Logic Tensor Networks and Conceptual Spaces

In my last blog post, I have introduced the general idea of Logic Tensor Networks (or LTNs, for short). Today I would like to talk about how LTNs and conceptual spaces can potentially fit together and  about the concrete strands of research I plan to pursue.

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What are “Logic Tensor Networks”?

About half a year ago, I mentioned “Logic Tensor Networks” in my short summary of the Dagstuhl seminar on neural-symbolic computation. I think that this is a highly interesting approach, and as I intend to work with it in the future, I will shortly introduce this framework today.

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Workshop “Concept Learning and Reasoning in Conceptual Spaces”

A few days ago, I had the chance to attend the workshop “Concept Learning and Reasoning in Conceptual Spaces” in Bochum. Here’s a link to the workshop’s website: CLRCS 2017

It was a really great event with researchers working on conceptual spaces from a wide variety of perspectives, ranging from AI and linguistics over psychology and neuroscience to philosophy. Today, I would like to give a short summary of the workshop for those who were not able to participate but who are nevertheless interested in what kinds of topics have been discussed.

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Relations between Concepts: Subsethood and Implication

It’s nice to have a mathematical definition of concepts in a conceptual space. It’s also nice that we can create new concepts based on old ones, for instance by intersecting them. But being able to talk about the relation of two concepts is certainly also useful. Last time, we talked about the size of a concept. We can use the size of concept to figure out that the concept of “animal” is more general than the concept of “Granny Smith” – simply because it is larger.

But there are also other ways of describing the relation of two concepts. Two of them, namely subsethood and implication, will be presented in today’s blog post.

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What’s the size of a concept?

A few weeks ago, I got the notification that my paper “Measuring Relations between Concepts in Conceptual Spaces” [1] (preprint available here) was accepted at the British SGAI Conference on Artificial Intelligence.

One of the question that I discuss there is posed in the title of this blog post: What’s the size of a concept?

In general, one can say that the size of a concept in a conceptual space tells you something about its specificity: Small concepts (like Granny Smith) are more specific, whereas large concepts (like fruit) are more general.

But how exactly can we measure the size of such a concept within my proposed formalization? My paper [1] gives a mathematical response to that, and today I would like to sketch the basic idea behind it.

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