A Canvas for Thought

A Canvas for Thought

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Procedia Computer Science 00 (2019) 000–000 Procedia Computer Science 14500 (2018) 805–812 Procedia Computer Science (2019) 000–000

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Postproceedings of the 9th Annual International Conference on Biologically Inspired Cognitive Postproceedings of the 9thBICA Annual International Conference Inspired Cognitive Architectures, 2018 (Ninth Annual MeetingonofBiologically the BICA Society) Architectures, BICA 2018 (Ninth Annual Meeting of the BICA Society)

A A Canvas Canvas for for Thought Thought Hedda R. Schmidtke Hedda R. Schmidtke

University of Oregon, Eugene, Oregon, USA University of Oregon, Eugene, Oregon, USA

Abstract Abstract A Common Model of Cognition needs to be open so as to encompass a broad range of approaches and provide a firm fundament A Common Modelwho of Cognition to beaspect open so to encompass broad can range of approaches andbeprovide firm fundament to which researchers study oneneeds particular of as cognition at morea detail refer. It should also open toaincorporate new to which even, researchers who studyifone aspect of cognition at more can refer. It should alsoexperiment be open to incorporate new findings or in particular, theyparticular come from an unconventional angle.detail A recent cognitive systems has surprisingly findings even, or in particular, if they come from an unconventional angle. A recent cognitive systems experiment has surprisingly shown that there is a fundamental link between logic and analogous representations. This paper discusses a field of functionality shown here that the there is a fundamental between logic analogous representations. This paper a field ofSketchpad, functionality called Canvas, comprisinglink or overlapping whatand is called in other models the Visual Buffer,discusses the Visuospatial the called here theSystem, Canvas,or comprising or overlapping what isresult. calledThe in other thethat Visual Buffer,like the the Visuospatial the Spatial Visual Imagery, leveraging this recent papermodels suggests a module Canvas is Sketchpad, a fundamental Spatial Visual or Imagery, leveraging recent result. Thetopaper suggests that moduleoflike the Canvas is aabilities, fundamental component forSystem, any model of cognition and ofthis crucial importance understanding the aorigins higher cognitive such component model The of cognition anddemonstrates, of crucial importance to understanding the origins of from higherthe cognitive abilities, as languagefor or any geometry. paper also how a fine-level research result benefits Common Model such as a as language or geometry. The paper alsoresearch demonstrates, a fine-level research result benefits fromtotheprovide Common Model as a common context within which fine-level can behow embedded, relieving the author from having a full cognitive common context within whichstudied. fine-level research can be embedded, relieving the author from having to provide a full cognitive architecture beyond the aspect architecture beyond the aspect studied. c 2018  2019 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. © c 2019  The Authors. Published by Elsevier B.V. This is This is an an open open access access article article under under the the CC CC BY-NC-ND BY-NC-ND license license (https://creativecommons.org/licenses/by-nc-nd/4.0/) (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under BY-NC-ND license under responsibility of the the CC scientific committee of (https://creativecommons.org/licenses/by-nc-nd/4.0/) the 9th Annual International Conference on Biologically Inspired Peer-review Peer-review under responsibility of the scientific committee of the 9th Annual International Conference on Biologically Inspired Cognitive Architectures. Cognitive Architectures. Keywords: Common Model of Cognition; Mental Imagery; Mental Maps; Logic-Perception Interface Keywords: Common Model of Cognition; Mental Imagery; Mental Maps; Logic-Perception Interface

1. Introduction 1. Introduction This paper proposes to give the Visual Buffer and Imagery a central role in the Common Model, in the form of a This Canvas paper proposes to give the Visual Buffer and Imagery a centralasrole in the Common Model,important in the form unified component or functionality. It investigates the Canvas a fundamental component forofthea unified Canvas component or functionality. It investigates the Canvas as a fundamental component important for the emergence of language and thus higher cognition as exhibited characteristically by human beings, such as analogy emergence of language and thus higher cognition as exhibited characteristically by human beings, such as analogy formation, general problem solving, imagination, and tasks of higher cognition required for higher cultural tasks, formation, generalThe problem imagination, tasks of higher cognition required higher tasks, including science. paper,solving, in line with proposalsand such as ACT-R [1, 34] and SOAR [18]for as well as cultural neuroimaging including science. The paper, in line with proposals such as ACT-R [1, 34] and SOAR [18] as well as neuroimaging ∗ ∗

Corresponding author. Tel.: +1-541-346-4856 ; fax: +1-541-346-2067. Corresponding Tel.: +1-541-346-4856 ; fax: +1-541-346-2067. E-mail address:author. [email protected] E-mail address: [email protected]

c 2019 1877-0509  The Authors. Authors. Published Published by by Elsevier Elsevier B.V. 1877-0509 © 2018 The B.V. c 2019 Thearticle 1877-0509  Authors. Published by Elsevier B.V. This isisan under the CC licenselicense (https://creativecommons.org/licenses/by-nc-nd/4.0/) This anopen openaccess access article under the BY-NC-ND CC BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility ofofthe scientific committee of the 9th 9th Annual International Conference on Biologically Inspired Cognitive ArchiPeer-review under responsibility the scientific committee of the Annual International Conference on Biologically Inspired Cognitive Peer-review under responsibility of the scientific committee of the 9th Annual International Conference on Biologically Inspired Cognitive Architectures. Architectures. tectures. 10.1016/j.procs.2018.11.027

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studies [15, 6], proposes to add the Canvas as a component including the Visual Buffer and interfacing with Working Memory, similar to the Imagery component in Sigma [25] and the Spatial Visual System in SOAR [18]. Structure of the Article. The next section briefly reviews the literature on imagery and analogous representations. Results from an experiment at printing a mental map are leveraged to discuss the benefits of a universal Canvas being added to the Common Model. Core functionalities and properties are discussed and a way of inclusion into the Common Model is proposed. The paper concludes with a short discussion of the role of the Canvas in the Common Model and for higher cognition and sketches opportunities for future works. 2. Background Human cognition encompasses both logical representations and analogous representations. Thus a key component of the human cognitive system could be a module able to translate between analogous and logical representations. This subsystem should be able to translate ordering information, including estimates of spatial positions or preferences, given as qualitative statements, into analogous information, which is quantitative or in some sense in a quasiquantitative format. This ability has a key role in human intelligence and characterizes many tasks that distinguish human from artificial intelligence. In particular, it allows human beings to exchange mental images and mental maps using a linguistic format [36]. A location X characterized as “to the west of A and to the north of B” is easily mentally pictured by a human listener, and experiments [16, 17] confirmed that the mental representation seems to have properties of an analogous format. Neuroimaging results [15, 6] allowed this ability to be localized in areas also responsible for higher visual functions providing further support for the hypothesis that mental images are perceived in a sense. The module called Canvas here is conjectured to be responsible both for translation between higher perception and logic or language and translation from linguistic or logical format into a format that can physically be drawn. While there is neurological evidence for a spatial representation in rats [24], human cognition seems to be more flexible and able to leverage analogous internal representations for a wide range of tasks, including preference reasoning. Depending on the tasks, preference reasoning can encompass both linear or dimensional and hierarchical or tree-like orderings and even mixtures of both [39]. Moreover, these representations are not fixed, as images would be, but people can easily reconceptualize [37, 38]. While there are many logical formats, theories, and mechanisms, both logical and numerical, which can be used to express, and reason about, ordered dimensions, such as time, space, or utility, there was until very recently no indication that there is a direct connection between logical representations and ordered dimensions leaving many open questions regarding the connection and the possibility of the evolution of language and logic. The author [28] recently demonstrated a surprising first result of more than a decade of research in the connection leveraging a logicbased approach. The result shows that the truth table of a formula and the disjunctive normal form (DNF) encode – in a unary format – analogous information related to the meaning of the formula. It is moreover easy to implement: a very simple filtering mechanism, as provided by perceptual attention systems, is sufficient to extract this analogous information from formulae. The mechanism first expands a set of conjunctive normal form (CNF) formulae into the DNF format that – essentially logical but not suitable for reasoning – takes an intermediate role between higher perceptual data and logical formats suitable for reasoning. The image corresponding to the sentences “A is north of B. B is north of C.” (logically: φ = [B ∧ N → A] ∧ [C ∧ N → B]), for instance, results in three objects in a row or column. We simply count as the north coordinate for an object O all models of the formula φ where O = 1 and N = 1. This yields for A the north coordinate 3, since A = 1 and N = 1 holds in three cases in which the formula φ evaluates to true. It yields coordinate 2 for B, and 1 for C. This direct connection is not only surprising but highly advantageous, as it can easily explain how the Canvas could have evolved without requiring any additional ontology or special mechanism for translating logic into an analogous format, simply from a perceptual filtering mechanism. The above only illustrates the case of very simple formulae that belong to a fragment of propositional logic, leaving logics beyond this to explore, and making the result [28] the first in a series of studies exploring a wider family of languages. The result is far-ranging, since the alternative of having a distinct ontology, i.e., a priori knowledge an individual is born with is problematic from an explanatory point of view [14]. If the system needs certain knowledge to participate



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in the sharing of knowledge, then how does it obtain this primary knowledge? If an innate ontology has to be assumed, it needs to be minimalistic. In mathematics, a smaller axiom system means less assumptions have to be believed without proof and is therefore generally preferable. A similar situation must have existed for our ancestors when they first developed language, but even harder, because they did not have a language to negotiate basic assumptions the language system would need in order to function. Studying the interface between logic and perception striving for a minimalist or zero ontology thus can provide insights into a root of language and logic itself. Assuming a model of the Canvas based on the DNF or truth tables, someone may nevertheless argue, is infeasible, since these are formats unsuitable for reasoning with worst case exponential time requirements. This is, however, an engineering perspective. Models of human working memory [3] contain several modal subsystems enabled to process and convert data into the declarative format required for working memory processing. Working memory itself has severe limitations as to the number of semantically unconnected objects that can be kept in memory at a time [2, 21]. Assuming a model of the Canvas based on the DNF, this can for for the visual modality be interpreted computationally: the task of keeping unconnected objects in mind could be a task of a computationally high complexity, such as maintaining the DNF representation of logical or linguistic content normally processed in CNF. The characteristic limitations of human working memory can thus be understood as support from a cognitive perspective. While the realization of higher cognitive functions on a neural substrate is still subject to debate, and the Common Model leaves this question as open as possible, one can see a spectrum of approaches between those assuming a computationally powerful substrate, such as graphical models in Sigma [25], and those striving for computationally minimalistic models such as the bit-vector approach [13]. Computationally powerful approaches are advantageous in so far as their explanatory reach is the furthest, while minimalist models, in contrast, may offer deeper insights into details. The Common Model avoids assumptions about the substrate, leaving room for different types of systems. However, it makes the assumption that there is a hybrid format with declarative data and quantitative metadata, which is a powerful assumption – from the point of view of representation formats – leading to a number of consequences, in particular with respect to what is here called the Canvas. The addition of quantitative metadata could entail that every declarative cognitive token could be provided with its own visualization or analogous representation, which would make a translation module such as the Canvas, unnecessary. However, the flexibility of reconceptualization and the ease with which a model can be extended when new information becomes available cannot be modeled with a static quantitative representation. This paper therefore proposes to include the Canvas as a translation component, so that different models extending or implementing the Common Model can differ with respect to how powerful the representation format is and how much work a dedicated translation component would carry. Both ACT-R [1] and SOAR [18] assume a Visual Buffer. The metaphor of a buffer was not chosen here, as it centers discussion on the processing of perceptual input data, not on higher cognitive functions, as are leveraged in drawing onto the Visuospatial Sketchpad [3]. The Spatial Visual System of SOAR [18] has both components, like the proposed Canvas. The Canvas metaphor is proposed here instead of the terms sketchpad or buffer to unite the two aspects without going to a more abstract level system, as neuroimaging studies on imagery seem to suggest [15, 6] a tight link. Likewise, a canvas can be used with a projector to show recorded images from perception or as a painting medium one can draw on, both in recreation of experiences from memory and in processing on the rational level. This module operates on the upper boundary of the Cognitive Level [23], an operation taking 1–10 sec: the minimum delay being the minimal reaction time for producing a trained response from perceptual input, the maximum boundary constituted by the task to conjure up a mental image with a more complex layout. The recent result [28] is based on a decade long study on the expressiveness and suitability of different logical languages to represent quasi-quantitative information and find a representation for continuous – or to be mathematically more accurate: dense – numerical domains that facilitates reasoning. In the background of the work is the attempt to bring the cognitive hierarchy [23, 10] together with the complexity theoretic and logical hierarchy [20], with the most striking difference being the handling of continuous domains. The efficient handling of reasoning about continuous domains, such as space, time, or measurement values, in logic has been studied in the area of qualitative reasoning [5, 7]. In a logical format, ordering information can be expressed with comparison relations and thresholds [8]. Integration of actual numerical representations into First Order Logic, however, comes at a high price in terms of complexity, and even more application oriented proposals for description logics [40, 11] have to fight an explosion in complexity.

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The contextual logic language family of Context Logics (CL) was specifically developed to overcome this issue. CL were designed to provide a semantics [30] for, and for verifying [32] of, early context-aware computing systems. The basic idea was to implement and analyze such systems as a distributed SOAR-like cognitive system [31], so as to make it possible to study the boundaries between perception and logic, on the one hand, and different layers of rational capabilities, on the other hand. The CL family today comprises languages [27, 30, 29] for reasoning about continuous domains on several complexity layers within the expressiveness-tractability spectrum [20] and the evolutionary cognitive hierarchy [9, 31]. CL is designed to facilitate ontological minimalism. This makes it easy to map to other logics but also to serve as a fundamental logic for cognition. Like hybrid logics [4], it facilitates representing indexicals (e.g., we, here, now, this pen, next Sunday) leveraged widely in natural language and a characteristic of a perceiving, embodied system. A central goal was the study of analogous representations in logic as received from perception [26]. The CL languages are characterized by formal ontological simplicity: the logic has only one type of entities, called contexts, which correspond cognitively to features, and can be used, together with a single relation  (part of or subcontext) to provide semantic equivalents to objects, relations, and possible worlds. Several approaches to solving the grounding problem have been proposed [e.g., 12, 33] and at least the direction from perception to language, where the Canvas solely functions as a Visual Buffer, can be explained well. However, a key problem when focussing only on this path is to explain how different agents arrive at sufficiently similar models if they communicate about contents that are inaccessible to perception. This may have been among the earliest benefits of language for survival: if you eat belladonna, you become sick. Explaining the path back from logic and language to continuous representation thus has high explanatory potential. The Common Model proposes that it may be necessary to assume innate ontologies, which would be one of the possible solutions to explain the path from logic to image. This solution, however, entails two fundamental issues: the first is, how this ontology could have evolved, and the second is how it attaches itself in a sufficiently similar way to symbols that a common understanding is reached. Note that these problems are not easily solved by a language game or social semantic fix point strategy, as this ontology would need to be more fundamental, a prerequisite to engaging in any language games at this higher level. In the proposed system [28], the only ontology required is to know which symbols represent relations and which objects, a distinction easily generically encodable, e.g., with a linguistic marker. Many species have associative memory, but none except humans have language and build coherent models of reality far transcending their perceptual capabilities. The claim that a learned or evolved common ontology is insufficient for grounding is known in philosophy as the Zero Semantical Commitment Condition [ZSC, 35]. A system that solves the grounding problem must be such that it can start from an empty knowledge base. With a necessary analogous property in logic and language it is much easier to explain how a common language where sentences about events and facts not visibly present may have evolved.

3. Experimental Validation Assuming that it is possible to convert back and forth between a logical and an analogous model has a number of advantages for a cognitive architecture. Intuitively, perceptual data undergoes multiple abstraction steps until a logical format is produced that can be processed. This is the functionality of higher-level perception, the visual processing components of the SOAR and ACT-R models. Higher-level perception needs to organize a wealth of information, a process that, inter alia, involves filtering, a step easily performed in a context dependent logical framework. Such a filter can, e.g., separate what is currently relevant from what is not [22]. Evolutionarily, the Canvas may have evolved for this purpose. The Canvas’ crucial function for the higher levels of cognition, however, comes from its ability to be used in the opposite direction, i.e., to generate images from logical representations. An experimental system based on CL that can do this and visualize – or more generally, cast into an analogous format – arbitrary spatial formulae of the simplest fragment of CL is the Imaginer [28]. It internally operates in a very simple manner on a simple bit-vector-based format making it symbolic and close to sub-symbolic representations at the same time. In a recent extension, the system was equipped with a protolanguage interface based on CL. CL, being based on simple descriptions of sensory data, is able to reflect basic language expressiveness. It is primitive enough to be a



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Fig. 1. Preliminary experiment: landmarks around the University of Oregon were described in simple English by a native language speaker and then processed automatically by the Imaginer system [28], a partial implementation of a Canvas.

candidate for a language in between our current natural languages and what is expressible and learnable from pointing gestures, alone. Figure 1 shows preliminary results of this study. It shows an image generated from a natural language description of landmarks around the University of Oregon. The system was implemented augmenting a partial Canvas implementation [28] with a straight-forward miniature parser for a simple fragment of English.1 The example illustrates the Canvas metaphor: the logical descriptions from the verbal input are converted into an analogous, numerical coordinate format. The coordinates obtained from the process can then be drawn (Fig. 1). The conversion process is the simple filtering mechanism sketched above. In generating Fig. 1, the only ontology comprises only that north is drawn at the top, east on the left – which are modern mapping conventions adopted for legibility in this paper –, and that south and east are the opposites of north and west, respectively. One of the interesting outcomes of this study was, in fact, that opposites in the proposed protolanguage logically function similar to active and passive verb forms, as they switch the roles of reference object and localization object. 1

The parser was generated using PLY: http://www.dabeaz.com/ply/ply.html

after all does not require unanimity – it is our attempt at providing a coherent summary along wit broadly shared set of assumptions held in the field. Specific areas of disagreement plus open issu discussed in the final section.

4.1 Structure and Processing The structure of aComputer cognitive Science architecture defines805–812 how information and processing are organized in Hedda R. Schmidtke / Procedia 145 (2018) components, and how information between components. The standard model posits that th H.R. Schmidtke / Procedia Computer Science 00 (2019)flows 000–000 is not an undifferentiated pool of information and processing, but is built of independent modules have distinct functionalities. Figure 4 shows the core components of the standard model, which i perception and motor, working memory, declarative long-term memory, and procedural long-term

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Declarative Long-term Memory

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Figure 4. The structure of the standard model.

Fig. 2. Embedding of the Canvas into the Common Model.

Fig. 3. The Common Model, reproduced from [19].

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4. Adding the Canvas to the Common Model The Canvas would evolutionarily be directly useful for speakers, as they can locate objects in the world with respect to thus communicable mental maps. As the process, being a simple general logical inference mechanism, can be assumed to be universal for speakers, the mental maps generated by two different speakers reading the same description will be isomorphic. Ancient Chinese maps depict the South at the top, not the North. A reader from this cultural context would likely picture what he/she reads differently, but systematically so. The difference between two readers would thus only appear if they physically drew the map, and – as the difference is systematic – applying a corresponding affine transform, i.e., rotating the drawn map, would suffice. This is the reason why a universal Canvas component could be vital for a model of cognition. The mental recreation of similar images from a natural language sentence provides grounding, a vital aspect of cognition and potentially fundamental for any form of higher cognition. Whereas Fig. 2 as well as the experiments so far only regard the visual modality, and no other claim can be made at the moment, the Common Model supports multiple modalities and also features quantitative metadata as a potential realization of analogous representations [19]. In contrast, the concrete interplay between the Canvas and specific other units is not yet part of the model. The Canvas receives input directly from perception – this is the Visual Buffer functionality mentioned in the Common Model –, but it can also visualize, i.e., translate into images, logical statements as provided through language and declarative semantic memory. This is represented by [19] with the double arrow in Fig. 3. Figure 2 analyzes and details this aspect. In comparison to other proposals, such as SOARs Spatial Visual System [18], the Canvas model also encompasses models of imagery that are analogous but less literally perceptual. Like the Imagery component in Sigma [25], the Canvas should be a central component of the Common Model required to translate back and forth between analogous and logical representations. 5. Conclusions and Future Work This paper proposed to extend the Common Model with a Canvas module that encompasses the functionality of both the Visual Buffer and Imagery, i.e., the Visuospatial Sketchpad. The paper presented results from an exemplary system that can partially implement the Canvas and theoretical reasons for its existence as motivated in the literature. ACT-R [1], SOAR [18], and Sigma [25] all feature components that could be captured under the Canvas label and benefit from the proposed mechanism. Sigma puts Imagery into the center of its Cognitive Model diagram. As the interface between sensory processing and higher logical cognition, this paper argues, its study is a worthwhile exploration towards a more complete picture of human cognition. The author’s experiments [28] are a first step, and there is a wealth of possible venues to explore, both on the theoretical side and the systems side. On the theoretical side, future work should move beyond the most basic logical



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language of the perceptual here and now to explore the link between logic or language and imagery or even imagination on the higher levels. On the systems side, the Canvas system itself should be incorporated into a more comprehensive cognitive system implementation, including perception, logical reasoning, and memory retrieval. The idea of the DNF as the missing link between perception and logic opens a range of new perspectives on known and unknown questions. 6. Acknowledgements Thanks to Andrew Houck for providing the natural language description of Eugene. References [1] Anderson, J.R., 2009. How can the human mind occur in the physical universe? Oxford University Press. [2] Baddeley, A., 1994. The magical number seven: Still magic after all these years? Psychological Review 101. [3] Baddeley, A.D., Hitch, G., 1974. Working memory. Psychology of Learning and Motivation 8, 47 – 89. doi:https://doi.org/10.1016/ S0079-7421(08)60452-1. [4] Blackburn, P., 2000. 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