## May 6, 2018

### Compositionality

#### Posted by John Baez

A new journal! We’ve been working on it for a long time, but we finished sorting out some details at Applied Category Theory 2018, and now we’re ready to tell the world!

Here’s the official announcement:

We are pleased to announce the launch of Compositionality, a new diamond open-access journal for research using compositional ideas, most notably of a category-theoretic origin, in any discipline. Topics may concern foundational structures, an organizing principle, or a powerful tool. Example areas include but are not limited to: computation, logic, physics, chemistry, engineering, linguistics, and cognition. To learn more about the scope and editorial policies of the journal, please visit our website at www.compositionality-journal.org/

Compositionality is the culmination of a long-running discussion by many members of the extended category theory community, and the editorial policies, look, and mission of the journal have yet to be finalized. We would love to get your feedback about our ideas on the forum we have established for this purpose:

http://reddit.com/r/compositionality

Lastly, the journal is currently receiving applications to serve on the editorial board; submissions are due May 31 and will be evaluated by the members of our steering board: John Baez, Bob Coecke, Kathryn Hess, Steve Lack, and Valeria de Paiva.

https://tinyurl.com/call-for-editors

We will announce a call for submissions in mid-June.

We’re looking forward to your ideas and submissions!

Best regards,

Brendan Fong, Nina Otter, and Joshua Tan

http://www.compositionality-journal.org/

Posted at May 6, 2018 5:11 PM UTC

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### Re: Compositionality

Gold open access is where authors pay to publish in a journal and their article is then free for others to read. The journal is usually peer-reviewed.

Green open access is where authors put their work in a repository that’s free for others to read — like the arXiv, or PubMed. This is often done in addition to publishing the paper in a journal, since these repositories are typically not peer-reviewed.

Diamond open access is where authors publish in a peer-reviewed journal that’s free for others to read, and the authors don’t have to pay to do this.

Posted by: John Baez on May 6, 2018 5:56 PM | Permalink | Reply to this

### Re: Compositionality

Please excuse, in the face of your enthusiasm, a piece of overfastidious carping :). I do not like the word compositionality and I can only excuse it for its self-referential quality: con-pos-ition-al-itas. We have compose (componere) from the prefix con (= together, in one place) and ponere (= place). We abstract to a verb-noun composition , and thence to an adjective compositional , and back again to a noun compositionality . What a merry-go-round! Why not throw out all the suffixes, windy adornments that pretend to learning, and stick to the root meaning, Compose ? Or, if you want to Greek it, Synthesis ? Or has that title already been reserved by others?

Posted by: Gavin Wraith on May 7, 2018 10:31 AM | Permalink | Reply to this

### Re: Compositionality

“Compositionality” means something different than “compose”. It means “the ability to determine properties of the whole from properties of the parts together with the way in which the parts are put together.” And it’s a common buzzword in engineering and computer science, these days.

From Wikipedia’s Principle of Compositionality:

In mathematics, semantics, and philosophy of language, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This principle is also called Frege’s principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the idea appears already among Indian philosophers of grammar such as Yāska, and also in Plato’s work such as in Theaetetus${}^{[citation \; needed]}$. Besides, the principle was never explicitly stated by Frege${}^{[1]}$ and it was arguably already assumed by George Boole${}^{[2]}$ decades before Frege’s work.

This concerns compositionality of meaning of an expression, but in engineering or computer science, compositionality now often refers to the behavior of a system. One wants to be able to easily analyze the behavior of the whole in terms of the behaviors of its parts.

So, the word should bring to mind algebras of operads, or functors between categories (as in “functorial semantics”).

“Compositionality” was not my first choice of title, but it’s what most the editors wanted. I wanted “Applied Category Theory”, but that has its own problems.

Luckily, I’m more interested in the journal than its title.

Posted by: John Baez on May 7, 2018 1:50 PM | Permalink | Reply to this

### Re: Compositionality

I rather wish you had named the journal “Applied Category Theory”, since the principle of compositionality (using the standard definition you provided above), although it may be natural to those working in computation, AI, engineering or computer science, seems to me not to fit well with the general principles of category theory. I’m a linguist, not a mathematician, but I previously posted a comment here (12 Feb. 2018) on the possible applications of category theory in descriptive (not formal) linguistic semantics and the problem of understanding the phenomenon of meaning as expressed in natural language systems. In my view, the fundamental syntactic relation is not the combination of previously existing semantic atoms (“meanings of constituent expressions”) into whole constructions by rules used to combine them, but the differentiation of a relatively undifferentiated whole, having the logical structure of a category, into a differentiated structure (schema), according to a principle of differentiation (a “one into two” operation). I call this process, common, I would claim, to the elaboration of all categorical structures in natural languages, “open-ended internal differentiation with unification”. (I think it would be consistent with Chomsky’s original phrase structure grammar conception, but not, it seems, with the current minimalist approach.) In short, I don’t think that the principle of compositionality reflects the way the phenomenon of meaning as expressed in natural languages actually works, but I do think that category theory, as far as I understand it, has a lot to offer for those who want to understand how meaning in natural languages actually does work. I hope to have a paper elaborating these ideas soon. (If anybody finds these ideas misguided or puzzling, please let me know.) The “application” in this case would be to the theoretical understanding of a natural phenomenon, within pure inquiry, rather than to the solution of practical problems, in “applied science” or technology; maybe you’re thinking of the latter, but You included “linguistics” in your areas of application, so I hope I’m not totally off base here. (BTW, the compositionality principle doesn’t seem to figure prominently in Frege, and seems to conflict with his “Priority Principle” of the logical priority of the sentence over the parts in the determination of meanings.)

Posted by: James Dennis on May 11, 2018 2:37 AM | Permalink | Reply to this

### Re: Compositionality

I think the journal wants to stay rather open-minded about the different formulations of compositionality in different fields.

In category theory, compositionality is captured by:

1. Functors, since functors preserve composition: $F(f \circ g) = F(f) \circ F(g)$

2. Monoidal functors, since monoidal functors also preserve tensor products: $F(f \otimes g) \cong F(f) \otimes F(g)$

3. Operad algebras, since these preserve operadic composition: $F(f \circ (g_1, \dots, g_k)) = F(f) \circ (F(g_1), \dots , F(g_k))$

and so on. All these are ways of saying the behavior of a big thing can be computed in a systematic way from the behavior of its parts, given how the parts are stuck together.

So, I would definitely say that some principles of compositionality fits well with the general principles of category theory. But I see no reason why all versions of compositionality have to be captured by simple schemas like 1-3.

Posted by: John Baez on May 14, 2018 7:14 PM | Permalink | Reply to this

### Re: Compositionality

$H(\mathbf{p} \circ (\mathbf{q}_1, \ldots, \mathbf{q}_n)) = H(\mathbf{p}) + \sum_i p_i H(\mathbf{q}_i)$

satisfied by entropy? People who use the word “compositionality” would include that as an instance, I assume…?

Posted by: Tom Leinster on May 15, 2018 12:10 AM | Permalink | Reply to this

### Re: Compositionality

My objections to the word compositionality are purely aesthetic. Neonymy, the invention of new words, is an important issue in mathematics and the sciences. Samuel Eilenberg expressed concerns about it. The trouble is that once a word has gained currency the community is stuck with it. So there is usually only a narrow window of opportunity to invent a new word that is apt, free of unwanted associations, grammatically flexible and open to further extension. So much of mathematical terminology is laden with overloaded classicism or opaque whimsy. The name of a topic is far less important than its content, but I still think it is worth some thought.

Posted by: Gavin Wraith on May 12, 2018 10:57 AM | Permalink | Reply to this

### Re: Compositionality

While bikeshedding about the title may be fun, it would probably be more useful and interesting to talk about other features of the new journal. I’m excited at the prospect of a new “selective” category theory journal, and at the openness of the editors to experiment with new ideas and possibilities. But one thing I’d be interested in hearing more folks’ opinions on is the idea of authors knowing the identity of referees, as discussed on reddit.

I’m certainly glad that this will be dual-consent (authors and referees both have to agree to it before identities will be shared), which reduces or eliminates a lot of the potential problems. But I’m still worried that there are other downsides that won’t be apparent to people when they make their choices, or will affect people other than those who are making the choices. It usually seems better to give people choices, but there are some contexts in which it’s actually better to not give people a choice — for instance, there’s an argument that it should be mandatory to postpone tenure clocks for pre-tenure faculty who have children, because otherwise some faculty who would prefer to postpone their clock will feel pressure not to do so. And I’m not convinced that there are significant advantages to be gained from onymous refereeing. However, I’m open to being convinced! What do others think?

Posted by: Mike Shulman on May 15, 2018 4:33 AM | Permalink | Reply to this

### Re: Compositionality

And I’m not convinced that there are significant advantages to be gained from onymous refereeing. However, I’m open to being convinced! What do others think?

I’ve often thought it would be very beneficial for the reviewer and author to engage in discussion. Even public discussion as far as possible (at least, say, making parts of the discussion public if the paper is accepted), so that anyone can benefit from the insights gained.

This is no doubt far too idealistic to be able to applied in practise, but I think in principle it would be a good process for helping the dissemination of mathematical ideas.

Posted by: Richard Williamson on May 15, 2018 9:17 AM | Permalink | Reply to this

### Re: Compositionality

I agree! In fact, in my experience, the refereeing process often approximates a discussion: the referee points out a problem or makes a suggestion, the author fixes it and/or makes a reply, and iterate a few times. Current journal design means that this way of having a discussion places a high burden on the editor as middleman, but with modern technology there’s no reason that has to be the case. Nor do I see any reason that a discussion between author and referee would have to identify the referee by name.

Posted by: Mike Shulman on May 15, 2018 5:23 PM | Permalink | Reply to this

### Re: Compositionality

Nor do I see any reason that a discussion between author and referee would have to identify the referee by name.

True! For some reason I was thinking that the referee would be identifiable, but I agree that indeed this need not be the case.

Posted by: Richard Williamson on May 16, 2018 7:25 PM | Permalink | Reply to this

### Re: Compositionality

Mike wrote:

But one thing I’d be interested in hearing more folks’ opinions on is the idea of authors knowing the identity of referees, as discussed on reddit.

People like to argue about this—and not just in this particular reddit thread; in general. Some people think it will be great; others think it will be terrible; others think it will be something in between. In general people’s opinions on this issue seem highly correlated to how much they like, or hate, the existing system.

The arguments tends to be highly theoretical, since don’t have enough data on what actually happens in such an alternative system. Obviously the details matter, but it’s not obvious how they matter.

Given this, it seems worthwhile to let people experiment with alternative refereeing systems on a dual-consent basis… just to find out what actually happens.

I guess the upshot of this remark is that if we do such an experiment, we should ask participants to report their experiences, so we learn something.

Posted by: John Baez on May 15, 2018 10:57 PM | Permalink | Reply to this

### Re: Compositionality

The arguments tends to be highly theoretical, since don’t have enough data on what actually happens in such an alternative system. Obviously the details matter, but it’s not obvious how they matter.

Given this, it seems worthwhile to let people experiment with alternative refereeing systems on a dual-consent basis… just to find out what actually happens.

I guess the upshot of this remark is that if we do such an experiment, we should ask participants to report their experiences, so we learn something.

The journal PeerJ has been using a dual-consent open refereeing system for a few years now, and a couple of people I know who publish there feel it has worked very well for them. Here is a blog post by the journal on how it was going, by 2014, here is a discussion of and a link to an example. Here is another example. No doubt there’s some selection bias here, with me spending not too long Googling for results, but it’s better to actually see the examples rather than talk about it.

Posted by: David Roberts on May 16, 2018 8:21 AM | Permalink | Reply to this

### Re: Compositionality

Well, I’m sorry for bringing it up again, then. I haven’t been a party to such an argument before, so I’m not familiar with the points that tend to be made. Have any such arguments been had in a public forum that you can post a link to? I’m particularly interested in hearing what advantages people think there will be to onymous refereeing, since I haven’t been able to think of many.

Posted by: Mike Shulman on May 16, 2018 5:27 AM | Permalink | Reply to this

### Re: Compositionality

Mike wrote:

Well, I’m sorry for bringing it up again, then.

No problem. It’s certainly more interesting than arguing about the title of the journal, especially since that’s already decided and I can’t do anything about it!

Have any such arguments been had in a public forum that you can post a link to?

I’m having a bit of trouble finding everything I’ve seen, but here are two:

The latter is an editorial in favor of anonymous refereeing, written by an anonymous author. It mentions that the British Medical Journal has abolished referee anonymity.

Posted by: John Baez on May 16, 2018 5:46 AM | Permalink | Reply to this

### Re: Compositionality

Thanks for the links; I’ll have a look.

we should ask participants to report their experiences, so we learn something.

Yes. Although there are so many indirect effects of a choice like this that it’ll be hard to learn everything that’s relevant, and merely surveying authors and referees as they go through the process could create a false sense of having found all the answers. How does it affect participants’ career trajectories 20 years in the future? How does it affect the ability of editors to find good referees, and the pool of authors submitting to the journal? How does it affect the lives of people who may read a paper and its open reviews but who never submit to or referee for the journal themselves? Etc.

Posted by: Mike Shulman on May 16, 2018 7:17 AM | Permalink | Reply to this

### Re: Compositionality

I had a look at your two links. The first one seems to be mainly about computer science, with its universally-acknowledged-to-be-messed-up system of “conference publication”. In his footnote 2 link the author explicitly mentions that

The situation may be different in other fields… In mathematics they can say “your proof is wrong”.

As you mentioned, the second one seems to be mainly addressing mandatory openness, although some of the problems it brings up are relevant to the voluntary case too. It does also mention the results of one previous experiment in voluntary openness:

Peter Strick, editor-in-chief of the Journal of Neurophysiology, notes that when the journal tried encouraging voluntary open review a decade ago, the editors quickly realized that this system promoted more problems than it solved, including bland and cautious reviews. The journal also experienced an occasional breakdown of the peer-review process, in which authors and referees bypassed the editors completely in negotiating how a paper should be revised.

If you or anyone can find a public argument in favor of voluntary open reviewing in mathematics, I’d be especially interested.

Posted by: Mike Shulman on May 16, 2018 8:12 AM | Permalink | Reply to this

### Re: Compositionality

I also have a comment/question about the term “applied category theory”. While I’m excited about and fully supportive of all the folks that are applying category theory to the “real world”, there’s another distinction that seems to be lost by this terminology. The reddit thread on why are we starting a new journal? mentions that existing journals like TAC

publish mainly pure category theory papers (i.e. applications to fields within mathematics).

However, to me “pure category theory” has always meant category theory without applications even to other fields within mathematics. Some of us like to describe category theory as “the mathematics of mathematics”, i.e. the study of patterns abstracted from mathematics in the same way that other parts of mathematics study patterns abstracted from the real world. According to this analogy, “pure category theory” would be the study of these patterns in isolation, while “applied category theory” would be the application of categorical ideas to the original source of the abstraction, i.e. to other fields of mathematics.

I’m not going to quarrel with the use of “applied category theory” to refer to applications outside of mathematics; that’s certainly a more comprehensible meaning for people not familiar with the “mathematics of mathematics” quip. However, can we find another pair of words to distinguish “category theory for its own sake” from “category theory with applications within mathematics”, both of which are “pure” as compared to this meaning of “applied category theory”?

Posted by: Mike Shulman on May 15, 2018 4:41 AM | Permalink | Reply to this

### Re: Compositionality

“applied category theory” would be the application of categorical ideas … to other fields of mathematics.

In particular, this is how I’ve always understood the journal titles “Theory and Applications of Categories” and “Applied Categorical Structures”. For instance, the policy page of TAC says

The scope of the journal includes: all areas of pure category theory, including higher dimensional categories; applications of category theory to algebra, geometry and topology and other areas of mathematics; applications of category theory to computer science, physics and other mathematical sciences; contributions to scientific knowledge that make use of categorical methods. [emphasis added]

while the subtitle of Applied categorical structures is

A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science

Posted by: Mike Shulman on May 15, 2018 5:05 AM | Permalink | Reply to this

### Re: Compositionality

Category theorists love terminology, and discussions about terminology. I don’t know snappy terms to make the distinction you’re pointing out, but people sometimes distinguish “applications within mathematics” and “applications outside mathematics”.

We could talk about “internally” and “externally” applied category theory… though I don’t think this is snappy enough to catch on. Then we could have “external applications of internal categories”, etc.

Posted by: John Baez on May 15, 2018 11:02 PM | Permalink | Reply to this

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