What is This Lojban Thing?

.i semo le lojbo

Module 4 of 7

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)
aL OR RL and/or R
eL AND Rboth L and R
oL IFF RL if and only if R
uLL, whether or not R
.enaiL AND !RL and not R
na.enai!L AND !Rneither L nor R
na.aL implies Rif L, then R
.anaiL IF RL if R
.onaiL XOR RL, 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...
bajrax1 runs on surface x2 using limbs x3 with gait x4
tavlax1 talks/speaks to x2 about subject x3 in language x4
viskax1 sees/views/perceives visually x2 under conditions x3
citkax1 eats/ingests/consumes (transitive verb) x2
plisex1 is an apple [fruit] of species/strain x2
crinox1 is green/verdant [color adjective]
cinsex1 in activity/state x2 exhibits sexuality/gender/sexual orientation x3 (ka) by standard x4
nanmux1 is a man/men; x1 is a male humanoid person [not necessarily adult]
ninmux1 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

  1. da plise .inaja mi nelci da
  2. da plise
  3. Conclusion: mi nelci da
  1. If something is an apple, then I like it.
  2. That something is an apple.
  3. Conclusion: I like it.

Modus Tollens and DeMorgan's Theorem

  1. mi citka da .ije da plise .inaja mi nelci da
  2. mi na nelci da
  3. Conclusion: mi na citka da .ija da na plise
  1. If I eat X and X is an apple, then I like X.
  2. It is not true that I like X.
  3. Conclusion: I don't eat X or X is not an apple.

Negation Over Quantifiers

  1. su'o lo ninmu cu cinse
  2. Implies: no lo ninmu na cinse
  1. One or more women are sexy.
  2. Implies: It is not true that no women are sexy.

nitcion's semantic analyzer

Example Semantic Analyses

(example adapted from the paper)

Automated Translation

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