---------- Forwarded message ---------- Date: Thu, 26 Jun 1997 13:57:18 +0300 (IDT) From: ZIPPIE Gonczarowski <zippie@actcom.co.il> To: cat-dist@mta.ca Dear Colleagues, I am applying tools of category theory to research in artificial perception and cognition. A basic category is proposed where every perception is an object and morphisms capture the flow between perceptions. Natural transformations capture paths to more cognitive perceptions. An Anonymous referee remarked that my category is `very closely related to comma categories'. Can anybody refer me to written material that introduces comma categories? Also, please let me know if you are aware of other research that applies categorical tools to research in artificial perception and cognition. Thanks Zippie e-mail zippie@actcom.co.il Dr. Zippora Arzi-Gonczarowski Typographics, Ltd. 46 Hehalutz St. Jerusalem 96222, Israel
This is not an answer to your question. But your posting prompts me to ask a question in the semantics underlying applications of cateogories. What is the underlying metaphysics of perception (event, processes, relations ?). How do you capture 'time'. It seems to me the dynamism is in the arrows -- and there perhaps is where time comes in. It has always seemed to me that the applications of Cat. The. (for example in the study of Dynamical Systems) has served as a language to talk about mathematical, computatianal and procedural complexities ONCE THESE ARE ALREADY IN PALCE. Cat. is not to replace them as an alternative. Dr. Farogh Dovlatshahi
Dear Colleagues,
I am applying tools of category theory to research in artificial perception and cognition. A basic category is proposed where every perception is an object and morphisms capture the flow between perceptions. Natural transformations capture paths to more cognitive perceptions. An Anonymous referee remarked that my category is `very closely related to comma categories'.
Can anybody refer me to written material that introduces comma categories? Also, please let me know if you are aware of other research that applies categorical tools to research in artificial perception and cognition.
Thanks
Zippie
e-mail zippie@actcom.co.il
Dr. Zippora Arzi-Gonczarowski Typographics, Ltd. 46 Hehalutz St. Jerusalem 96222, Israel
Not that I am blowing my own horn (but why not), you will find something about comma categories in Barr & Wells, Category Theory for Computing Science. But no, I know of no other research along those lines. Michael Barr
Since there have been some replies to the query about artificial perception, I suppose it's OK to mention my own work in progress. I have been doing research in the formal semantics of neural networks. I am working on a mathematical model in which concepts (formulas) are formed in memory as colimits. The diagrams involve neural structures representing other concepts, going all the way back to simple percepts. A concept is stored in memory as a neuron or neuron pool together with its attendant synaptic connections. Logically closed portions of memory are theories. Functors and natural transformations enter in in the usual fashion of categorical model theory. There is still a lot of work to do on this, and I am still learning the mathematics. I do have a proposed neural implementation of it, and am working on a paper. Previous work along these lines has involved geometric logic, so that I could understand some of the basics of learning, which for me involves working with an observational logic. I have a paper on this, too. Finding reviewers for this kind of material in the neural network community has been difficult. If any of this sounds interesting enough to discuss, I certainly wouldn't mind getting some feedback from category theorists. Sincerely, Mike Healy -- =========================================================================== e Michael J. Healy A FA ----------> GA (425)865-3123 | | FAX(425)865-2964 | | Ff | | Gf c/o The Boeing Company | | PO Box 3707 MS 7L-66 \|/ \|/ Seattle, WA 98124-2207 ' ' USA FB ----------> GB e "I'm a natural man." michael.j.healy@boeing.com B -or- mjhealy@u.washington.edu ============================================================================
participants (4)
-
categories -
Dr. Farogh Dovlatshahi -
Michael Barr -
Michael J. Healy 206-865-3123