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)
VowelLogicalEnglish
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
OperatorLogicalEnglish
.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...
gismuDefinition
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