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