why the prenex? not n= eeded for any terms in propositional logic and not in most cases for predic= ate either.
Letter names are names of letters but get used for all sorts= of things in Lojban, here, I take it, as metavariables.
Lojban (an SAE = language) goes in for one term before the predicate, the rest after (SVO);&= nbsp; logic tends to put all the terms after the predicate. Why all t= he terms in front? (also possible in Lojban without any marks).
{lo patf= u be la maks} is a description and a constant in the sense that it keeps th= e same reference for some stretch of the discourse. The relation betw= een constants of the description sort and quantifiers is complex and at lea= st partially interchangeable: particular quantiers ("there is a") can be re= placed by constants -- function expressions -- and decriptions can be replaced by quantifiers, with the loss of transsentential identity. {patfu= } is not specified as to what type of father is involved and so there may b= e several things which satisfy it for a single x2, but context will usually= reduce this to one without explicit restriction.
Typically, proper name= s are transparent to negation, so moving {na(ku)} around {la maks} shouldn'= t make a difference, although one can imagine pragmatic purposes for the mo= ves: *Max* is not at home (but Billy) is or Max is not *at home* (where he = should be) or some such.
For compound sentences, I am not sure you need = the {zo'u} but it doesn't hurt (and Polish notation is always safe for thes= e, if you think of it in time).
The use of {tu'e ... tu'u} for thi= s purpose is certainly discouraged, if not just wrong; these are genuine pr= agmatic parentheses. The easiest would be la seb na zdazva ije la maks zdazva
I suppose= that in the totally schematic forms, the= parentheses are OK, but they don't say much about how to say it in Lojban<= /font>. Again, Polish helps, of course, and ther= e are various devices for marking the end of units or the relative depth of= connectives. Iff is, by the way, {ijo}
Don't ever need parens around a simple sentence no= r around an entire compound one.
Note that you have the material conditional backwards; it is the a= ntecedent that is negated in the disjunctive form.
"unl= ess" is easiest as just "or", usually inclusive but sometimes exclusive .

From:<= /b> jongausib <so.cool.ogi@gmail.com>
To: lojban@googlegroups.com
Sent: Sunday, January 20, 2013 7:00 AM
= Subject: [lojban] lojban and = propositional logic

coi rodo

I've just finished a beginner's class of logic at the swedish university (what don't you do to achieve lo ka jbocre someday? zo'o), and now I just want to test if I'm able to express some different logical propositions bau la lojban. Would you please correct me if you see any errors? mi ba ckire

Yes, it's a bit long, but if you don't find it interesting, don't read it.=20

The text hereunder is just about propositional logic. Maybe I continue with quantifiers (e.g. predicate logic) later in the already existing threads about =E2=80=9Dexact quantifiers=E2=80=9D and =E2=80=9Dfree variables=E2=80=9D, respectively. Bu= t as far as I understand it, the text hereunder show at least how clumsy the scope of {zo'u} is to use, when expressing compound propositions. Please correct me if I'm wrong about something, so I don't learn wrongly.

1. Atomic sentence ({slebri} ? {stodzabri} ?)

FOL: SameShape(a, b)

lojban: [abuboi by zo'u] abu by tairmi'u

but as =E2=80=9Dabu=E2=80=9D and =E2=80= =9Dby=E2=80=9D could be interpreted as variables rather than individual constants, maybe the following sentence is a better translation?

lojban: [la abus la bys zo'u] la abus la bys tairmi'u=20

2. Atomic sentence with complex terms

FOL: Taller (father(max), max)

lo= jban: [lo patfu be la maks la maks zo'u] lo patfu be la maks la maks rajyclamau [zo'e]

In FOL the complex term =E2=80=9Dfather(max)=E2=80=9D is interpreted as a function, a =E2=80= =9Dname-like=E2=80=9D term.

In lojban {lo patfu be la maks} is interpreted as a description with an inner predicate/selbri, and according to the xorlo gadri proposal =E2=80=9Dany term without an explicit outer quantifier is a constant, i.e. not a quantified term.=E2=80=9D.

Probably I should add the inner quantifier {lo pa patfu be la maks}. Otherwise, it would mean =E2=80=9Dsomething whatever which has something to do with Max' father=E2=80=9D, right?

3. Negations of atomi= c sentence: literals ({nafcumslebri} ?)

FO= L: =C2=ACHome(max)=

lo= jban: [la maks zo'u] la maks na zdazva [default: his own home]

question: Is di'u logical equivalent to the following three sentences?

lo= jban: naku la maks zo'u la maks ku zdazva

lo= jban: la maks naku zo'u la maks ku zdazva

lo= jban: [la maks zo'u] la maks ku naku zdazva

4. Boolean connective= s (of logical sentences/bridi) ijek and negations

FO= L: =C2=AC(Home(seb) =E2= =88=A7 Home(max))

lo= jban: naku zo'u la seb zdazva ije la maks zdazva

di'u negates both sentences, ki'u according to CLL =E2=80=9DIn general, the scope of a prenex that precedes a sentence extends to following sentences that are joined by ijeks=E2=80=9D

FO= L: =C2=ACHome(seb) =E2=88= =A7 Home(max)

lojban: naku zo'u tu'e la seb zdazva tu'u ije la maks zdazva

So here I use {tu'e...tu'u} to terminate the scope of zo'u. A bit clumsy? Wouldn't it have been better if {zo'u} got it's own terminator?

Or

lo= jban: la seb zdazva na.ije la maks zdazva

5. DeMorgan's First L= aw

FO= L: =C2=AC(P =E2=88=A7 Q) =E2=87=94 ( =C2=ACP =E2=88=A8 =C2=ACQ)

lojba= n: bu'a bu'e zo'u tu'e naku zo'u bu'a ije bu'e ti'u idu'ibo tu'e na bu'a ija na bu'e tu'u tu'u

6. A tautology ({?}): Law of excluded middle, and conditionals=

FO= L: Cube(a) =E2=88=A8 =C2=ACCube(a)

lo= jban: [la abus zo'u] <= span style=3D"font-weight:normal;">tu'e la abus kubli tu'u ija tu'e naku zo'u la abus kubli

or without prenex:

lo= jban: la abus kubli ija la abus na kubli

which is logical equivalent to the material conditional:

FO= L: Cube(a) =E2=86=92 Cube(a)

lojba= n: la abus kubli ijanai la abus kubli

7. =E2=80=9DUnless=E2= =80=9D and biconditional

gl= ico: Seb is at school unless Max is home

lo= jban: la seb ku zvati le ckule se.ijanai (?) naku zo'u la ma= ks ku zdazva

the e= nglish proposition is equivalent to and the lojban proposition should be eq= uivalent to:

gl= ico: Unless Max is home, then Seb is at school

lo= jban: naku zo'u tu'e la maks ku zdazva tu'u ijanai la seb ku zvati le ckule

FO= L: =C2=ACHome(max) =E2=86= =92 School(seb)

and the biconditional:

FO= L: Home(max) =E2=86=94=20 School(seb)

lo= jban: la maks ku zdazva ijo la seb ku zvati le ckule

gl= ico: Max is at home if and only if Seb is at school

or

gl= ico: Max is at home just in case Seb is at school

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