Modal logic example
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From: Gboro54 on 14 May 2007 14:01 On May 14, 1:38 pm, "Jesse F. Hughes" <j...(a)phiwumbda.org> wrote: > Gboro54 <gbor...(a)gmail.com> writes: > > This is my problem....I have found some examples but everyone he says > > that he can do it with just straigh first order logic and that the > > example does not demostarte why someone would want to learn modal > > logic.... I liked the example at the bottem of this one > >http://www.rpi.edu/~brings/LOG+AI/lai/node7.html#SECTION0004100000000... > > but he said this does not show the use for modal logic because he > > could solve it using just first order logic > > Well, I always thought that modal logic could be reduced to first > order logic, since the modalities are typically given in terms of > quantifiers over possible worlds/states/whatever. > > But modal operators are useful nonetheless, since doing the same work > with quantifiers ends up fairly messy. The modal operators are given > fairly simple axioms appropriate to the reasoning we want to do with > them and thus they simplify our arguments. At least, that's how I > always thought about these things. > > Aatu will be sure to show us where I went wrong in my confused > notions. Unless he's tired of correcting my mistakes and added me to > his killfile. > > But he seems pretty tireless. > > -- > "It has been shown that no man can sit down to write without a very profound > design. Thus to authors in general trouble is spared. A novelist, for example, > need have no care of his moral. It is there -- that is to say, it is somewhere > -- and the moral and the critics can take care of themselves." --E.A. Poe This was my point to my professor and he does not grasp that....every example i give him he tells me that he can solve it in first-order logic and thus modal logic is pointless to learn if that is the case...
From: Aatu Koskensilta on 14 May 2007 15:09 On 2007-05-14, in sci.logic, Jesse F. Hughes wrote: > Aatu will be sure to show us where I went wrong in my confused > notions. Unless he's tired of correcting my mistakes and added me to > his killfile. I don't have a killfile, which might explain some things. Anyhow, there's nothing to correct; modal logic reduces to the two variable fragment of first order logic. The idea that this shows that there is no point in learning modal logic is as silly as saying that there is no point in studying number theory since analysis exists and naturals are reals. Modal logic is interesting in itself, and has many applications e.g. in computer science -- often restricted systems have interesting properties that they do not share with more comprehensive systems they can be embedded in, and that's certainly the case with modal logic. > But he seems pretty tireless. 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. -- Aatu Koskensilta (aatu.koskensilta(a)xortec.fi) "Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: galathaea on 14 May 2007 17:17 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
From: Frederick Williams on 14 May 2007 18:01 Gboro54 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 There are modal logics (even normal ones) that are not complete w.r.t. any possible world semantics. I'll supply references if you want them. Every modal logic is complete w.r.t. some algebraic semantics (an uninteresting fact because the semantics is just the syntax rewritten in algebraic form). -- Remove "antispam" and ".invalid" for e-mail address. We have lingered in the chambers of the sea By sea-girls wreathed with seaweed red and brown Till human voices wake us, and we drown.
From: Jesse F. Hughes on 14 May 2007 23:15
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. -- "I'm the guy. I have always been the guy. Your post will sit here for a while, soon be ignored, except for people coming to read my reply, and your satisfaction will fade as you move on, and I'll still be the guy." -- James S. Harris will *always* be the guy. Duh. |