Doing logic in Lojban

[John Cowan <cowan@ccil.org>]

This is a precis of what I think jboskologists think about logic in Lojban,
or at least what I think that I think. :-)

The four Aristotelian functions are expressed by Q da poi S cu P, where
S is the subject term, P is the predicate term, and Q is a quantifier.
Any quantifier is meaningful, but the standard A, E, I, and O functions
are expressed by the Qs "ro", "no", "su'o", and "me'iro". 
These can be translated "every", "no", "some", and "not every".
(The formulation "Some S is not P" is apparently a mistranslation by
Boethius of Aristotle's original "Not every S is P".

Existential import is required by quantifiers which do not allow 0 as a
possible value: specifically, "ro" and "su'o" have import, "no" and "me'iro"
do not. Existential import means that if the S term doesn't apply to
anything, the statement is false.

The standard Aristotelian relationships apply: A and O are contradictories,
E and I are contradictories, A and E can't be both true (contraries), 
I and O can't be both false (subcontraries), A implies I, E implies O,
some S is P implies some P is S, no S is P implies no P is S.

Frege-style logic does not have "da poi" constructions, and there are
only quantified variables and predicate terms joined by logical operators.
The standard rewriting of A, E, I, and O as (x) S(x) -> P(x),
(x) S(x) -> ~P(x), (Ex) S(x) & P(x), (Ex) S(x) & ~P(x) apply.

-- 
John Cowan jcowan@reutershealth.com
"You need a change: try Canada" "You need a change: try China"
--fortune cookies opened by a couple that I know