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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