2013/1/20 John E Clifford <kali9putr= a@yahoo.com>

why the prenex? not needed for any terms in propositional logic an= d not in most cases for predicate either.

My thought was that if you can express things with prenex, y= ou can be sure that you can also express things without it.

<= /div>

Letter names are names of letters but get used for all sorts of th= ings in Lojban, here, I take it, as metavariables.
Lojban (an SAE langua= ge) goes in for one term before the predicate, the rest after (SVO);=C2=A0 = logic tends to put all the terms after the predicate.=C2=A0 Why all the ter= ms in front? (also possible in Lojban without any marks).

You can't simulate FOL'= ;s use of terms after the predicate without using FA, so I put the terms in= front just to separate the terms from the selbri (=3Deasier to read?). But= the order doesn't really matter logically.

=C2=A0

{lo patfu be la ma= ks} is a description and a constant in the sense that it keeps the same ref= erence for some stretch of the discourse.=C2=A0 The relation between consta= nts of the description sort and quantifiers is complex and at least partial= ly 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.

Hmm... I think I'll have t= o read this a few times to really comprehend.

=C2=A0

Typically, proper names are transparent to negation, so moving {na= (ku)} around {la maks} shouldn't make a difference, although one can im= agine pragmatic purposes for the moves: *Max* is not at home (but Billy) is= or Max is not *at home* (where he should be) or some such.

This explanation was most clar= ifying. Thankyou!

<= div style=3D"font-size:12pt;font-family:times new roman,new york,times,seri= f"> For compound sentences, I am not sure you need the {zo'u} but it doesn&= #39;t hurt (and Polish notation is always safe for these, if you think of i= t in time).
The use of=C2=A0 {tu'e ... tu'u} for this purpose is= certainly discouraged, if not just wrong; these are genuine pragmatic pare= ntheses.=C2=A0 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 Loj= ban.=C2=A0 Again, Polish helps, o= f course, and there are various devices for marking the end of units or the= relative depth of connectives.=C2=A0

I know that it's often a lot eas= ier not to use the prenex at all, but if you for some reason need it or wan= t to have it there, it seems unpractical that the scope of zo'u ranges = over ijeks by default (according to CLL; I don't know if BPFK agrees).<= /div>

Iff is, by the way, = {ijo}

Yes, I know and I used it in m= y last example.

=C2=A0

<= div style=3D"font-size:12pt;font-family:times new roman,new york,times,seri= f"> Don't ever need parens around a simple sentence nor around an entire compound one.
Note that you have the material conditional backwa= rds; it is the antecedent that is negated in the disjunctive = form.
"unless" is easiest as just "or", usua= lly inclusive but sometimes exclusive .

I've learned that it doesn't m= atter if you negate the antecedent or the sentence after the disjunction. I= n both cases you get the material conditional, right?

That I'm most unsure about is the following (at least if you'r= e trying to imitate the order of words in the english sentence):

glico:=C2=A0Seb is at school unless Max is home

lojban:=C2=A0la seb ku zvati le ckule s= e.ijanai=C2=A0(?)=C2=A0naku zo'u la maks ku zdazva<= /font>

ui mi mutce lo ka ckire lo nu do c= iksi spuda i=C2=A0ki'e

i mu'omi'e jongausib

=C2=A0

From: jongausib <so.cool.ogi@gmail.com>
To: lojban@googlegroups.com
<= span style=3D"font-weight:bold">Sent: Sunday, January 20, 2013 7= :00 AM
Subject: [lojban] lojban an= d propositional logic

coi rodo

I've just finished a beginner's cl= ass 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 t= o 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&#= 39;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=9D= by=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] <= font face=3D"Verdana, sans-serif">la abus la bys tairmi'u=20

2. Atomic sentence with complex terms

FOL: Taller (father(max), max)

lojb= an: [lo patfu be la maks la maks zo'u] <= font size=3D"3">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 atomic sentence: literals ({nafcumslebri} ?)

FOL<= /span>: =C2=ACHome(max)=

lojb= an: [la maks zo'u] la m= aks na zdazva [default: his own home]

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

lojb= an: naku la maks zo'u l= a maks ku zdazva

lojb= an: la maks naku zo'u l= a maks ku zdazva

lojb= an: [la maks zo'u] la m= aks ku naku zdazva

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

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

lojb= an: 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

FOL:= =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

lojb= an: la seb zdazva na.ije la maks zdazva

5. DeMorgan's Firs= t Law

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

lojban: 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=

FOL:= Cube(a) =E2=88=A8 =C2=ACCube(a)

lojb= an: [la abus zo'u] tu'e la abus kubli tu'u ija tu'e naku zo'u la abus kubli

or without prenex:

lojb= an: la abus kubli ija la abus na kubli

which is logical equivalent to the material conditional:

FOL:= Cube(a) =E2=86=92 Cube(a)

lojban: la abus kubli ijanai la abus kubli

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

glic= o: Seb is at school unless Max is home

lojb= an: la seb ku zvati le ckule se.ijanai (?) naku zo'u la maks ku z= dazva

the eng= lish proposition is equivalent to and the lojban proposition should be equi= valent to:

glic= o: Unless Max is home, then Seb is at school

lojb= an: naku zo'u tu'e la maks ku zdazva tu'u ijanai la seb ku zvati le ckul= e

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

and the biconditional:

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

lojb= an: la maks ku zdazva ijo la seb ku zvati le ckule

glic= o: Max is at home if and only if Seb is at school

or

glic= o: Max is at home just in case Seb is at school

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