Knowledge Representation in Bicategories of Relations · HackerPapers discussions

Knowledge Representation in Bicategories of Relations — mentioned by lidHanteyk

Mon, 10 Feb 2020 23:17:33 GMT

Don't worry about me specifically. https://arxiv.org/abs/1706.00526 is more food for thought, if you need it.

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Knowledge Representation in Bicategories of Relations — mentioned by lidHanteyk

Sun, 25 Aug 2019 14:04:17 GMT

Haskell is not really category-theoretic. The category Hask doesn't quite line up with real-world Haskell. The disconnection is well-understood and well-documented [0][1]. Category theory can directly give us systems from theories. See the papers behind FQL/CQL for more details, especially [2] and [3]. [0] https://wiki.haskell.org/Hask [1] http://www.cse.chalmers.se/~nad/publications/danielsson-et-a... [2] https://arxiv.org/abs/1102.1889v2 [3] https://arxiv.org/abs/1706.00526

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Knowledge Representation in Bicategories of Relations — mentioned by myWindoonn

Sun, 23 Dec 2018 15:37:59 GMT

Mathematics is metaphysics. I'd like your refutation to center on any nuance which might separate the two disciplines other than the sad fact that many philosophers don't learn much maths. Logic is metaphysics: https://philpapers.org/archive/ALVLIM-3.pdf Logic is mathematical, logic is categorical (structured in a deep way amenable to category theory), maths is categorical: http://math.ucr.edu/home/baez/rosetta.pdf https://ncatlab.org/nlab/show/internal+logic https://ncatlab.org/nlab/show/topos Ontology is categorical: https://arxiv.org/abs/1102.1889v2 https://arxiv.org/abs/1706.00526 The…

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Knowledge Representation in Bicategories of Relations — mentioned by myWindoonn

Sun, 08 Jul 2018 21:29:13 GMT

Unfortunately, Kialo does not have any features for structural reasoning, where the logical connections between arguments are completely formalized and precise. It relies on a human element to check each argument. Edit: How to do this formally? Look at formal systems for hints of how to do it in the 1900s, or category theory for how to do it in the modern day. [0][1] [0] https://arxiv.org/abs/1102.1889v2 [1] https://arxiv.org/abs/1706.00526

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Knowledge Representation in Bicategories of Relations — mentioned by DonbunEf7

Thu, 10 May 2018 13:42:45 GMT

You seem intelligent, so I'm going to drop you into the deep end. In category theory, a topos [0][1] (plural topoi) is a structure-place where logic can be done. Boolean logic corresponds to a particular topos. Actually, there are at least two topoi which do Boolean logic; one of them has the law of excluded middle, and another has the axiom of choice. [2] And there's an infinite other number of topoi to choose from! Topoi can be custom-made to categorical specifications. We can insist that there are three truth values, and then we can use a topos construction to determine what the resulting…

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Knowledge Representation in Bicategories of Relations — mentioned by mncharity

Sat, 11 Nov 2017 21:57:38 GMT

Thanks. In a similar vein, there's a recent Knowledge Representation in Bicategories of Relations https://arxiv.org/pdf/1706.00526.pdf .

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Knowledge Representation in Bicategories of Relations — mentioned by jesuslop

Sun, 11 Jun 2017 17:12:18 GMT

Recently Coecke comments on Gärdenfors geometric meaning in the context of his categorical semantics that I'm finding interesting, in arXiv:1608.01402. What I would welcome is a computational link relating that semantics and oldie semantic-network based ideas. For instance in arXiv:1706.00526 description logic based knowledge representation is cast in string diagrammatic, categorical terms, and that at least puts the meaning realm in the same mathy foot.

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