# Reduced logical form

sentence = selbri-2 [[[FA] variable] ... /VAU/
| gek sentence gik sentence
| NA KU ZOhU sentence
| tag /KU/ ZOhU sentence
| [tag] [quantifier] variable [relative-clauses] ZOhU sentence

variable = KOhA [XI number] (da, de, di; ko'a, ko'e, ..., fo'u)
selbri-2, gek, gik, tag, quantifier, relative-clauses, number as in the EBNF grammar

The above grammar is a sub-grammar of the Lojban grammar. By that I mean that every sentence it generates is a valid sentence of the Lojban grammar. I contend that every Lojban sentence has a corresponding reduced logical form generated from this grammar. The idea is simple: to get the reduced logical form eliminate indicators and free modifiers, move quantifiers and negations to the prenex, expand all logical connectives to forethought sentence connectives and finally move all the arguments behind the selbri. The devil is, of course, in the details. I intend to work out an algorithm for producing the reduced logical form for any Lojban sentence. (In fact I think there are a couple of tricky places where it may not be doable, but at least this will show what they are.) The purpose of this exercise is to clarify the argument for the scope of NA. In the reduced logical form the relative scopes of the different operators are fairly obvious. mi'e xorxes

## Algorithm

to reduce any Lojban text to its logical form as defined in the above grammar (Work in progress)

Step 1: Reduce text to paragraphs
Step 2: Reduce fragment to statement
Step 3: Reduce statement to subsentence
Step 4: Reduce paragraphs to subsentence
Step 5: Reduce bridi-tail to bridi-tail-3
Step 6: Reduce afterthought sumti and termset connectives to forethought, and quantified terms to KOhA1-form.
Step 7: Reduce pre-selbri terms to KOhA
Step 8: Reduce bridi-tail to selbri-6 and KOhA. Obtain final form.

This reduction does not handle:

1. Indicators and free modifiers
2. VUhO relative-clauses
3. tags when they double up with other connectives

Created by xorxes. Last Modification: Monday 08 of November, 2004 20:24:13 GMT by xorxes.