Modal logic example
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From: Lee Rudolph on 15 May 2007 07:20 "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: >Aatu Koskensilta <aatu.koskensilta(a)xortec.fi> writes: > >> Rest assured, I'll stalk you all around Usenet, picking nits and >> correcting even the most trivial of your errors, until the end of >> time. > >Strangely comforting, that. Not strange at all. We can infer, surely, that Aatu has a proof that Usenet will persist until (and possibly) after the end of time. What could be *more* comforting? Lee Rudolph
From: Barb Knox on 16 May 2007 04:25 In article <87bqgovh86.fsf(a)phiwumbda.org>, "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote: > Barb Knox <see(a)sig.below> writes: > > > In article <1178895613.409524.257520(a)p77g2000hsh.googlegroups.com>, > > Gboro54 <gboro54(a)gmail.com> wrote: > > > >> Hi everyone, i am a third yr computer science major at Albright > >> College. I am taking a course in AI and i am writting a research paper/ > >> giving a report on Modal Logic...I understand the basic theorems with > >> no problem but my professor wants to see an example in which a problem > >> can be solved by modal logic and not first-order logic... In other > >> words he wants an example of probelm solving in modal logic for an > >> agent(something along the lines of resoultion refutation and CNF in > >> first-order logic)...Does anyone know of any good examples that i > >> could present that would satisfy this requirement??? Thanks > > > > One real-world example is Arthur Prior's use of modal logic for temporal > > reasoning. > > Are you sure that couldn't be done in purely first order logic? It > all comes down to quantifying over paths, doesn't it? Well, in general most of regular modal logic can be done in FOL, by quantifying over worlds. -- --------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | -----------------------------
From: Jesse F. Hughes on 16 May 2007 07:07 Barb Knox <see(a)sig.below> writes: > In article <87bqgovh86.fsf(a)phiwumbda.org>, > "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote: > >> Barb Knox <see(a)sig.below> writes: >> >> > In article <1178895613.409524.257520(a)p77g2000hsh.googlegroups.com>, >> > Gboro54 <gboro54(a)gmail.com> wrote: >> > >> >> Hi everyone, i am a third yr computer science major at Albright >> >> College. I am taking a course in AI and i am writting a research paper/ >> >> giving a report on Modal Logic...I understand the basic theorems with >> >> no problem but my professor wants to see an example in which a problem >> >> can be solved by modal logic and not first-order logic... In other >> >> words he wants an example of probelm solving in modal logic for an >> >> agent(something along the lines of resoultion refutation and CNF in >> >> first-order logic)...Does anyone know of any good examples that i >> >> could present that would satisfy this requirement??? Thanks >> > >> > One real-world example is Arthur Prior's use of modal logic for temporal >> > reasoning. >> >> Are you sure that couldn't be done in purely first order logic? It >> all comes down to quantifying over paths, doesn't it? > > Well, in general most of regular modal logic can be done in FOL, by > quantifying over worlds. Yes, certainly. -- "What if [...] these people HATE mathematics itself, but possibly hang out here to prove to themselves that there's nothing really to it and live in the fantasy that they can conquer mathematics itself? You know, like arsonists who become firefighters." --James S Harris
From: Lee Rudolph on 16 May 2007 07:34 "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: >Barb Knox <see(a)sig.below> writes: > >> In article <87bqgovh86.fsf(a)phiwumbda.org>, >> "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote: >> >>> Barb Knox <see(a)sig.below> writes: >>> >>> > In article <1178895613.409524.257520(a)p77g2000hsh.googlegroups.com>, >>> > Gboro54 <gboro54(a)gmail.com> wrote: >>> > >>> >> Hi everyone, i am a third yr computer science major at Albright >>> >> College. I am taking a course in AI and i am writting a research paper/ >>> >> giving a report on Modal Logic...I understand the basic theorems with >>> >> no problem but my professor wants to see an example in which a problem >>> >> can be solved by modal logic and not first-order logic... In other >>> >> words he wants an example of probelm solving in modal logic for an >>> >> agent(something along the lines of resoultion refutation and CNF in >>> >> first-order logic)...Does anyone know of any good examples that i >>> >> could present that would satisfy this requirement??? Thanks >>> > >>> > One real-world example is Arthur Prior's use of modal logic for temporal >>> > reasoning. >>> >>> Are you sure that couldn't be done in purely first order logic? It >>> all comes down to quantifying over paths, doesn't it? >> >> Well, in general most of regular modal logic can be done in FOL, by >> quantifying over worlds. > >Yes, certainly. But this is ahistorical (not that there's anything wrong with that). Lee Rudolph Fun Fact Post Scriptum: In this world (not just some slew of the possible worlds), Saul Kripke could afford to retire early because his father died, leaving him the money he'd made as an old friend of Warren Buffett back there in Omaha.
From: Gboro54 on 16 May 2007 09:36
On May 14, 5:17 pm, galathaea <galath...(a)gmail.com> wrote: > On May 11, 8:00 am, Gboro54 <gbor...(a)gmail.com> wrote: > > > Hi everyone, i am a third yr computer science major at Albright > > College. I am taking a course in AI and i am writting a research paper/ > > giving a report on Modal Logic...I understand the basic theorems with > > no problem but my professor wants to see an example in which a problem > > can be solved by modal logic and not first-order logic... In other > > words he wants an example of probelm solving in modal logic for an > > agent(something along the lines of resoultion refutation and CNF in > > first-order logic)...Does anyone know of any good examples that i > > could present that would satisfy this requirement??? Thanks > > although there is always a functional reinterpretation of modalities > what is important are the modalities chosen > as they are intended to extend notions of truth > > studying modal logic is the language > in which these logical functions are normally investigated > and the study is just as important no matter how it is specified > > for a good example of where naive use of first-order logic > can lead one to paradox and computational deadlock > i'd suggest looking up the > > " cheating muddy children puzzle " > and how the modal dynamic epistemic logic > can provide a resolution > > -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar where can i find this puzzle at...google does not like the search for it |