TY - JOUR
TI - Homunculus' Brain and Categorical Logic
AU - Heller, Michael
T2 - ArXiv
AB - The interaction between syntax (formal language) and its semantics (meanings of language) is well studied in categorical logic. Results of this study are employed to understand how the brain could create meanings. To emphasize the toy character of the proposed model, we prefer to speak on homunculus' brain rather than just on the brain. Homunculus' brain consists of neurons, each of which is modeled by a category, and axons between neurons, which are modeled by functors between the corresponding neuron-categories. Each neuron (category) has its own program enabling its working, i.e. a "theory" of this neuron. In analogy with what is known from categorical logic, we postulate the existence of the pair of adjoint functors, called Lang and Syn, from a category, now called BRAIN, of categories, to a category, now called MIND, of theories. Our homunculus is a kind of "mathematical robot", the neuronal architecture of which is not important. Its only aim is to provide us with the opportunity to study how such a simple brain-like structure could "create meanings" out of its purely syntactic program. The pair of adjoint functors Lang and Syn models mutual dependencies between the syntactical structure of a given theory of MIND and the internal logic of its semantics given by a category of BRAIN. In this way, a formal language (syntax) and its meanings (semantics) are interwoven with each other in a manner corresponding to the adjointness of the functors Lang and Syn. Categories BRAIN and MIND interact with each other with their entire structures and, at the same time, these very structures are shaped by this interaction.
DA - 2019///
PY - 2019
DP - Semantic Scholar
VL - abs/1903.03424
KW - Emergence
KW - Sketchy
ER -
TY - CONF
TI - Applications of Categories to Biology and Cognition
AU - Ehresmann, Andrée C.
DA - 2018///
PY - 2018
DO - 10/ggdf93
DP - Semantic Scholar
KW - Biology
KW - Emergence
KW - Neuroscience
ER -
TY - JOUR
TI - Conciliating neuroscience and phenomenology via category theory
AU - Ehresmann, Andrée C.
AU - Gomez-Ramirez, Jaime
T2 - Progress in Biophysics and Molecular Biology
T3 - Integral Biomathics: Life Sciences, Mathematics, and Phenomenological Philosophy
AB - The paper discusses how neural and mental processes correlate for developing cognitive abilities like memory or spatial representation and allowing the emergence of higher cognitive processes up to embodied cognition, consciousness and creativity. It is done via the presentation of MENS (for Memory Evolutive Neural System), a mathematical methodology, based on category theory, which encompasses the neural and mental systems and analyzes their dynamics in the process of ‘becoming’. Using the categorical notion of a colimit, it describes the generation of mental objects through the iterative binding of distributed synchronous assemblies of neurons, and presents a new rationale of spatial representation in the hippocampus (Gómez-Ramirez and Sanz, 2011). An important result is that the degeneracy of the neural code (Edelman, 1989) is the property allowing for the formation of mental objects and cognitive processes of increasing complexity order, with multiple neuronal realizabilities; it is essential “to explain certain empirical phenomena like productivity and systematicity of thought and thinking (Aydede 2010)”. Rather than restricting the discourse to linguistics or philosophy of mind, the formal methods used in MENS lead to precise notions of Compositionality, Productivity and Systematicity, which overcome the dichotomic debate of classicism vs. connectionism and their multiple facets. It also allows developing the naturalized phenomenology approach asked for by Varela (1996) which “seeks articulations by mutual constraints between phenomena present in experience and the correlative field of phenomena established by the cognitive sciences”, while avoiding their pitfalls.
DA - 2015/12/01/
PY - 2015
DO - 10/f75jzr
DP - ScienceDirect
VL - 119
IS - 3
SP - 347
EP - 359
J2 - Progress in Biophysics and Molecular Biology
LA - en
SN - 0079-6107
UR - http://www.sciencedirect.com/science/article/pii/S0079610715001005
Y2 - 2019/11/28/23:48:27
KW - Biology
KW - Emergence
KW - Neuroscience
KW - Psychology
KW - Sketchy
ER -
TY - CONF
TI - Towards a Categorical Theory of Creativity for Music, Discourse, and Cognition
AU - Andreatta, Moreno
AU - Ehresmann, Andrée
AU - Guitart, René
AU - Mazzola, Guerino
A2 - Yust, Jason
A2 - Wild, Jonathan
A2 - Burgoyne, John Ashley
T3 - Lecture Notes in Computer Science
AB - This article presents a first attempt at establishing a category-theoretical model of creative processes. The model, which is applied to musical creativity, discourse theory, and cognition, suggests the relevance of the notion of “colimit” as a unifying construction in the three domains as well as the central role played by the Yoneda Lemma in the categorical formalization of creative processes.
C1 - Berlin, Heidelberg
C3 - Mathematics and Computation in Music
DA - 2013///
PY - 2013
DO - 10/ggdndz
DP - Springer Link
SP - 19
EP - 37
LA - en
PB - Springer
SN - 978-3-642-39357-0
KW - Emergence
KW - Neuroscience
KW - Psychology
KW - Sketchy
ER -
TY - JOUR
TI - MENS, an Info-Computational Model for (Neuro-)cognitive Systems Capable of Creativity
AU - Ehresmann, Andrée C.
T2 - Entropy
AB - MENS is a bio-inspired model for higher level cognitive systems; it is an application of the Memory Evolutive Systems developed with Vanbremeersch to model complex multi-scale, multi-agent self-organized systems, such as biological or social systems. Its development resorts to an info-computationalism: first we characterize the properties of the human brain/mind at the origin of higher order cognitive processes up to consciousness and creativity, then we ‘abstract’ them in a MENS mathematical model for natural or artificial cognitive systems. The model, based on a ‘dynamic’ Category Theory incorporating Time, emphasizes the computability problems which are raised.
DA - 2012///
PY - 2012
DO - 10/ggdf9t
DP - Semantic Scholar
VL - 14
SP - 1703
EP - 1716
KW - Emergence
KW - Neuroscience
ER -
TY - JOUR
TI - Category Theory and Higher Dimensional Algebra: potential descriptive tools in neuroscience
AU - Brown, R.
AU - Porter, T.
T2 - arXiv:math/0306223
AB - We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as potential yoga for dealing with processes and processes of processes.
DA - 2008/02/10/
PY - 2008
DP - arXiv.org
LA - en
ST - Category Theory and Higher Dimensional Algebra
UR - http://arxiv.org/abs/math/0306223
Y2 - 2019/11/22/17:35:38
KW - Emergence
KW - Neuroscience
KW - Rewriting theory
KW - Sketchy
ER -
TY - CHAP
TI - Neural Algebra and Consciousness: A Theory of Structural Functionality in Neural Nets
AU - Engeler, Erwin
T2 - Algebraic Biology
A2 - Horimoto, Katsuhisa
A2 - Regensburger, Georg
A2 - Rosenkranz, Markus
A2 - Yoshida, Hiroshi
AB - Thoughts are spatio-temporal patterns of coalitions of ﬁring neurons and their interconnections. Neural algebras represent these patterns as formal algebraic objects, and a suitable composition operation reﬂects their interaction. Thus, a neural algebra is associated with any neural net. The present paper presents this formalization and develops the basic algebraic tools for formulating and solving the problem of ﬁnding the neural correlates of concepts such as reﬂection, association, coordination, etc. The main application is to the notion of consciousness, whose structural and functional basis is made explicit as the emergence of a set of solutions to a ﬁxpoint equation.
CY - Berlin, Heidelberg
DA - 2008///
PY - 2008
DP - Crossref
VL - 5147
SP - 96
EP - 109
LA - en
PB - Springer Berlin Heidelberg
SN - 978-3-540-85100-4 978-3-540-85101-1
ST - Neural Algebra and Consciousness
UR - http://link.springer.com/10.1007/978-3-540-85101-1_8
Y2 - 2019/11/22/18:24:23
KW - Emergence
KW - Neuroscience
KW - Sketchy
ER -
TY - BOOK
TI - The Topos of Music: Geometric Logic of Concepts, Theory, and Performance
AU - Mazzola, Guerino
AB - Topos of Music is an extensive and elaborate body of mathematical investigations into music and involves several and ontologically different levels of musical description. Albeit the author Guerino Mazzola lists 17 contributors and 2 collaborators, the book should be characterized as a monograph. Large portions of the content represent original research of Mazzola himself, and the material from other work is exposed from Mazzola's point of view and is well referenced. The preface preintimates an intended double meaning of the term topos in the title. On the one hand, it provides a mathematical anchor, which is programmatic for the entire approach: the concept of a cartesian closed category with a subobject classifier. (...)Zentralblatt MATH
DA - 2002///
PY - 2002
DP - www.springer.com
LA - en
PB - Birkhäuser Basel
SN - 978-3-7643-5731-3
ST - The Topos of Music
UR - https://www.springer.com/gp/book/9783764357313
Y2 - 2019/11/28/23:59:18
KW - Emergence
KW - Psychology
KW - Sketchy
ER -
TY - CONF
TI - Category Theory and Consciousness
AU - Kato, Goro C.
AU - Struppa, Daniele C.
AB - We propose a new research program which provides an approach to consciousness and the t problem ofdeep reality. Our model is based on category theory. The need to t relate l t local l behavior to global behavior has convinced us early on that a good model l for conscious entities had to be found in the notion of sheaf. With t this t i formulation, f l ti , every presheaf represents a brain (orr conscious entity). An important rtant aspect t of the theory we will develop is the notion of sheafification of a presheaf which i will ill allow us to include complementarity as part of the description of the t universe. i . OUf model is intended to describe a notion of consciousness which is i pervasive throughout the universe and not localized in individual conscious entities. i i . At the same time, we will provide a way of describing how consciousness can arise i from fr non-consciousness; it has always been a major problem to understand how it it is i possible i that the fundamental components of a brain are in fact non-conscious, i ,
DA - 2002///
PY - 2002
DO - 10/ggdf92
DP - Semantic Scholar
KW - Emergence
KW - Sketchy
ER -
TY - CONF
TI - Category theory applied to neural modeling and graphical representations
AU - Healy, M.J.
T2 - Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium
AB - Category theory can be applied to mathematically model the semantics of cognitive neural systems. Here, we employ colimits, functors and natural transformations to model the implementation of concept hierarchies in neural networks equipped with multiple sensors.
C1 - Como, Italy
C3 - Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium
DA - 2000///
PY - 2000
DO - 10/dr29pc
DP - Crossref
SP - 35
EP - 40 vol.3
LA - en
PB - IEEE
SN - 978-0-7695-0619-7
UR - http://ieeexplore.ieee.org/document/861277/
Y2 - 2019/11/22/17:36:08
KW - Emergence
KW - Neuroscience
KW - Sketchy
ER -
TY - JOUR
TI - On Emergence and Explanation
AU - Baas, Nils Andreas
AU - Emmeche, Claus
T2 - Intellectica. Revue de l'Association pour la Recherche Cognitive
AB - Emergence is a universal phenomenon that can be defined mathematically in a very general way. This is useful for the study of scientifically legitimate explanations of complex systems, here defined as hyperstructures. A requirement is that observation mechanisms are considered within the general framework. Two notions of emergence are defined, and specific examples of these are discussed.
DA - 1997///
PY - 1997
DO - 10/ggdf9z
DP - Crossref
VL - 25
IS - 2
SP - 67
EP - 83
LA - en
SN - 0769-4113
UR - https://www.persee.fr/doc/intel_0769-4113_1997_num_25_2_1558
Y2 - 2019/11/22/17:59:11
KW - Biology
KW - Emergence
ER -
TY - CHAP
TI - Tools for the Advancement of Objective Logic: Closed Categories and Toposes
AU - Lawvere, F. William
T2 - The Logical Foundations of Cognition
A2 - Macnamara, John
A2 - Reyes, Gonzalo E.
DA - 1994///
PY - 1994
DP - PhilPapers
SP - 43
EP - 56
PB - Oxford University Press USA
ST - Tools for the Advancement of Objective Logic
KW - Compendium
KW - Emergence
KW - Psychology
KW - Sketchy
ER -
TY - JOUR
TI - Structures, Learning and Ergosystems: Chapters
AU - Gromov, Misha
AB - We introduce a concept of an ergosystem which functions by building its ”internal structure“ out of the ”raw structures“ in the incoming ﬂows of signals.
DP - Zotero
SP - 159
LA - en
KW - Biology
KW - Compendium
KW - Emergence
KW - Neuroscience
KW - Sketchy
ER -