rar@ADS.COM (Bob Riemenschneider) (06/17/88)
Date: Thu, 16 Jun 88 13:49 EDT From: Bob Riemenschneider <rar@ads.com> To: ailist@ai.ai.mit.edu, bnevin@CCH.BBN.COM cc: rar@ads.com In-Reply-To: bnevin@CCH.BBN.COM's message of 13 Jun 88 19:49:00 GMT Subject: Re^2: definition of information => From: bnevin@CCH.BBN.COM (Bruce E. Nevin) => => My understanding is that Carnap and Bar-Hillel set out to establish a => "calculus of information" but did not succeed in doing so. I'm not sure what your criteria for success are, but it looks pretty good to me. They didn't completely solve the problem of laying a foundation for Carnap's approach to inductive logic. (But it certainly advanced the state of the art--see, e.g., the second of Carnap's _Two Essays on Entropy_, which was, obviously, heavily influenced by this work.) Advances have been made since the original paper as well: see the bibiographies for Hintikka's paper and Carnap's later works on inductive logic (especially "A System of Inductive Logic" in _Studies in Inductive Logic_, vols. 1 and 2). [Disclaimer: There are very serious problem's with Carnap's approach to induction, which I have no wish to defend.] => Communication theory refers to a physical system's capacity to transmit => arbitrarily selected signals, which need not be "symbolic" (need not mean => or stand for anything). To use the term "information" in this connection => seems Pickwickian at least. "Real information"? Do you mean the => Carnap/Bar-Hillel program as taken up by Hintikka? Are you saying that => the latter has a useful representation of the meaning of texts? The Carnap and Bar-Hillel approach is based on the idea that the information conveyed by an assertion is that the actual world is a model of the sentence (or: "... is a member of the class of possible worlds in which sentence is true", or: "the present situation is a situation in which the sentence is true", or: <fill in your own, based on your favorite model-theory-like semantics>). This is certainly the most popular formal account of information. They, and Hintikka, count state descriptions to actually calculate the amount of information an assertion conveys, but that's just because Carnap (and, I suppose, the others) are interested in the logical notion of probability. If you start with a probability measure over structures (or possible worlds, or situations, or ... ) as given, you can be much more elegant--see, e.g., Scott and Krauss's paper on probabilities over L-omega1-omega-definable classes of structures. (It's in one of those late-60's North-Holland "Studies in Logic" volumes on inductive logic, maybe _Aspects of Inductive Logic_.) I don't recall what, if anything, you said about the application you have in mind, but, as the dynamic logic crowd discovered, L-omega1-omega is a natural language for talking about computation in general. => Bruce Nevin => bn@cch.bbn.com => <usual_disclaimer> -- rar