Ben,
I am following up on a recommendation you made for me to review the literature on partially ordered sets (posets). Yo made your recommendation based on an opinion expressed by a friend of yours, an expert in posets, that my work on causal sets (causets), and more in particular my term "emergent inference" for causets, was probably "exotic terminology" for something that was well-known in poset theory. Causets are a particular case of posets. Anything said about posets applies also to causets. But the converse is not true. There are things that apply to causets and not to posets, EI being one of them. In my review, I found that most literature about posets applies to continuous sets. The case of discrete sets has been only lightly considered. I was able to find only one book specific to discrete posets, which is Finite Ordered Sets, by N. Caspard, B. Leclerc, and B. Monjardet, Cambridge University Press, 2012. I have now reviewed this book. As the name indicates, this book is focused on order and maps, but it does not associate posets with algorithms and it does not consider self-organization. The closest the authors come to algorithms is an appendix on Algorithmic Complexity, but it refers to the complexity of the algorithms used to calculate properties of causets, not to algorithms considered as causets. For example, Chapter 3, on morphisms, only considers orders imposed on posets by an external algorithm. The book does contain several mathematical conclusions that apply for posets and therefore also for causets. They include theorems of decomposition, the Arrowian theorems, Moore families and Galois analysis, cluster analysis (done manually), Dilworth's and Diltworth and Sperner theorems. These theorems will, no doubt, be very useful for the development of efficient algorithms needed for applications in causet theory, but they are not themselves part of causet theory itself and are unrelated to my work. The book conveys no notion of execution, transformations of algorithms, compression, structural hierarchies, inference, causality, Information Theory, deterministic chaos in posets. These terms, which refer either to the theory or to important applications of causets, do not even appear in the index. I also reviewed Ordered Sets, by Bernd Schröder, but did not draw any additional conclusions applicable to the subject under consideration. I did not review the Handbook on Boole algebras (Elsevier), based on the view that, if self-organization existed in posets, then in would be a topic of such importance that the literature I did review would not have missed it. In fact, causets have been ignored to the point that there is not even a Wikipedia page for "causets." A search for causets yields a page almost completely dedicated to quantum gravity, and which only mentions causets on passing. The Wikipedia page on causal structure does have lots of useful information about causets, but nothing about inference or hierarchical structures or block systems or self-organization. The section for further reading has many references, but they all refer to quantum gravity. I continued my review far further than that, but at some point noticed that I was not making any progress on the subject-matter, because all my notes were about causets and not posets. I concluded that any further search would be a waste of time. I now expect your friend expert to surface and explain or retract the conclusions from his review of my work. Sergio ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
