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Revision as of 03:00, 18 August 2011

n-value logics

Hi Ornithikos hope this is ok. Feel free to delete if you're not interested. :)

My main issue with, say, a standard 3-value logic (t/f/u) and the truth tables that go with them seem to give inaccurate answers, at least assuming that the data could fit into a 2-value paradigm. This is actually an example from a book called "Database in Depth" (C.J. Date) about relational databases. When no 'null' (u) values are allowed and constraints are set up properly, you basically end up with a self-consistent set of propositions of a (2-value) predicate logic. (The relational model as per Date. Of course, there are very few databases that are fully relational.)

Now, E.F. Codd didn't have a problem with NULLs, although Date argues that adding the third value basically means that the database is no longer guaranteed to be consistent once a third truth value is allowed. Anyway, in "Database in Depth" he examines the consequences of allowing nulls and what the logic looks like and comes up with this as one of the scenarios; he's using the same truth tables as Kleene logic that are in the three-valued logic article on Misplaced Pages.

But so, here's my paraphrase of an example he gives: define a predicate P, where P(x,y) is 'Product x is made in city y'. And then say we make a proposition from that predicate, where x = 'SuperMegaX', and y = unknown. So, we have a proposition that says 'Product x is made in an unknown city.' Now, say you had another product where x = 'SuperUltraX' and y = unknown. So far so good. If you try to see if SuperMegaX's city is the same as SuperUltraX's city, you will appropriately get unknown as a result.

Ok, so here's the unexpected result: ask whether SuperMegaX's city is the same as SuperMegaX's city, of course both still unknown. In this case though, the result given by the logic is: Unknown. But this actually is the 'wrong' result, at least if we were relating this to the real world, because whether the city is unknown for a product or not, it has one. And even if we don't *know* the city (e.g. it's 'unknown'), we know that the city is the same as itself.

Now, I can imagine ways to try to tackle this (the two that come to mind are: take the attitude of "don't worry about it, it's no worse than 2-value material implication", hehe, or set up an identity predicate, and have separate truth tables for when identity(x,y)) but it just seems that whatever you do to 'fix' it, there is always going to be some sort of gap. You had mentioned fuzzy logic, which I am only vaguely familiar with, but I do figure there are some fields where it's ok if x == x is not axiomatic. Anyway, since you seem to be very much up on it, I was hoping you might be willing to discuss. :)

Shelleybutterfly (talk) 01:28, 11 August 2011 (UTC)

Editing around Misplaced Pages

Hi Ornithikos, I see you've apparently had some disappointing interactions here on Misplaced Pages. My talk page is always open if you run into problems and want an outside perspective. I also hope you understand that my removal of Ramos1990's addition was not due to disagreement (or agreement) with the content - it was because the sources made no such claim and it was a big leap and extrapolation to come up with such (as Ramos decided he agreed about - check the conversation out directly below the Welcome message). Anyway, that aside, feel free to drop by my talk page at any time, whether it is with a question, to give or ask for advice, for help (or to offer help) or simply to say "Hi!". Best, ROBERTMFROMLI | /_CN 02:41, 18 August 2011 (UTC)