Results 1 to 10 of about 673 (251)
A category theory perspective on the Language of Thought: LoT is universal [PDF]
Frontiers in PsychologyThe Language of Thought (LoT) hypothesis proposes that some collections of mental states and processes are symbol systems to explain language-like systematic properties of thought.
Steven Phillips
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Brain's geometries for movements and beauty judgments. A contribution of topos geometries [PDF]
Frontiers in PsychologyWe present a theory on the neural basis of aesthetic experience, and judgment of beauty. It is based on both empirical facts concerning brain mechanisms and theoretical mathematical theories.
Daniel Bennequin, Alain Berthoz
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Shared Protentions in Multi-Agent Active Inference [PDF]
EntropyIn this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals.
Mahault Albarracin +5 more
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First steps in synthetic guarded domain theory: step-indexing in the topos of trees [PDF]
Logical Methods in Computer Science, 2012 We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms,
Lars Birkedal +3 more
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The Sierpinski Object in the Scott Realizability Topos [PDF]
Logical Methods in Computer Science, 2020 We study the Sierpinski object $\Sigma$ in the realizability topos based on Scott's graph model of the $\lambda$-calculus. Our starting observation is that the object of realizers in this topos is the exponential $\Sigma ^N$, where $N$ is the natural ...
Tom de Jong, Jaap van Oosten
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Gelfand spectra in Grothendieck toposes using geometric mathematics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A) of sheaves on a locale and a commutative C*-algebra, a, within that topos.
Bas Spitters +2 more
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Point-free Construction of Real Exponentiation [PDF]
Logical Methods in Computer Science, 2022 We define a point-free construction of real exponentiation and logarithms, i.e.\ we construct the maps $\exp\colon (0, \infty)\times \mathbb{R} \rightarrow \!(0,\infty),\, (x, \zeta) \mapsto x^\zeta$ and $\log\colon (1,\infty)\times (0, \infty ...
Ming Ng, Steven Vickers
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On the Nielsen-Schreier Theorem in Homotopy Type Theory [PDF]
Logical Methods in Computer Science, 2022 We give a formulation of the Nielsen-Schreier theorem (subgroups of free groups are free) in homotopy type theory using the presentation of groups as pointed connected 1-truncated types.
Andrew W Swan
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On the Structure of Abstract H*-Algebras [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 Previously we have shown that the topos approach to quantum theory of Doering and Isham can be generalised to a class of categories typically studied within the monoidal approach to quantum theory of Abramsky and Coecke.
Kevin Dunne
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Mathematics, 2021 The purpose of this paper is to promote new methods in mathematical modeling inspired by neuroscience—that is consciousness and subconsciousness—with an eye toward artificial intelligence as parts of the global brain.
Ileana Ruxandra Badea +3 more
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