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\section*{Jocelyn Ireson-Paine}

[[!redirects Jocelyn Ireson-Paine]]

\hypertarget{contents}{}\subsubsection*{{Contents}}\label{contents}

\hypertarget{contents_2}{}\subsubsection*{{Contents}}\label{contents_2}

[[!include contents]]

I am a .  says more about this and other things I do.

But I was tempted into category theory, not least by my friends Hendrik Hilberdink, , Petros Stefaneas, and . And their supervisor, [[Joseph Goguen]].

Using experience gained from writing , I have implemented some Web-based category theory demonstrations. Their main input page is ; and there is  that I've adapted to use the same notation as the nLab  page. If I could get funding, I'd like to make these easier for novices to learn from.  offered to host them on the Oxford Computing Lab's servers: a good next step would be to tidy up and document the whole system, then make the source publicly available.

I'd also like to popularise category theory through my . That's partly because I find it intrinsically fascinating; but also because I feel it has huge potential in Artificial Intelligence and cognitive science. I've written about that . Places where I think category theory could benefit AI and cognitive science include , , and .

One benefit is the tools category theory gives us to ``achieve independence from the often overwhelmingly complex details of how things are represented or implemented''. (I quote [[Joseph Goguen]]`s .) For example, holographic reduced representations represent symbolic structured data as high-dimensional vectors, storing and extracting items via operations similar to correlation and convolution. They can use the same operations to do analogical reasoning of the kind ``What is to Sweden as Paris is to France?''. This is important because any intelligent machine needs to do such reasoning; but it's something computers are notoriously bad at. If we could characterise HRRs categorically, it might help us discover which properties of their representational substrate are essential, and which merely accidental.

Perhaps --- I don't know whether I'm joking or not --- categorical characterisations could help us understand other phenomena. Could we find a universal property that a computational system satisfies if and only if it is conscious?!

Or --- a simpler question, and one that must be sensible --- that it satisfies if and only if it can represent and reason about itself? The latter would be an interesting project in dynamical systems; but perhaps it's assuming too much to regard the reasoner as a dynamical system.

Category theory also gives us tools for unifying disparate mathematical and computational phenomena. AI and cognitive science, of course, are full of disparate mathematical and computational phenomena, usually ones whose relatedness is badly understood. That is why my n-Category Caf\'e{} posting above mentioned neural networks: in it, I cited Michael Healy's paper . He uses colimits, functors, and natural transformations to map concepts expressed as logic onto concepts represented in one kind of neural network.

As another example, I cited a paper by Goguen on analogical reasoning via ``conceptual blending'': . He uses institutions and 3/2-colimits to (for example) represent the meaning of the word ``houseboat'' as an optimal blend of the meanings of ``house'' and ``boat''. Could we apply the same constructions to HRRs? That would unify two kinds of analogical reasoning implemented on very different representational substrates.

And as yet another, I suggest at [[generalisation as an adjunction]] that generalisation can be represented as an adjunction. More precisely, that generalisation and instantiation can be represented as an adjoint pair. Perhaps this could unify lots of different topics in machine learning.

Read the following quote from `s novel . That's how I want category theory to unify cognitive science and AI:

Incidentally, category theory also inspired me to invent a way of , and of  for anyone to download into their own spreadsheets.

Note the Markdown method for block-level code (which cannot produce a blank line at the beginning or end of the block), now also at the [[Sandbox]]. ---[[Toby Bartels]]

category: people



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