planning, and the structure of behavior

[ray melton]

Is anyone else here working on planning, and the structure of behavior?  As in the planning of motion, say? Generating such plans?

[Linas Vepstas]

Hi Ray,

On Thu, Feb 13, 2020 at 11:46 AM ray melton <rtme...@gmail.com> wrote:

Is anyone else here working on planning, and the structure of behavior?  As in the planning of motion, say? Generating such plans?

Not at this time, not that I know of. What do you want to do? What's wrong with stock, off-the-shelf motion planners for quadricopters or rolling bots or whatever?

I am interested in in attaching natural language to motion, i.e. to issue commands "go here, go there" or to provide directions: "go to the first light and then take a left" or to answer questions about navigation: "what's the best way to get from here to there?" -- well, I guess that sounds silly, because "siri already does it" so I'm more about "how do I talk about space and motion using natural language".  ... well, I already have some fairly fixed ideas on how to do this, just no forum in which to explore them.

If by "structure of behavior" .. hmm, yes, there are also some very interesting things about motion of football players (or motion of military troops, or protesters, or Mexican border-crossers, if we want to get Orwellian) and how those motions are strategized and planned.  Worked on that once, but there's a huge gap between what one can imagine, and existing software.

--linas

--

cassette tapes - analog TV - film cameras - you

[Raymond T. Melton]

Linas Vepstas:

Belated Thank You for the reply.

By "structure of behavior", I have in mind an application of the type of results found in a paper by Goguen, 'Realization is Universal', wherein he shows that behavior of machines is adjoint to minimal realization.  While reading "Plans and the Structure of Behavior", by Miller and others, their description of Plans versus Images seems to describe a duality.  And adjoints are sometimes as close as you can get to duals.  My question then is really, Has anyone here chased this idea down, tried to apply it to motion planning, and shown that it must be a dead end?

If not, I'm going to run with it.

Regards, Ray.

P.S. Oops, sorry for top posting.

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[Linas Vepstas]

Hi Ray,

Let me top-post a hot take. As such, it may be off-target, miss the point, and be randomly disconnected. etc. (and I sometimes manage to word things in an offensive manner, if so, apologies in advance; I mean to be direct).

Goguen, 'Realization is Universal', seems to be from 1972; I did not find a PDF, but I did get https://core.ac.uk/download/pdf/82200864.pdf Nerode - Universal Realization (1979) and This: https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/categorical-manifesto/89D0DC6DDF8A8176522AEF1450AD5E54 Goguen - A categorical Manifesto (1991)

So ... these are old, dated, maybe hopelessly dated. Not in a bad way, but in a good way, actually. Category theory was considered to be obscure through the 1980's; category theory applied to comp sci was just arcane black art. That has changed in the last 3 decades. -- We've got more than a few programming languages -- ML, CaML, Haskell, F# that are explicitly categorical, and they're not even obscure, people actually write commercial applications in them... so the world has changed.  There are at least a couple of books that teach how to program in ML/CaML by teaching category theory (I don't have titles/authors; spotted them in the university library)  I'm quite certain I saw a development of "realization is universal" in chapter 2 or 3 or 4 in one of these books.

There's even this:  http://www.tac.mta.ca/tac/reprints/articles/22/tr22.pdf (1998) and this: http://www.cs.man.ac.uk/~david/categories/book/book.pdf (no year given) and I'm fairly certain  that they recap what Goguen and Nerode were trying to say years earlier. And they probably say it more clearly. In the sciences, it pays to read the most modern stuff available.

------

Moving on to "Plans and the Structure of Behavior", by Miller, Galanter, Pribram (1960) wow .. that's ... really old. It predates the first AI summer, when "planning languages" (for motion and navigation and action) and "expert systems" and 100 other flowers blossomed. Vast quantities of stuff was discovered in the subsequent decades, uniting computation, logic, language, syntax, constraints, categories and types, and forming a bedrock of modern comp-sci.  

So sure .. at a certain abstract level, motion and behavior are structured, and can be realized via state machines or monoids or more complex algorithms .. and this is definitely fun to read about and understand ... I mean, I did, and I liked it ... but ...

.. but how useful is it? For example: a famous paper from microsoft shows that SQL and noSQL databases are category-theoretic duals to one-another. Knowing this sharply clarifies one's thinking, and also lets you sleep easy at night, as you no longer have "fear of missing out" (i.e. of using the wrong technology)

It's also folk-knowledge that functions returning error codes are category-theoretic duals to try/catch exception mechanisms. Helps with sleep at night, and also helps design high-performance code.

Garbage-collection is category-theory dual to reference counting. (Java vs. C++ smart pointers, in real life.)

Monodial actions are category-theoretic adjoints to finite state machines ... (I think this close to what "realization is universal" is about!? Not sure.)

Types, categories and languages are locked in with one another (this is one deep fundamental reason why I keep nattering on about "link grammar")

I do NOT know of any dualities involving motion-planning; surely some of these must be known; I'd love to actually hear about them.  Searching for them in the 1960's and 1970's is the wrong place to look, though. Look into the last 10-20 years, instead.

The exciting place to hunt for dualities is in neural-nets vs. sheaves, which is where I'm looking.

So I dunno. Do plow into the two PDF's I gave above... they give a foundational cornerstone. Then, whether there are category-theoretic duels involving motion planning... let me know if you find any.

-- Linas

p.s. totally off-topic, but I recently found this to be kick-butt:  "Forced moves or good tricks in design space?  Landmarks in the  evolution of neural mechanisms for action selection", Tony J. Prescott    (2007)  https://www.academia.edu/30717257/Forced_Moves_or_Good_Tricks_in_Design_Space_Landmarks_in_the_Evolution_of_Neural_Mechanisms_for_Action_Selection

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