Article View: sci.logic
Article #123Re: Set theory and modal logic
From: suchenek
Date: Thu, 16 Apr 1992 19:38
Date: Thu, 16 Apr 1992 19:38
31 lines
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1495 bytes
In article <1992Apr14.085858.11068@husc3.harvard.edu>, zeleny@zariski.harvard.edu (Mikhail Zeleny) writes: [...] > > MS: >>How, without the necessitation rule (and scheme K), can you get >> >> p \supset \box (\box (p \supset q) \supset (\box p \supset \box q)) >> >>(which is a theorem of S4 and S5), without proving too much, e.g. >> >> p \supset \box p >> >>(which is not a theorem of S4 and S5), where p is a propositional variable? > [MZ:] > Easy. We select a subsystem generated by all axioms of S5 (or S4). Do you > doubt that these axioms could be obtained from A \equiv \box A ? In fact, > on the purely syntactic level of abstraction we are considering, we needn't > even concern ourselves with RNec and other such matters. Not really. Using A \equiv \box A you prove too much, e.g. the unwanted sentence p \supseteq \box p, where p is a propositional variable. Greetings, Marek A. Suchenek Computer Science Cal State Dominguez Hills 1000 E Victoria St Carson CA 90747
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Path: arc1-ca.pugleaf.net!sparky!uunet!wupost!csus.edu!nic.csu.net!suchenek From: suchenek@nic.csu.net Newsgroups: sci.logic Subject: Re: Set theory and modal logic Message-ID: <1992Apr16.123806.1776@nic.csu.net> Date: 16 Apr 92 12:38:05 PDT References: <1992Apr11.130906.796@gacvx2.gac.edu> <1992Apr12.193331.11012@husc3.harvard.edu> <1992Apr13.114824.1745@nic.csu.net> <1992Apr14.085858.11068@husc3.harvard.edu> Organization: Information Resources and Technology Lines: 32