@article{heller_homunculus_2019,
title = {Homunculus' {Brain} and {Categorical} {Logic}},
volume = {abs/1903.03424},
abstract = {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.},
journal = {ArXiv},
author = {Heller, Michael},
year = {2019},
note = {ZSCC: 0000000
arXiv: 1903.03424},
keywords = {Emergence, Sketchy}
}
@article{hur_provably_2015,
title = {A {Provably} {Correct} {Sampler} for {Probabilistic} {Programs}},
abstract = {We consider the problem of inferring the implicit distribution speciﬁed by a probabilistic program. A popular inference technique for probabilistic programs called Markov Chain Monte Carlo or MCMC sampling involves running the program repeatedly and generating sample values by perturbing values produced in “previous runs”. This simulates a Markov chain whose stationary distribution is the distribution speciﬁed by the probabilistic program.},
language = {en},
author = {Hur, Chung-Kil and Nori, Aditya V and Rajamani, Sriram K},
year = {2015},
note = {ZSCC: 0000017},
keywords = {Bayesian inference, Implementation, Probabilistic programming, Programming language theory},
pages = {21}
}
@article{ehresmann_mens_2012,
title = {{MENS}, an {Info}-{Computational} {Model} for ({Neuro}-)cognitive {Systems} {Capable} of {Creativity}},
volume = {14},
doi = {10/ggdf9t},
abstract = {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.},
journal = {Entropy},
author = {Ehresmann, Andrée C.},
year = {2012},
note = {ZSCC: 0000017},
keywords = {Emergence, Neuroscience},
pages = {1703--1716}
}
@article{philipona_is_2003,
title = {Is {There} {Something} {Out} {There}? {Inferring} {Space} from {Sensorimotor} {Dependencies}},
volume = {15},
shorttitle = {Is {There} {Something} {Out} {There}?},
doi = {10/frg7gs},
abstract = {This letter suggests that in biological organisms, the perceived structure of reality, in particular the notions of body, environment, space, object, and attribute, could be a consequence of an effort on the part of brains to account for the dependency between their inputs and their outputs in terms of a small number of parameters. To validate this idea, a procedure is demonstrated whereby the brain of a (simulated) organism with arbitrary input and output connectivity can deduce the dimensionality of the rigid group of the space underlying its input-output relationship, that is, the dimension of what the organism will call physical space.},
journal = {Neural computation},
author = {Philipona, David and O’Regan, J. and Nadal, Jean-Pierre},
month = oct,
year = {2003},
note = {ZSCC: 0000225},
keywords = {Algebra, Neuroscience},
pages = {2029--49}
}
@article{jones_probabilistic_1989,
title = {Probabilistic {Non}-determinism},
language = {en},
author = {Jones, Claire},
year = {1989},
note = {ZSCC: 0000000},
keywords = {Denotational semantics, Probabilistic programming, Programming language theory},
pages = {198}
}
@article{gromov_structures_nodate,
title = {Structures, {Learning} and {Ergosystems}: {Chapters}},
abstract = {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.},
language = {en},
author = {Gromov, Misha},
note = {ZSCC: 0000010},
keywords = {Biology, Compendium, Emergence, Neuroscience, Sketchy},
pages = {159}
}
@article{boutillier_kappa_nodate,
title = {The {Kappa} {Language} and {Kappa} {Tools}},
language = {en},
author = {Boutillier, Pierre and Feret, Jérôme and Krivine, Jean and Fontana, Walter},
note = {ZSCC: NoCitationData[s0]},
keywords = {Biology, Implementation, Systems biology},
pages = {52}
}