This paper proposes how various disciplinary theories of cognition may be combined into a unifying, sub-symbolic, computational theory of cognition. The following theories are considered for integration: psychological theories, including the theory of event coding, event segmentation theory, the theory of anticipatory behavioral control, and concept development; artificial intelligence and machine learning theories, including reinforcement learning and generative artificial neural networks; and theories from theoretical and computational neuroscience, including predictive coding and free energy-based inference. In the light of such (...) a potential unification, it is discussed how abstract cognitive, conceptualized knowledge and understanding may be learned from actively gathered sensorimotor experiences. The unification rests on the free energy-based inference principle, which essentially implies that the brain builds a predictive, generative model of its environment. Neural activity-oriented inference causes the continuous adaptation of the currently active predictive encodings. Neural structure-oriented inference causes the longer term adaptation of the developing generative model as a whole. Finally, active inference strives for maintaining internal homeostasis, causing goal-directed motor behavior. To learn abstract, hierarchical encodings, however, it is proposed that free energy-based inference needs to be enhanced with structural priors, which bias cognitive development towards the formation of particular, behaviorally suitable encoding structures. As a result, it is hypothesized how abstract concepts can develop from, and thus how they are structured by and grounded in, sensorimotor experiences. Moreover, it is sketched-out how symbol-like thought can be generated by a temporarily active set of predictive encodings, which constitute a distributed neural attractor in the form of an interactive free-energy minimum. The activated, interactive network attractor essentially characterizes the semantics of a concept or a concept composition, such as an actual or imagined situation in our environment. Temporal successions of attractors then encode unfolding semantics, which may be generated by a behavioral or mental interaction with an actual or imagined situation in our environment. Implications, further predictions, possible verification and falsifications, as well as potential enhancements into a fully spelled-out unified theory of cognition are discussed at the end of the paper. (shrink)

The system called F is essentially a sub-theory of Frege Arithmetic without the ad infinitum assumption that there is always a next number. In a series of papers (Systems for a Foundation of Arithmetic, True” Arithmetic Can Prove Its Own Consistency and Proving Quadratic Reciprocity) it was shown that F proves a large number of basic arithmetic truths, such as the Euclidean Algorithm, Unique Prime Factorization (i.e. the Fundamental Law of Arithmetic), and Quadratic Reciprocity, indeed a sizable amount of arithmetic. (...) In particular, F proves some (but not all) of the Peano Axioms; that is, F proves the axioms of a sub-theory - call it FPA - of second-order Peano-Arithmetic. This short technical note will demonstrate that the converse also holds, in the following sense. F has the same language as second-order Peano Arithmetic except that, in addition, it has a two-place predicate symbol “Μ”. Then it is possible to provide a definition, indeed a reasonable definition, for “Μ” such that FPA proves all the axioms of F. So F and FPA effectively have the same proof-theoretic strength. In particular FPA, which lacks the Successor Axiom stating that every natural number has a successor, is able to prove the Euclidean Algorithm, Unique Prime Factorization, and Quadratic Reciprocity, indeed (again) a sizable amount of arithmetic. (shrink)

As a multi-layered theory of the foundations of “‘mathematicizing’ logic”, Husserlian pure logic is stratified on three levels (sub-theoretical, theoretical, meta-theoretical), which are then themselves transversally split in two sides (apophantic and ontological). This paper investigates how symbolic knowledge works in this framework—viz. in terms of ‘How can the subjective operating with symbols be justified in the process of obtaining objective contents of knowledge?’ To do so, it innovates in showing how Husserl’s theory of semiotic intentionality provides the epistemological-transcendental (...) foundation for the syntactic-semantic correspondence of the meaning relationship that is operative at the kernel of pure logic—i.e. on the theoretical level, between systems of axioms and formal manifolds. And thereby, it bridges the gap between the two volumes of the first edition of the Logical Investigations (namely, the Prolegomena and the six Investigations). (shrink)

Despite studies such as Biber, quantitative methodologies remain under-exploited resources in discourse analysis. This study employs a quantitative, statistical approach to re-examine and rethink the rather well-explored topic of register. Using the extensively documented register of Sports Announcer Talk as a case study, careful quantitative analysis exposes the limitations of traditional descriptive approaches to registers. Quantitative analysis reveals significant inter-register variation in the distribution of core SAT features in a television broadcast and a radio broadcast of a basketball game. Further, (...) SAT features appear to function differently in the broadcasts: out of necessity in the radio broadcast and symbolically in the television broadcast. Such inter-register variation of variable frequency and feature function may be a product of differences in communication situation and communicative function related to broadcast media. Quantitative approaches allow more precise defining of registers and provide the researcher insight into the communicative function of discourse features. (shrink)

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested (...) in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration. (shrink)

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested (...) in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration. (shrink)

Barsalou's elision of the personal and sub-personal levels tends to conceal the fact that he is, at best, providing the “specs” but not yet a model for his hypothesized perceptual symbols.

Stereotypically, computation involves intrinsic changes to the medium of representation: writing new symbols, erasing old symbols, turning gears, flipping switches, sliding abacus beads. Perspectival computation leaves the original inscriptions untouched. The problem solver obtains the output by merely alters his orientation toward the input. There is no rewriting or copying of the input inscriptions; the output inscriptions are numerically identical to the input inscriptions. This suggests a loophole through some of the computational limits apparently imposed by physics. There can be (...) symbol manipulation without inscription manipulation because symbols are complex objects that have manipulatable elements besides their inscriptions. Since a written symbol is an ordered pair of consisting of a shape and the reader's orientation to that inscription, the symbol can be changed by changing the orientation rather than inscription. Although there are the usual physical limits associated with reading the answer, the computation is itself instantaneous. This is true even when the sub-calculations are algorithmically complex, exponentially increasing or even infinite. (shrink)

The purpose is to study the strength of Ramsey’s Theorem for pairs restricted to recursive assignments ofk-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number$k \ge 2$, Ramsey’s Theorem for pairs and recursive assignments ofkcolors is equivalent to the Limited Lesser Principle of Omniscience for${\rm{\Sigma }}_3^0$formulas over Heyting Arithmetic. Alternatively, the same theorem over intuitionistic arithmetic is equivalent to: for every recursively enumerable infinitek-ary tree there is some$i < k$and some branch with infinitely many (...) children of indexi. (shrink)

Bafomé, a mais duradoura criação do escritor Éliphas Lévi, é um ícone do universo esotérico: é a imagem “satânica” mais conhecida da história. Na tentativa de desvendar a sua rica composição simbólica, uma exegese iconográfica será conduzida por intermédio da psicologia analítica, fundada pelo psiquiatra suíço Carl Gustav Jung. As origens de Bafomé na alquimia, na cabala e no gnosticismo serão perscrutadas e os conceitos Junguianos do inconsciente coletivo e dos arquétipos irão, em grande parte, balizar a interpretação proposta neste (...) trabalho. Tal análise será dividida em oito subáreas, entre elas: o significado do seu aspecto animalesco na escatologia cristã, o hermafroditismo na psicologia e nas ciências arcanas, as qualidades mágicas do pentagrama e a importância hermética do caduceu. Por fim, conclui-se que o Bafomé é um símbolo de self, o arquétipo da totalidade psíquica. Bafomé tem por finalidade ser uma alternativa à imagem primordial cristã de autorrealização, mais integradora e menos repressora que esta. Palavras-chave: Alquimia. Cristianismo. Magia. Psicologia junguiana. Religião e psicologia.Baphomet, the lasting creation of the French writer Éliphas Lévi, is an icon of the esoteric universe: it is the history’s best-known “satanic” image. In an attempt to unravel its rich symbolic composite, an iconographic exegesis will be conducted through the use of analytical psychology, founded by the Swiss psychiatrist Carl Gustav Jung. The origins of Baphomet in alchemy, Kabbalah and Gnosticism will investigated mostly through the application of Jungian concepts such as the collective unconscious and the archetypes. Such analysis will be divided into eight sub-areas, including: the significance of his animal appearance in Christian eschatology, hermaphroditism in psychology and the arcane sciences, the magical qualities of the pentagram and the importance of the caduceus in hermetism. Finally, we conclude that Baphomet is a symbol of the self, the archetype of psychic wholeness. Baphomet aims to be an alternative to the Christian primordial image of self-realization, more inclusive and less repressive than the latter. Keywords: Alchemy. Christianity. Jungian psychology. Magic. Religion and psychology. (shrink)

The dialogue develops arguments for and against a broad new world system - info-computationalist naturalism - that is supposed to overcome the traditional mechanistic view. It would make the older mechanistic view into a special case of the new general info-computationalist framework (rather like Euclidian geometry remains valid inside a broader notion of geometry). We primarily discuss what the info-computational paradigm would mean, especially its pancomputationalist component. This includes the requirements for a the new generalized notion of computing that would (...) include sub-symbolic information processing. We investigate whether pancomputationalism can provide the basic causal structure to the world and whether the overall research program of info-computationalist naturalism appears productive, especially when it comes to new approaches to the living world, including computationalism in the philosophy of mind. (shrink)

A rule-based expert system is demonstrated to have both a symbolic computational network representation and a sub-symbolic connectionist representation. These alternate views enhance the usefulness of the original system by facilitating introduction of connectionist learning methods into the symbolic domain. The connectionist representation learns and stores metaknowledge in highly connected subnetworks and domain knowledge in a sparsely connected expert network superstructure. The total connectivity of the neural network representation approximates that of real neural systems and hence avoids (...) scaling and memory stability problems associated with other connectionist models. (shrink)

We live in an information society where the usage, creation, distribution, manipulation, and integration of information is a significant activity. Computations allow us to process information from various sources in various forms and use the derived knowledge in improving efficiency and resilience in our interactions with each other and with our environment. The general theory of information tells us that information to knowledge is as energy is to matter. Energy has the potential to create or modify material structures and information (...) has the potential to create or modify knowledge structures. In this paper, we analyze computations as a vital technological phenomenon of contemporary society which allows us to process and use information. This analysis allows building classifications of computations based on their characteristics and explication of new types of computations. As a result, we extend the existing typologies of computations by delineating novel forms of information representations. While the traditional approach deals only with two dimensions of computation—symbolic and sub-symbolic, here we describe additional dimensions, namely, super-symbolic computation, hybrid computation, fused computation, blended computation, and symbiotic computation. (shrink)

We live in an information society where the usage, creation, distribution, manipulation, and integration of information is a significant activity. Computations allow us to process information from various sources in various forms and use the derived knowledge in improving efficiency and resilience in our interactions with each other and with our environment. The general theory of information tells us that information to knowledge is as energy is to matter. Energy has the potential to create or modify material structures and information (...) has the potential to create or modify knowledge structures. In this paper, we analyze computations as a vital technological phenomenon of contemporary society which allows us to process and use information. This analysis allows building classifications of computations based on their characteristics and explication of new types of computations. As a result, we extend the existing typologies of computations by delineating novel forms of information representations. While the traditional approach deals only with two dimensions of computation—symbolic and sub-symbolic, here we describe additional dimensions, namely, super-symbolic computation, hybrid computation, fused computation, blended computation, and symbiotic computation. (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)

During the last decades, many cognitive architectures (CAs) have been realized adopting different assumptions about the organization and the representation of their knowledge level. Some of them (e.g. SOAR [35]) adopt a classical symbolic approach, some (e.g. LEABRA[ 48]) are based on a purely connectionist model, while others (e.g. CLARION [59]) adopt a hybrid approach combining connectionist and symbolic representational levels. Additionally, some attempts (e.g. biSOAR) trying to extend the representational capacities of CAs by integrating diagrammatical representations and (...) reasoning are also available [34]. In this paper we propose a reflection on the role that Conceptual Spaces, a framework developed by Peter G¨ardenfors [24] more than fifteen years ago, can play in the current development of the Knowledge Level in Cognitive Systems and Architectures. In particular, we claim that Conceptual Spaces offer a lingua franca that allows to unify and generalize many aspects of the symbolic, sub-symbolic and diagrammatic approaches (by overcoming some of their typical problems) and to integrate them on a common ground. In doing so we extend and detail some of the arguments explored by G¨ardenfors [23] for defending the need of a conceptual, intermediate, representation level between the symbolic and the sub-symbolic one. In particular we focus on the advantages offered by Conceptual Spaces (w.r.t. symbolic and sub-symbolic approaches) in dealing with the problem of compositionality of representations based on typicality traits. Additionally, we argue that Conceptual Spaces could offer a unifying framework for interpreting many kinds of diagrammatic and analogical representations. As a consequence, their adoption could also favor the integration of diagrammatical representation and reasoning in CAs. (shrink)

Philosophical and sociological approaches in technology have increasingly shifted toward describing AI (artificial intelligence) systems as ‘(moral) agents,’ while also attributing ‘agency’ to them. It is only in this way – so their principal argument goes – that the effects of technological components in a complex human-computer interaction can be understood sufficiently in phenomenological-descriptive and ethical-normative respects. By contrast, this article aims to demonstrate that an explanatory model only achieves a descriptively and normatively satisfactory result if the concepts of ‘(moral) (...) agent’ and ‘(moral) agency’ are exclusively related to human agents. Initially, the division between symbolic and sub-symbolic AI, the black box character of (deep) machine learning, and the complex relationship network in the provision and application of machine learning are outlined. Next, the ontological and action-theoretical basic assumptions of an ‘agency’ attribution regarding both the current teleology-naturalism debate and the explanatory model of actor network theory are examined. On this basis, the technical-philosophical approaches of Luciano Floridi, Deborah G. Johnson, and Peter-Paul Verbeek will all be critically discussed. Despite their different approaches, they tend to fully integrate computational behavior into their concept of ‘(moral) agency.’ By contrast, this essay recommends distinguishing conceptually between the different entities, causalities, and relationships in a human-computer interaction, arguing that this is the only way to do justice to both human responsibility and the moral significance and causality of computational behavior. (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)

The traditional model of human cognition (TMHC) postulates an ontological and/or structural gap between conscious and unconscious mental representations. By and large, it sees higher-level mental processes as commonly conceptual or symbolic in nature and therefore conscious, whereas unconscious, lower-level representations are conceived as non-conceptual or sub-symbolic. However, experimental evidence belies this model, suggesting that higher-level mental processes can be, and often are, carried out in a wholly unconscious way and/or without conceptual representations, and that these can be (...) processed unconsciously. This entails that the TMHC, as well as the theories on mental representation it motivates and that in turn support it, is wrong. (shrink)

Cognitive science is considered to be the study of mind (consciousness and thought) and intelligence in humans. Under such definition variety of unsolved/unsolvable problems appear. This article argues for a broad understanding of cognition based on empirical results from i.a. natural sciences, self-organization, artificial intelligence and artificial life, network science and neuroscience, that apart from the high level mental activities in humans, includes sub-symbolic and sub-conscious processes, such as emotions, recognizes cognition in other living beings as well as extended (...) and distributed/social cognition. The new idea of cognition as complex multiscale phenomenon evolved in living organisms based on bodily structures that process information, linking cognitivists and EEEE (embodied, embedded, enactive, extended) cognition approaches with the idea of morphological computation (info-computational self-organisation) in cognizing agents, emerging in evolution through interactions of a (living/cognizing) agent with the environment. (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)

Despite recent breakthroughs in the field of artificial intelligence (AI) – or more specifically machine learning (ML) algorithms for object recognition and natural language processing – it seems to be the majority view that current AI approaches are still no real match for natural intelligence (NI). More importantly, philosophers have collected a long catalogue of features which imply that NI works differently from current AI not only in a gradual sense, but in a more substantial way: NI is closely related (...) to consciousness, intentionality and experiential features like qualia (the subjective contents of mental states)1 and allows for understanding (e.g., taking insight into causal relationships instead of ‘blindly’ relying on correlations), as well as aesthetical and ethical judgement beyond what we can put into (explicit or data-induced implicit) rules to program machines with. Additionally, Psychologists find NI to range from unconscious psychological processes to focused information processing, and from embodied and implicit cognition to ‘true’ agency and creativity. NI thus seems to transcend any neurobiological functionalism by operating on ‘bits of meaning’ instead of information in the sense of data, quite unlike both the ‘good old fashioned’, symbolic AI of the past, as well as the current wave of deep neural network based, ‘sub-symbolic’ AI, which both share the idea of thinking as (only) information processing: In symbolic AI, the name explicitly references to its formal system based, i.e. essentially rule-based, nature, but also sub-symbolic AI is (implicitly) rule-based, only now via globally parametrized, nested functions. In the following I propose an alternative view of NI as information processing plus ‘bundle pushing’, discuss an example which illustrates how bundle pushing can cut information processing short,and suggest first ideas for scientific experiments in neuro-biology and information theory as further investigations. (shrink)

As part of the development of the Symbolic and Sub-symbolic Robotics Intelligence Control System, we have implemented a memory store to allow a robot to retain knowledge from previous exp...