Re: [lojban] lojban and propositional logic

Your final example is "If Max is not at home, then Seb is at school.", so yes "Seb is at school unless (or) Max is at home." The difference is stylistic, but it's useful to stick to the models.

From: Sebastian Fröjd <so.cool.ogi@gmail.com>
To: lojban@googlegroups.com
Sent: Sunday, January 20, 2013 1:38 PM
Subject: Re: [lojban] lojban and propositional logic

2013/1/20 John E Clifford <kali9putra@yahoo.com>

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

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

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); logic tends to put all the terms after the predicate. Why all the terms 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 (=easier to read?). But the order doesn't really matter logically.

{lo patfu be la maks} is a description and a constant in the sense that it keeps the same reference for some stretch of the discourse. The relation between constants of the description sort and quantifiers is complex and at least partially interchangeable: particular quantiers ("there is a") can be replaced 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 be 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 to read this a few times to really comprehend.

Typically, proper names are transparent to negation, so moving {na(ku)} around {la maks} shouldn't make a difference, although one can imagine 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 clarifying. Thankyou!

For compound sentences, I am not sure you need the {zo'u} but it doesn't hurt (and Polish notation is always safe for these, if you think of it in time).
The use of {tu'e ... tu'u} for this purpose is certainly discouraged, if not just wrong; these are genuine pragmatic 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. Again, Polish helps, of course, and there are various devices for marking the end of units or the relative depth of connectives.

I know that it's often a lot easier not to use the prenex at all, but if you for some reason need it or want 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).

Iff is, by the way, {ijo}

Yes, I know and I used it in my last example.

Don't ever need parens around a simple sentence nor around an entire compound one.
Note that you have the material conditional backwards; it is the antecedent that is negated in the disjunctive form.
"unless" is easiest as just "or", usually inclusive but sometimes exclusive .

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

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

glico: Seb is at school unless Max is home

lojban: la seb ku zvati le ckule se.ijanai (?) naku zo'u la maks ku zdazva

ui mi mutce lo ka ckire lo nu do ciksi spuda i ki'e

i mu'omi'e jongausib

From: 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.

The text hereunder is just about propositional logic. Maybe I continue with quantifiers (e.g. predicate logic) later in the already existing threads about ”exact quantifiers” and ”free variables”, respectively. But 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 ”abu” and ”by” 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

2. Atomic sentence with complex terms

FOL: Taller (father(max), max)

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

In FOL the complex term ”father(max)” is interpreted as a function, a ”name-like” 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 ”any term without an explicit outer quantifier is a constant, i.e. not a quantified term.”.

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

3. Negations of atomic sentence: literals ({nafcumslebri} ?)

FOL: ¬Home(max)

lojban: [la maks zo'u] la maks na zdazva [default: his own home]

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

lojban: naku la maks zo'u la maks ku zdazva

lojban: la maks naku zo'u la maks ku zdazva

lojban: [la maks zo'u] la maks ku naku zdazva

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

FOL: ¬(Home(seb) ∧ Home(max))

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

di'u negates both sentences, ki'u according to CLL ”In general, the scope of a prenex that precedes a sentence extends to following sentences that are joined by ijeks”

FOL: ¬Home(seb) ∧ 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

lojban: la seb zdazva na.ije la maks zdazva

5. DeMorgan's First Law

FOL: ¬(P ∧ Q) ⇔ ( ¬P ∨ ¬Q)

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) ∨ ¬Cube(a)

lojban: [la abus zo'u] tu'e la abus kubli tu'u ija tu'e naku zo'u la abus kubli

or without prenex:

lojban: la abus kubli ija la abus na kubli

which is logical equivalent to the material conditional:

FOL: Cube(a) → Cube(a)

lojban: la abus kubli ijanai la abus kubli

7. ”Unless” and biconditional

glico: Seb is at school unless Max is home

lojban: la seb ku zvati le ckule se.ijanai (?) naku zo'u la maks ku zdazva

the english proposition is equivalent to and the lojban proposition should be equivalent to:

glico: Unless Max is home, then Seb is at school

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

FOL: ¬Home(max) → School(seb)

and the biconditional:

FOL: Home(max) ↔ School(seb)

lojban: la maks ku zdazva ijo la seb ku zvati le ckule

glico: Max is at home if and only if Seb is at school

or

glico: Max is at home just in case Seb is at school

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