smryan@garth.UUCP (Steven Ryan) (09/26/88)
---- Forwarded Message Follows ---- Return-path: <@AI.AI.MIT.EDU:ailist-request@AI.AI.MIT.EDU> Received: from AI.AI.MIT.EDU by ZERMATT.LCS.MIT.EDU via CHAOS with SMTP id 195108; 19 Sep 88 03:49:35 EDT Received: from BLOOM-BEACON.MIT.EDU (TCP 2224000021) by AI.AI.MIT.EDU 19 Sep 88 03:55:37 EDT Received: by BLOOM-BEACON.MIT.EDU with sendmail-5.59/4.7 id <AA07167@BLOOM-BEACON.MIT.EDU>; Mon, 19 Sep 88 03:44:20 EDT Received: from USENET by bloom-beacon.mit.edu with netnews for ailist@ai.ai.mit.edu (ailist@ai.ai.mit.edu) (contact usenet@bloom-beacon.mit.edu if you have questions) Date: 19 Sep 88 01:18:29 GMT From: garth!smryan@unix.sri.com (Steven Ryan) Organization: INTERGRAPH (APD) -- Palo Alto, CA Subject: Re: state and change/continuous actions Message-Id: <1432@garth.UUCP> References: <18249@uflorida.cis.ufl.EDU> Sender: ailist-request@ai.ai.mit.edu To: ailist@ai.ai.mit.edu >Foundations of Artificial Intelligence," I find it interesting to >compare and contrast the concepts described in Chapter 11 - "State >and Change" with state/change concepts defined within systems >theory and simulation modeling. The authors make the following statement: >"Insufficient attention has been paid to the problem of continuous >actions." Now, a question that immediately comes to mind is "What problem?" Presumably, they are referring to that formal systems are strictly discrete and finite. This has to do to with `effective computation.' Discrete systems can be explained in such simple terms that is always clear exactly what is being done. Continuous systems are computably using calculus, but is this `effective computation?' Calculus uses a number of existent theorems which prove some point or set exists, but provide no method to effectively compute the value. Or is knowing the value exists sufficient because, after all, we can map the real line into a bounded interval which can be traversed in finite time? It is not clear that all natural phenomon can be modelled on the discrete and finite digital computer. If not, what computer could we use? >Any thoughts?
steve@hubcap.UUCP ("Steve" Stevenson) (09/26/88)
From a previous article, by smryan@garth.UUCP (Steven Ryan): > > Continuous systems are computably using calculus, but is this `effective > computation?' Calculus uses a number of existent theorems which prove some > point or set exists, but provide no method to effectively compute the value. Clearly numerical analysis emulates continuous systems. In the phil of math, this is, of course, an issue. For those denying reals but allowing the actual infinity of integers, NA is as good as the Tm. Not only are there existence theorems for point sets, but such theorems as the Peano Kernel Theorem are effective computations. At the point set level, one uses things called ``simple functions''. BTW, you're being too restrictive. There are many ``continuous'' systems which have a denumerable number of points of nondifferentiablity: there are several ways to handle this (e.g., measure theory). These are not ``calculus'' in the usual sense. Important applications are in diffusion and probability. So, is Riemann-Stiltjes the only true calculus? Nah. There's one per view. -- Steve (really "D. E.") Stevenson steve@hubcap.clemson.edu Department of Computer Science, (803)656-5880.mabell Clemson University, Clemson, SC 29634-1906