(A page from the Loglan web site.)
(From Lognet 94/3. Used with the permission of The Loglan Institute, Inc..)
Logic and Economy
For some months now, I've been kicking around some ideas on the relationship between logical and economical language. Recently, something that Randall Holmes wrote in private correspondence brought it together for me.
by James Jennings
Loglan is intended to be a logical language: this means that the ostensible argument of a predicate really is the argument of that predicate. .... Unfortunately, the picture is confused because Loglan actually has some pseudo-arguments in it already: a sentence A, e B, e C preda actually has no argument A, e B, e C (there is no such object!), except grammatically, but is a logically opaque transform of A preda, ice B preda, ice C preda.
(One moment while I put on my heretic costume.) I have been thinking that logic is not fundamental to human thought (and that maybe Loglan has started off on the wrong foot) but is merely a not-always-consistent side effect of the two driving forces behind language evolution (or, in our case, language design).
Note that these forces are opposed: more content means more words, more compression means fewer words.
- Content. (You want to impart information.)
- Compression. (You want to do it quickly.)
One reason I find this compelling is because I have found that many of the standard data compression techniques have linguistic analogs. For example
- The Zipf rule, the use of shorter words for the more frequently used concepts, is obviously an economy measure. It is also a variation on Huffman encoding, which uses fewer bits to encode the more frequently used bytes.
- Anaphora, the use of a pronoun to stand in for a recently-seen noun phrase, has a lot in common with dictionary methods such as Lempel-Ziv-Welch encoding where the computer remembers several thousand possible substrings in the recently-scanned data and substitutes a short code when any pattern appears a second time.
In this view, logical operators are just a grammar-based pattern-matching compression scheme. As Randall put it, a logically opaque transform. Instead of
- Mike eats meat. Jane eats meat. Spot eats meat. (9 words)
The thing that makes this logic rather than just a neat trick is the fact that the information content is the same. If you had several different patterns (logical operators) to use in your compression, you'd want to make sure that the meaning of all possible compressions remained the same. It's that consistency of meaning under transformation that makes logic interesting.
- Mike, Jane, and Spot eat meat. (6 words)
And yet natural language is not logical. I maintain that the reason it isn't logical is because pure logic doesn't give the highest compression ratios. The English word and is really a compression marker, and only sometimes can it be expanded in the logical way. Other times you need to take context into account, like in
where you know that the color-words red and blue are mutually exclusive; so you conclude that some areas of the ball's surface are red and others are blue.
- The ball is red and blue.
When the mathematicians invented formal logic as a reasoning tool, they greatly restricted the ways one can use and and therefore the ways logical statements could be compressed. When Loglan adopted a version of the logical and, it gave up many options for compression. English sentences like:
are very compressed and very difficult to render into Loglan.
- Bill and Mike ate lunch with Alice and Carol, respectively.
- There are two kinds of truth, shallow and deep.
As I see it, there are three possible responses to the problem of highly-compressed English sentences.
Currently, (2) is the path we are taking and are likely to take in the future. I suspect that (3) is too ambitious, that we don't know enough about what makes a useful construction to pull it off. On the other hand, (3) raises some interesting possiblities.
- Fatalistic: Ambiguity is just lossy compression after all. ('Lossy' is computer jargon meaning 'loses information'.) So of course Loglan is more verbose than English.
- Practical: We should handle the special cases as they come up, tweaking the language and inventing new constructs (compression schemes) as necessary.
- Ambitious: We should embark on the Grand Compression Revision (GCR), cataloging all of the useful constructions and designing a comprehensive pattern-matching compression scheme that leaves the logic perfectly invariant.
Loglan anaphora started out as just the words da de di do and du. The fact that these were not marked by gender, number, or anything else made them very hard to use. We're pretty good at figuring out that he refers to the masculine noun because they share a masculine quality, but not so good at counting back the number of terms we've used. Nowadays, we can use letterals as free variables (pronouns) that share a quality (starting letter) with the terms (noun phrases) they refer to.
It seems likely that the GCR would, if we embarked on it, identify a large number of types of structures or patterns that can be compressed. If we had a set of free variables/anaphora that referred to those structures, then pronouns would be driven by content rather than by coincidental word-spelling.
--Hue Djeimz Djeninz
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