers on various occasions when survivor was exhibited. Regardless of how much which pertains to human mental functions the tool embodies or doesn’t, it is the effect on the human perceivers which matters most to us, and enables us to understand something more about human cognition. Arguably this project is instructive in respect of the ethical-social implications of the synthetic method, i.e. the construction of inorganic systems in order to understand autonomous intentional action; in this project, the latter pertains to the humans involved. (shrink)

This work deals with the exponential fragment of Girard's linear logic without the contraction rule, a logical system which has a natural relation with the direct logic . A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut-elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be (...) introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry-Howard isomorphism with respect to the logical system in question. MSC: 03B40, 03F05. (shrink)