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Session Spencer Breiner
Duration 1 hour
Date/Time 18 March 2020 16:00 GMT
9:00am PDT/12:00pm EDT
4:00pm GMT/5:00pm CET
Convener KenBaclawski
Track How


Knowledge graphs, closely related to ontologies and semantic networks, have emerged in the last few years to be an important semantic technology and research area. As structured representations of semantic knowledge that are stored in a graph, KGs are lightweight versions of semantic networks that scale to massive datasets such as the entire World Wide Web. Industry has devoted a great deal of effort to the development of knowledge graphs, and they are now critical to the functions of intelligent virtual assistants such as Siri and Alexa. Some of the research communities where KGs are relevant are Ontologies, Big Data, Linked Data, Open Knowledge Network, Artificial Intelligence, Deep Learning, and many others.     (2A)

Agenda     (2B)

Abstract: This talk will present a very simple example of knowledge representation involving open-shop scheduling, a standard problem in operations research. Based on this example, I will argue that graphs alone are not sufficiently expressive to describe even simple and intuitive conceptual relationships, and explain how the language of category theory can be used to enrich graphical representations.     (2B2)

Bio: Dr. Spencer Breiner is a mathematician at the US National Institute for Standards and Technology, working in the Software & Systems Division of the Information Technology Lab. His research focuses on applications of category theory to problems in systems modeling and interoperability. Dr. Breiner received his Ph.D. from Carnegie Mellon University in 2013 before joining NIST in 2015 under the National Research Council's Postdoctoral Research Apprenticeship Program.     (2B3)

Conference Call Information     (2C)

Attendees     (2D)

Discussion     (2E)

Main Thread     (2E1)

[12:02] RaviSharma: hello Spencer Welcome     (2E1A)

[12:02] Spencer Breiner: Hi!     (2E1B)

[12:03] RaviSharma: it would be nice to simplify for someone like me who is supposedly a theoretical physicist.     (2E1C)

[12:05] David Eddy: "integration" is WRONG word... INTEROPERABLE is the only realistic choice going forward     (2E1D)

[12:11] John Sowa: Some of us know category theory. I studied it years ago.     (2E1E)

[12:12] John Sowa: I wouldn't dream of giving a lecture on the topic to this audience.     (2E1F)

[12:13] RaviSharma: Spencer - what are 2356 and 8 in slide 4 called?     (2E1G)

[12:13] Ram D> Sriram: @John: Spencer talked about CT to this group sometime ago     (2E1H)

[12:14] David Eddy: @JohnS... simmer down... it's a window into what academia is NOT teaching     (2E1I)

[12:17] David Eddy: @JohnS... they teach fancy math because it's easy <sigh>     (2E1J)

[12:17] RaviSharma: Spencer - what is E⇒N called?     (2E1K)

[12:24] John Sowa: Category theory is used to justify the DOL standard by the OMG.     (2E1L)

[12:25] John Sowa: DOL is used to determine the mappings among the many logics of the Semantic Web, Common Logic, and related theories.     (2E1M)

[12:25] John Sowa: That is a very important result.     (2E1N)

[12:26] David Eddy: DOL = ?     (2E1O)

[12:26] John Sowa: It explains what mappings and operation are possible.     (2E1P)

[12:26] John Sowa: Even more important, it is the basis for the HeTS tools, which do the mapping among the many versions of logic.     (2E1Q)

[12:27] John Sowa: But the OMG standard does not discuss category theory. It just points to the documents.     (2E1R)

[12:28] John Sowa: The OMG standard states the results in ordinary language that typical readers understand.     (2E1S)

[12:29] John Sowa: Basic point: Category theory is important for doing the foundational work.     (2E1T)

[12:30] John Sowa: But the people who work above the foundations will never see what went into the construction.     (2E1U)

[12:31] Ram D> Sriram: @John: We hope to address your points in future     (2E1V)

[12:36] John Sowa: That is the Distributed Ontology, Modeling, and Specification Language     (2E1X)

[12:36] RaviSharma: Spencer - R0 implies one machine in slide 11 or What?     (2E1Y)

[12:36] David Eddy: @JFS - thx     (2E1Z)

[12:39] RaviSharma: Spencer - thus there can not be any probabilistic function?     (2E1AA)

[12:39] RaviSharma: what is Bayes then?     (2E1AB)

[12:44] RaviSharma: Spencer - Does R0 mean library of zero type?     (2E1AC)

[12:44] Mike Bennett: I feel as if I have wandered into the back of the wrong classroom.     (2E1AD)

[12:44] John Sowa: See page 143 of the DOL standard for a diagram of the mappings between the various SW logics and Common Logic     (2E1AE)

[12:45] John Sowa: That's page 155 of 209.     (2E1AF)

[12:46] John Sowa: Till Mossakowski and colleagues did the specifications for DOL.     (2E1AG)

[12:47] John Sowa: They also developed free and open-source software to do the mappings.     (2E1AH)

[12:48] John Sowa: The software is called HeTS (Heterogeneous Tool Set) -- which can do reasoning with any of the logics and mappings among them.     (2E1AI)

[12:51] John Sowa: If you browse through the DOL standard, you can see some category theory diagrams with push outs and pull backs.     (2E1AJ)

[12:51] janet singer: @Mike: Good to have all of this collected in one presentation (Were on shelter-in-place orders here, so will have plenty of time to rerun the lecture)     (2E1AK)

[12:53] TerryLongstreth: I have to leave. I agree with John that the DOL spec is easier to understand, but it's comforting to have some of the underlying theory explained.     (2E1AL)

[12:53] RaviSharma: Spencer - what is advantage in relation to Knowledge graphs or just graphs of Categories vs Sets?     (2E1AM)

[13:09] RaviSharma: Spencer - thanks for your clarifications, i am yet to go through your slides and email you a non-practitioner's set of Qs.     (2E1AN)

[13:09] janet singer: Taking off on what John and Terry said: To what extent is it just good to know this is available in the foundations but its not relevant to others? Or how can it be made more accessible, and who should it be made more accessible to?     (2E1AO)

[13:12] Eswaran Subrahmanian: There is a NIST workshop report on applied category theory. If you are interested we can send the link. It provides an overview what is needed to advance field. This is the link:     (2E1AP)

[13:14] RaviSharma: Spencer - what would be nice to see a process flow chart of all elements required before we see a knowledge graph constructed, in particular what is the result of machine-job type in your example as a knowledge graph?     (2E1AQ)

[13:15] Eswaran Subrahmanian: There is a categorical database in the data migration and Integration space. This was initially funded by NIST SBIR.     (2E1AR)

[13:17] janet singer: Spencer says CT is all about form, not content, so it will not solve problems for you: CT is arguably best for helping humans deal with complexity     (2E1AS)

[13:19] Spencer Breiner: I'll reply to the chat comments below, in the order they were asked.     (2E1AT)

[13:20] Spencer Breiner: @David Eddy: I disagree. I really am interested in putting different collections of information together and combining them in new ways. To me, this goes over and above interoperability (though it is required)     (2E1AU)

[13:20] Spencer Breiner: Note that I am not advocating integration at the physical level.     (2E1AV)

[13:21] Spencer Breiner: @RaviSharma: On slide 4 I only gave images for some of the inputs (red and green arrows) b/c all 8 was too cluttered.     (2E1AW)

[13:23] Spencer Breiner: @RaviSharma: The pair of maps <s:E→N,t:E→N> is called a schema (curly G)     (2E1AX)

[13:25] Spencer Breiner: @John Sowa: As I mentioned in the question section, the DOL/HeTS work is at a higher meta-level than what I presented today. Here I use CT to map between different theories in a single logic; there they use CT to map between different logics.     (2E1AY)

[13:27] Spencer Breiner: Personally, I am not a big fan of institutions because in most cases I know the semantics is subordinate to the syntax. This can be handled more easily using functorial semantics.     (2E1AZ)

[13:27] Spencer Breiner: @David Eddy: DOL = Distributed Ontology Language     (2E1AAA)

[13:28] Spencer Breiner: @RaviSharma: R^0={*} is the zero-dimensional vector space (just an origin)     (2E1AAB)

[13:34] Spencer Breiner: @RaviSharma: As I mentioned in the question period, there are more complicated approaches to introducing probabilistic mappings. The most common is to use the Kleisli category of the distribution monad. See, e.g.,     (2E1AAC)

[13:38] Spencer Breiner: @RaviSharma: As mentioned during the question section, CT and Set theory are not at odds; one big chunk of CT (sheaves & presheaves) is about using CT to more easily manage complicated assemblies of sets and functions. As for the advantage of CT over ST, I would point to a higher-level, more abstract perspective that often generalizes the set theoretic version without much extra work (but applies more broadly).     (2E1AAD)

[13:44] Spencer Breiner: @janet singer: To paraphrase my answer in the questions section, I think it is important for system designers/architects because it provides robust design patterns for many situations with well-understood relationships & interactions. Less important for users. This echoes John S's points regarding DOL/HeTS. I do think it is important that users have access to categorical structures (like functors between path graphs rather than graph homomorphism) because they provide added flexibility at little cost, but they don't need to think of them in those terms, and they are likely to be more useful if they are wrapped in domain-specific terminology & assumptions.     (2E1AAE)

Category Theory and Limericks     (2E2)

[12:51] John Sowa: I once won first place in a limerick contest about such topics. Prize: 5 marks and a bottle of wine.     (2E2A)

[12:52] David Eddy: @JFS... German Mark currency? German limericks?     (2E2B)

[12:55] John Sowa: My poem was published in the Bulletin of the EATCS -- European Association for Theoretical Computer Science.     (2E2C)

[12:55] John Sowa: That makes me a published poet who actually earned some money -- more than most poets can say.     (2E2D)

[12:56] Mike Bennett: @John can you post the limerick here?     (2E2E)

[12:56] David Eddy: @MikeB... likely not fit for public consumption     (2E2F)

[12:56] John Sowa: There was a young lady from Grambling, Who programmed graph grammars while gambling.     (2E2G)

[12:57] David Eddy: ... there was a Lady from Crew... YOU finish it.     (2E2H)

[12:57] John Sowa: Her pull backs, they said, were something to dread. But her push outs were simply outstanding.     (2E2I)

[12:57] Gary Berg-Cross: When there are physical meetings again Mike Bennett may buy John a glass of wine for any poetry posting.     (2E2J)

[12:57] Mike Bennett: Applause!     (2E2K)

[12:58] Mike Bennett: Will do!     (2E2L)

[12:58] David Eddy: @JFS... and when did you write that?     (2E2M)

[12:58] David Eddy: now write me a database/storage/access mechanism that can instantly retrieve that limerick from decades earlier?     (2E2N)

[12:58] janet singer: Ok, lets elevate the tone     (2E2O)

[13:00] David Eddy: <redacted>     (2E2P)

[13:05] John Sowa: That was at a conference in Germany in 1978. Michael Arbib was the organizer who proposed the contest and awarded the prize.     (2E2Q)

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