What is This Lojban Thing?

.i semo le lojbo

David Montenegro

Seacoast Linux Users Group

Logical Connectives

four logical vowels: a, e, o, u
can be negated with na (prefix) and/or nai (suffix)

Vowel	Logical	English
`a`	`L OR R`	L and/or R
`e`	`L AND R`	both L and R
`o`	`L IFF R`	L if and only if R
`u`	`L`	L, whether or not R

Operator	Logical	English
`.enai`	`L AND !R`	L and not R
`na.enai`	`!L AND !R`	neither L nor R
`na.a`	`L implies R`	if L, then R
`.anai`	`L IF R`	L if R
`.onai`	`L XOR R`	L, only if not R

Logical Connective Examples

use to connect sumti or bridi
le bakni .e le jipci - the beef AND the chicken
le bakni .enai le jipci - the beef AND NOT the chicken
le bakni na.enai le jipci - NITHER the beef NOR the chicken
mi nelci le plise .ije mi citka le plise
I like the apple AND I eat the apple.
le ninmu cu cinse .inaja la ben. nelci le ninmu
IF the woman is sexy, THEN Ben likes the woman.

The Truth About selbri - Places

selbri have places, numbered x1, x2, x3...

Example Places

the defined places for some common gismu...

gismu	Definition
`bajra`	x1 runs on surface x2 using limbs x3 with gait x4
`tavla`	x1 talks/speaks to x2 about subject x3 in language x4
`viska`	x1 sees/views/perceives visually x2 under conditions x3
`citka`	x1 eats/ingests/consumes (transitive verb) x2
`plise`	x1 is an apple [fruit] of species/strain x2
`crino`	x1 is green/verdant [color adjective]
`cinse`	x1 in activity/state x2 exhibits sexuality/gender/sexual orientation x3 (ka) by standard x4
`nanmu`	x1 is a man/men; x1 is a male humanoid person [not necessarily adult]
`ninmu`	x1 is a woman/women; x1 is a female humanoid person [not necessarily adult]

Predicate Calculus

selbri represent predicates, sumti represent arguments, bridi represent predications
eats(me,X) AND apple(X) -> likes(me,X)
If I eat X and X is an apple, then I like X.
mi citka da .ije da plise .inaja mi nelci da
draw inferences by same mechanisms as in predicate logic:
- Law of Modus Ponens
- Law of Modus Tollens
- negation of quantifiers
- ...lots of other logical transformations

Law of Modus Ponens

da plise .inaja mi nelci da
da plise
Conclusion: mi nelci da

If something is an apple, then I like it.
That something is an apple.
Conclusion: I like it.

Modus Tollens and DeMorgan's Theorem

mi citka da .ije da plise .inaja mi nelci da
mi na nelci da
Conclusion: mi na citka da .ija da na plise

If I eat X and X is an apple, then I like X.
It is not true that I like X.
Conclusion: I don't eat X or X is not an apple.

Negation Over Quantifiers

su'o lo ninmu cu cinse
Implies: no lo ninmu na cinse

One or more women are sexy.
Implies: It is not true that no women are sexy.

nitcion's semantic analyzer

the analyzer converts Lojban to equivalent Prolog predicates
reads output of the LLG parser
written in NU-Prolog (with lex prefilter)
extracts information from Lojban text
stores it in logical form
answers simple questions on the content
nitcion wrote a paper on the parser
(analyzer executes infinite recursion under GNU Prolog, so no live demo!)

Example Semantic Analyses

(example adapted from the paper)

mi se prami do (I am loved by you.)
prami(do, mi, _FJJXH, _FJJXI, _FJJXJ)
mi prami lo prenu ku poi ke'a citka lo cakla
(I love a person who eats a chocolate.)
q(suho(1), _FJKWJ, prenu(_FJKWJ, _FJKDO, _FJKDP, _FJKDQ, _FJKDR), q(suho(1), _FJKGU, cakla(_FJKGU, _FJKLJ, _FJKLK, _FJKLL, _FJKLM), _FJKIQ, citka(_FJKWJ, _FJKGU, _FJKGV, _FJKGW, _FJKGX)), prami(mi, _FJKWJ, _FJJZA, _FJJZB, _FJJZC))

Automated Translation

Lojban-English translator (web application) called jbofi'e

mi citka le plise
[₁(₂[citka1 (eat-er(s)) :] mi I, me)₂ [is, does] «₃citka eat-ing»₃ (₄[citka2 (eaten thing(s)) :] le the plise apple(s))₄]₁