Article View: sci.logic
Article #114Re: Set theory and modal logic
From: logic
Date: Sat, 11 Apr 1992 19:09
Date: Sat, 11 Apr 1992 19:09
28 lines
1648 bytes
1648 bytes
In article <1992Apr10.161709.5397@vax.oxford.ac.uk>, loader@vax.oxford.ac.uk (R Loader) writes: > In article <1992Apr8.100146.689@gacvx2.gac.edu>, logic@gacvx2.gac.edu writes: >> In article <1992Apr7.124948.5325@vax.oxford.ac.uk>, loader@vax.oxford.ac.uk (R Loader) writes: >> >>> S4 and S5 (and most other common modal logics), are subsystems of classical >>> (non-modal) logic extended with the axiom: A iff \box A. >> >> Other stuff deleted.... >> >>> Ralph Loader, >>> Mathematical Institute, Oxford. >> >> S4 and S5 are supersystems, not subsystems, of classical logic.. Neither >> contain the axiom "A iff \box A", both contain the axiom "if \box A then A". >> >> Al Hart > > Sorry, My original posting was ambiguous: I meant ". . . are subsystems > of the logic obtained by adding A iff \box A to classical logic" > -- > Ralph Loader, Oxford. I see the ambiguity now - missed it during my first post.. however, not having extracted your first post, i'm not sure i see the point. extending classical logic with the axiom A iff \box A obviously makes \box completely superfluous. confused, al hart
Technical Details
Message-ID:
<1992Apr11.130906.796@gacvx2.gac.edu>Path:
arc1-ca.pugleaf.net!sparky!uunet!olivea!spool.mu.edu!umn.edu!noc.MR.NET!gacvx2.gac.edu!logicReferences:
<1992Apr5.213320.27618@morrow.stanford.edu> <1992Apr7.124948.5325@vax.oxford.ac.uk> <1992Apr8.100146.689@gacvx2.gac.edu> <1992Apr10.161709.5397@vax.oxford.ac.uk>Show Full Headers
Complete Article Headers
Path: arc1-ca.pugleaf.net!sparky!uunet!olivea!spool.mu.edu!umn.edu!noc.MR.NET!gacvx2.gac.edu!logic From: logic@gacvx2.gac.edu Newsgroups: sci.logic Subject: Re: Set theory and modal logic Message-ID: <1992Apr11.130906.796@gacvx2.gac.edu> Date: 11 Apr 92 19:09:06 GMT References: <1992Apr5.213320.27618@morrow.stanford.edu> <1992Apr7.124948.5325@vax.oxford.ac.uk> <1992Apr8.100146.689@gacvx2.gac.edu> <1992Apr10.161709.5397@vax.oxford.ac.uk> Organization: Gustavus Adolphus College, St. Peter, Minnesota Lines: 28