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

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

• 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