User talk:Nahaj/Modal logic et al.

Modal logic et al.

Since EJ lept into the middle of this here, without saying what was being talked about... The page being discussed below is: [K4] which he seems to be claiming is the system S4.4.1 instead. (In fact he called the claim that it was K4 instead of S4.4.1 "patent nonsense".) I can find no literature so far on his system S4.4.1. The full discussion is in Talk:Provability_logic Nahaj 21:32:52, 2005-09-09 (UTC)

I've pointed to references that K4 and that "K+4" basis describes K4. EJ started this with insults (both of my references and of my page). Below he has started throwing out massive numbers of references for K+4 generating K4, and none that say that this basis is a distinct system from the other. And hurling insults because I keep pointing at the references and asking for his. But it is a matter of record that I asked in the first round of this, back on provablility logic, for his reasons for beliveing the systems distinct. - Nahaj

It is always possible, given the mess that names for systems has that some confusion in names is occuring. That's why I list specificly which one I'm pointing at on my pages, with references. Of course, if that were true it wouldn't make the page false or non-sensical, it would just mean that there was yet another set of systems using the same name. - Nahaj 21:52:21, 2005-09-11 (UTC)

If other readers here can't follow the chain of pages he mentions below, note that there is a very nice diagram of the systems involved in Hughes and Cresswell's "Introduction to Modal Logic", page 346. (While it doesn't agree with EJ, it does agree with my pages, and agrees with the text in the same book. Nahaj 21:42:36, 2005-09-11 (UTC)

First of all, I'd like to appologize for anything which you might consider as insulting. I certainly didn't want to attack or insult you, maybe I chose wrong words in some places (English is not my native language).

Engilsh "Crazy X's Y" is the "Y of 'Crazy X", but "X's Crazy Y" is the Crazy Y of X". But "Crazy" is not exacly a polite term to apply to work you've not read. And "patent nonsense" is not a exactly a polite term for a page either. Nahaj 19:59:50, 2005-09-09 (UTC)

Now, specific points. Ad K4: well, I probably don't understand what you are trying to say. K4 is just about the second most basic normal modal logic right after K, and unlike some other logics, its name is almost universally agreed on by modal logicians. I cannot exclude the possibility that in some point in history someone used the name for some other system, but one would expect the page to at least mention its usual meaning first. Also the other logics on the list like K4W, K4Z, K4.1,... clearly refer to this meaning of K4, not to the one defined on the page. As for S4.4.1, I have no reference for it, and I've never seen the name, but there *is* some kind of system in the usual naming convention for modal systems after all: if I take S4.4 and add the McKinsey axiom (named as .1 in logics like K4.1, S4.1), I get S4.4.1 (or S4.1.4).

Let me be more blunt. If you take S4.4, and add on (LMp implies MLp) the standard literature says you get K4. (And, this was pointed out on my page that you called "patent nonsense") You were pointed at a specific reference (a specific book and even a page number) [which you merely dismissed out of date] You've continued the argument that this is your system S4.4.1 (which I can't find any standard reference work mentioning) without saying why you think you are right and the standard references wrong and K4 formed in that manner should be called S4.4.1 . Nahaj

"The other logics on the list ... clearly refer to this meaning of K4, not to the one defined on the page" No they don't, since I wrote those pages I can safely tell you that they refer to the system K4. It doesn't matter which basis you use for the that system, and I can't find anything on my pages that cares one way or the other what basis one uses to get a system, as long as it is the same system. Nahaj 21:32:52, 2005-09-09 (UTC)

Yes, K4 is the common name of that system, that's why I called my page k4.html. You were the one that said what I had was S4.4.1. Where are you saying I called it something else? And I've given my references, and I've asked for yours. Where can I read about S4.4.1? (There are, by the way, a number of different axiomatic bases for K4, very few of which I've gotten around to listing. If you are claiming you don't see your favorate basis, then you'll need to give me a reference, and if it is equivalent to the same system I'll probably add it.) Nahaj 19:59:50, 2005-09-09 (UTC) [Update: I've added a second citation for the fact that what I listed is K4, and I added yet another equivalent axiomatic basis for the K4 system..] Nahaj 21:32:52, 2005-09-09 (UTC)

If you take (for example) S4 and bolt an axiom on, it does not follow that you have S4.xxx you might have an axiomatic base that is equivalent to the basis for some other popular logic). It is exactly that reasoning that has lead to the current naming mess. (More later when I have some time.) And your assumption that you can flip components of the name is contrary to much usage. (I refer you to Hughes and Cresswell for a number of examples.) The convention was often to call a system S4.X if the author believed that the system was between S4 and S5, for example. I believe you are over generalizing from a few examples as to how the naming scheme has historicly been done. Nahaj 19:59:50, 2005-09-09 (UTC)

I still believe this. Nahaj 02:25:59, 2005-09-13 (UTC)

You've still not given any references for your system S4.4.1, nor given the reason why you believe that that system is distinct from K4. Nahaj 19:59:50, 2005-09-09 (UTC)

Forget about S4.1.4, the problem is not with S4.1.4, but with K4. Frankly, I don't know how to deal with this. We are talking about a basic thing which one learns somewhere in the first one or two lectures in an introductory course on modal logic. The discussion so far looks like this: your page claims 1+1=3. I claim that this is patent nonsense, and that 1+1=2. You ask me to give references for that, and whether I am sure that 2 is different from 3. But OK, if you ask for it, here are some references for K4 in its usual meaning (which is, K4=K+4):

Note that the system that was called K4 when I took modal logic was the S4 based one. Nahaj 02:25:59, 2005-09-13 (UTC)

The system K plus the axiom 4 has been repeatedly proven to be he same system. Why do you belive (contrary to the literature) that the two different axiomatic basis are different systems? All of the different axiomatic basis for the same system produce the same system Your insistance that the bases define different systems is strange... If you don't like the traditional proofs that those sets of axioms define the same system, have the same models, and are inferentially the same, could you please give a reference? [ I was wrong on this point. Badly. - Nahaj 02:25:59, 2005-09-13 (UTC) Nahaj 13:30:25, 2005-09-10 (UTC)

• canonical reference texts on modal logic:

We disagree on the cononical texts, but you can go to my pages and see mine. Nice job of googeling, but not one of them gives any reason to disbelieve the equivalences of the two different axiomatic bases for the same system. Nahaj 13:30:25, 2005-09-10 (UTC)

• A. Chagrov, M. Zakharyaschev, Modal logic, Oxford Logic Guides 35, Oxford University Press, 1997.
• P. Blackburn, M. de Rijke, Y. Venema, Modal logic, Cambridge Tracts in Theoretical Computer Science 53, Cambridge University Press, 2001.
• I don't have a copy of Hughes & Cresswell around, but I would be surprised if it didn't define K4 as well.

Yep, they do. And they say that the system is S4.4 plus the axiom, just as I do... and they say it is K+4 as well. Nahaj 13:30:25, 2005-09-10 (UTC)

• Stanford Encyclopedia of Philosophy

Note that the modal logic page lists my pages as a place to go for more information. :) Nahaj 13:30:25, 2005-09-10 (UTC)

• canonical reference texts on provability logic:

• G. Boolos, The logic of provability, Cambridge University Press, 1993.

Checked. Nothing I find that mentions the S4.4 + MS = K4, much less makes the your claim it is patent nonsense. Nahaj 13:15, 17 September 2005 (UTC)

• G. Japaridze, D. de Jongh, The logic of provability, in: Handbook of Proof Theory, S. Buss (ed.), Studies in Logic and the Foundations of Mathematics 137, Elsevier, Amsterdam, 1998, pp. 475-546.
• S. Artemov, L. Beklemishev, Provability logic, in: Handbook of Philosophical Logic vol. 13, D. Gabbay and F. Guenthner (eds.), 2nd ed., Kluwer, Dordrecht, 2004, pp. 229-403.

• from your own page on K4:

• L. A. Nguyen, A new space bound for the modal logics K4, KD4, and S4, in: Proceedings of the MFCS'99, M. Kutylowski, L. Pacholski, T. Wierzbicki (eds.), LNCS 1672, Springer, 1999, pp. 321-331.

Checked. Nothing I find that mentions the S4.4 + MS = K4, much less makes the your claim it is patent nonsense. Nahaj 13:15, 17 September 2005 (UTC)

• (the same topic and author, but more explicit definition) L. A. Nguyen, On the complexity of fragments of modal logics, in: Advances in Modal Logic vol. 5, R. Schmidt et el. (eds.), King's College Publications, 2005, pp. 318-330.

Checked. Nothing I find that mentions the S4.4 + MS = K4, much less makes the your claim it is patent nonsense. Nahaj 13:15, 17 September 2005 (UTC)

• random selection from the thousands of existing research papers on modal logic:

Since it is a specialized issue, no reasonable person would expect a random selection to cover it. Why a random list instead of an on topic one? Nahaj 00:00:08, 2005-09-11 (UTC)

• K. Fine, Logics containing K4, part I, Journal of Symbolic Logic 39 (1974), no. 1, pp. 31-42.
• K. Fine, Logics containing K4, part II, Journal of Symbolic Logic 50 (1985), no. 3, pp. 619-651.
• S. Ghilardi, Best solving modal equations, Annals of Pure and Applied Logic 102 (2000), no. 3, pp. 183--198.
• I. Shapirovsky, On PSPACE-decidability in Transitive Modal Logic, in: Advances in Modal Logic vol. 5, R. Schmidt et el. (eds.), King's College Publications, 2005, pp. 269-287.
• M. Mouri, Constructing counter-models for modal logic K4 from refutation trees, Bulletin of the Section of Logic 31 (2002), no. 2, pp. 81-90.

Checked. Nothing I find that mentions the S4.4 + MS = K4, much less makes the your claim it is patent nonsense. Nahaj 13:15, 17 September 2005 (UTC)

• K. Sasaki, Logics and provability, PhD thesis, University of Amsterdam, 2001. ILLC Dissertation series DS-2001-07.
• Ç. Gencer, Description of modal logics inheriting admissible rules for K4, Logic Journal of the IGPL 10 (2002), no. 4, pp. 401-411.
• L. Maksimova, Projective Beth's properties in infinite slice extensions of the modal logic K4, in: Advances in Modal Logic vol. 3, F. Wolter et. al. (eds.), World Scientific, 2002, pp. 349-363.
• E. E. Zolin, Embeddings of propositional monomodal logics, Logic Journal of the IGPL 8 (2000), no. 6, pp. 861-882.
• S. Demri, R. Goré, An O((n.log n)³)-time transformation from Grz into decidable fragments of classical first-order logic, in: Automated Deduction in Classical and Non-Classical Logics, LNAI 1761, Springer, 2002, pp. 153-167.

I have other work to do now than looking up references for you, so do me a favor and continue the search yourself.

I did not ask you for the list. You insultingly dropped it into the discussion (and they don't seem to support your case). I already given references that support my case. You have yet to come up with even one literature reference that makes the claim you do. And although you've flooded me with off topic references, so far I've not found anything in your list of references that even touches on the topic. And given that your researched list doesn't seem to have any papers that support you, I sure wouldn't want to have you doing searches for me.Nahaj 00:00:08, 2005-09-11 (UTC)

Try Google, if you do not know where to start. Alternatively, just ask any modal logician what K4 is, such as anybody on the AiML list (except, apparently, yourself). -- EJ 13:12, 10 September 2005 (UTC)

I keep talking to Modal Logicians, without finding one that agrees with you. Instead of my wasting any more time on it, why don't you just point me at one that does agree with you.? 20:48:09, 2005-09-11 (UTC)

They tell me that the system K4 has (as most modal logics do) a number of different axiomatic bases. And that those bases define the same system. Did you actually try asking the question of the that list? Please note, for the record, that I have been listed there for years. (John Halleck, just like my user page has said all along) More evidence, to me, that you didn't actually read the references you've googled up. Nahaj 13:30:25, 2005-09-10 (UTC)

Now it's you who keeps insulting. I studied about half of the references before, and for the rest (which I indeed googled) I checked what they say about K4. Yes, I noticed you are on the list, which is the reason I excluded you from the list of people to ask in the previous post.

It would be nice if you could tell me which specific ones in that half you checked, so I don't have to keep wading through references that don't even discuss your claim. If you have checked what they say about K4, and you think that they support your view, then just point me at one that claims the (S4.4+Axiom) basis isn't K4. If you do that, and it really does make that claim, then I'll publicly appologise. [Done... See K4 section above]. If you can't I expect you to appologize. Nahaj 20:48:09, 2005-09-11 (UTC)

Max Cresswell is also on the list. His book contradicts your claim. I've even given you the page number to check. So, you've inserted a fancy sounding list into the discussion, and it contains at least one person other than me that has published the opposite of your claim, and so far you can't point to even a single person on the list that agrees with you. I'll repeat my question "Did you actually ask anyone on the list?" If you find anyone on the list that supports your claim I'd be interested to hear about it.Nahaj 00:00:08, 2005-09-11 (UTC)

If you feel insulted, I'm sorry. Sometimes if people insult me long enough I slip into returning the favor. Nahaj 14:16:48, 2005-09-10 (UTC)

To sum up the several paragraphs you inserted above: you claim that the system defined on your page on K4 is deductively equivalent to K + the transitivity axiom. It obviously isn't, and repeatedly insisting on that claim will not make it true. According to your page: K4 = S4.4 + $\Box \Diamond p\to \Diamond \Box p$, S4.4 = S4 + $\Diamond \Box p\to (p\to \Box p)$, and S4 is the usual S4 (T + 4). Now, K4 (the usual one) does not prove T, does not prove the McKinsey axiom $\Box \Diamond p\to \Diamond \Box p$, and does not prove $\Diamond \Box p\to (p\to \Box p)$. You can easily verify it youself by constructing suitable Kripke models. -- EJ 14:08, 10 September 2005 (UTC)

You wouldn't expect the two logics to prove each others axioms. Basic fact of logic: If system A is system B plus axioms, and system A is also system C plus axioms, there is no requirement whatsoever that B be able to prove theorems of C or the other way around, only that each full basis be able to prove the other. Your argument above is an invalid argument, no matter how much fancy TeX graphics you throw into it. Nahaj 00:00:08, 2005-09-11 (UTC)

Note also that the page you quote has the specific references (Specific books, right down to the page number again) for the relationships given. If you have some reason to disbelieve the work quoted, other than opinion, please produce a specific reference (Possibly you've confused the system T referenced on those pages with one of the axioms of that name that have appeared in the literature? [Nope, he's just confused the two K4's. - Nahaj 02:25:59, 2005-09-13 (UTC)). (The reason that my pages have specific links on each reference to a named system or axiom is to avoid people assuming that the name refers to some different one.) 21:03:31, 2005-09-11 (UTC)

I have pointed to several books that say that K4 is S4.4 plus + [LMp implies MLp]. (Right down to page number). You have yet to point to a single one that supports your view that this is false. And you make arguments like the above strawman argument instead. [ I appologize for calling the argument a "strawman argument", and retract that claim. Nahaj 14:55, 25 September 2005 (UTC)]

Oh, and I forgot to say that I'll be off internet for a week now, so don't be surprised I will not answer for some time. Hopefully you will calm down and think about it meanwhile. -- EJ 14:26, 10 September 2005 (UTC)

I've given supporting documentation, over and over and over again, and I'm still waiting for you to do the same. Maybe when you get back..