Simone Pinna

The human mind is constantly engaged in predicting the future using past experiences to anticipate what is likely to happen next. The predictive coding approach focuses on this ongoing activity and proposes a unified mechanism that underlies both perception and action. In this paper, we show that some applications of the predictive coding model to memory and perception processes often face the ambiguity of two controversial aspects. (I) How can the brain apply similar mechanisms to handle qualitatively different degrees of prediction (e.g. imaginative and procedural predictions)? (II) How is it possible to reconcile the presence of stable mental representations with the continuous dynamic change of perceptual data? We suggest that the relation between different degrees of prediction can be seen as analogous to the relation between a perception and its recollection, and we argue that this relation can be better understood within a timing-based approach that looks at the temporal architectures underlying these cognitive phenomena. Therefore, based on the interpretation of some empirical data from the study of auditory perception, we show how the timing-based approach we delineate can help to clarify aspects (I) and (II).

In this chapter I show, first, what modifications are needed in order to make the design of a Turing machine more suitable for being used as a model of human computation. The result of these modifications is a special kind of TM-inspired computational system, i.e. the Bidimensional Turing machine. Second, I introduce the notion of a Galilean model, namely, a concept of empirical adequacy for cognitive models (Giunti 1995) and I propose to consider Bidimensional Turing machines as a possible Galilean models.

In the paper On computable numbers, with an application to the Entscheidungsproblem (1936), Alan Turing described his computational machines as the idealized formal counterparts of the mechanisms at work in a real cognitive system, namely the one consisting of a human being performing calculations with paper and pencil. After a semi-formal description of Turing machines, I briefly present the mathematical meaning of Turing’s 1936 paper, showing that the soundness of Turing’s solution to the Entscheidungsproblem ultimately lies on some cognitive considerations, namely, the intuitive correctness of his analysis of the notion of effective procedure. Then, I discuss the historical and philosophical reasons that led to the widely accepted classic-computational interpretation of the Turing machine. Following Andrew Wells, I argue that this interpretation is wrong, because it treats the tape of a Turing machine as its internal memory, rather than as the external environment. Lastly, I introduce a different interpretation of the Turing machine’s architecture, namely Wells’ Ecological Functionalism, that recognizes the cognitive importance of Turing’s theory of computation.

In this chapter I first sketch an overview on the principal contemporary approaches to cognitive arithmetic, showing that these approaches somewhat underestimate the role of online symbolic transformations like those performed in the execution of an algorithm (Rumelhart et al. 1986). Second, I propose to inspect arithmetical skills from an algorithmic stance. Assuming that the Bidimensional Turing machine is a reliable model of the various elements at stake in algorithmic performances, I formulate a set of hypotheses about the development of algorithmic skills and the related algorithmic performances, which may in principle be empirically verified. An eventual confirmation of those hypotheses may also help answering the question about the role of external devices, like paper and pencil, in algorithmic performances. Last, I describe some experiments made on a feed-forward neural network in order to test a developmental hypothesis on the acquisition of a set of basic number facts (in this case, the set of all possible results of single-digit additions).

In this paper we argue that the debate between representational and anti-representational cognitive theories cannot be reduced to a difference between the types of model respectively employed. We show that, on the one side, models standardly used in representational theories, such as computational ones, can be analyzed in the context of dynamical systems theory and, on the other, non-representational theories such as Gibson’s ecological psychology can be formalized with the use of computational models. Given these considerations, we propose that the true conceptual difference between representational and anti-representational cognitive descriptions should be characterized in terms of style of explanation, which indicates the particular stance taken by a theory with respect to its explanatory target.

Knowledge representation is a central issue for Artificial Intelligence and the Semantic Web. In particular, the problem of representing n-ary relations in RDF-based languages such as RDFS or OWL by no means is an obvious one. With respect to previous attempts, we show why the solutions proposed by the well known W3C Working Group Note on n-ary relations are not satisfactory on several scores. We then present our abstract model for representing n-ary relations as directed labeled graphs, and we show how this model gives rise to a new ontological pattern (parametric pattern) for the representation of such relations in the Semantic Web. To this end, we define PROL (Parametric Relational Ontology Language). PROL is an ontological language designed to express any n-ary fact as a parametric pattern, which turns out to be a special RDF graph. The vocabulary of PROL is defined by a simple RDFS ontology. We argue that the parametric pattern may be particularly beneficial in the context of the Semantic Web, in virtue of its high expressive power, technical simplicity, and faithful meaning rendition. Examples are also provided.

The vision underlying the development of the Semantic Web is that the whole complex of our knowledge forms a huge semantic network, which should be represented and made explicit by means of languages such as RDF, RDFS or OWL. However, these languages have important expressive limits, since none of them reaches the full expressive power of a first-order language. As a result, large parts of our knowledge—in particular, mathematical and scientific theories—cannot currently be made available on the Semantic Web as linked data, not even in principle. In this work, we are going to define FOOL (first-order ontology language), a new ontological language compatible with RDF, which allows the expression of any formula of a first-order language as a connected RDF graph. FOOL is as expressive as a first-order language, but unlike it, its statements do not have a serialized form. Instead, like a RDF statement, each statement of a FOOL knowledge base is a connected graph, and different statements link to each other through the meaningful nodes they share. In this way, the semantic relationships between statements are made explicit, and given FOOL’s compatibility with RDF, virtually the entire complex of our knowledge can in principle be made available on the Semantic Web as linked data. The semantic relationships made explicit by a FOOL ontology are not those of logical consequence, but they are meaning connections between statements represented as graphs. It is not far-fetched to think that, by devising appropriate measures of the linking patterns between statements, such relations can be mechanized, thus opening the way to new and possibly unforeseen results and applications.

This book describes a novel methodology for studying algorithmic skills, intended as cognitive activities related to rule-based symbolic transformation, and argues that some human computational abilities may be interpreted and analyzed as genuine examples of extended cognition. It shows that the performance of these abilities relies not only on innate neurocognitive systems or language-related skills, but also on external tools and general agent–environment interactions. Further, it asserts that a low-level analysis, based on a set of core neurocognitive systems linking numbers and language, is not sufficient to explain some specific forms of high-level numerical skills, like those involved in algorithm execution. To this end, it reports on the design of a cognitive architecture for modeling all the relevant features involved in the execution of algorithmic strategies, including external tools, such as paper and pencils. The first part of the book discusses the philosophical premises for endorsing and justifying a position in philosophy of mind that links a modified form of computationalism with some recent theoretical and scientific developments, like those introduced by the so-called dynamical approach to cognition. The second part is dedicated to the description of a Turing-machine-inspired cognitive architecture, expressly designed to formalize all kinds of algorithmic strategies.

Gibson’s ecological psychology represents one of the theoretical basis of the dynamical approach to cognition. In this chapter I, first, present an overview of the main lines of research that can be included in the general formulation “dynamical approach”. Second, I elaborate on the original aspects of this approach, with a particular focus on the theoretical differences with classic computationalism. Third, I show the analogies between the dynamical approach on the one side and Wells’ Ecological Functionalism on the other. Last, I argue that, for current purposes, Turing machines are better viewed as genuine dynamical systems. By this assumption, it is possible to analyze a specific set of cognitive abilities, namely, those related to deliberate execution of explicitly specified algorithms.

In this chapter I focus on the theoretical grounds of Wells’ Ecological Functionalism. In the first section, I briefly present and discuss the Extended Mind hypothesis, with special regard to the so-called parity principle, and to the concept of active externalism. In the second section, I explain the reasons why, on the one side, we should not worry (at least for the moment) about some ontological issues concerning the Extended Mind hypothesis (e.g., the question: Are the external devices we use in some cognitive activities constitutive parts of our mind?). On the other side, we should focus our attention on the explanation of the functional role of any relevant feature of a cognitive system, be it internal or external to the organism. In the third section, I discuss Wells’ arguments against the Computational Theory of Mind and the connectionist approach. In the last section, I present Wells’ original view of Turing machines as formal models for Gibson’s concept of affordance.