Re: [lojban] &Lang

[And Rosta <and.rosta@gmail.com>]

Let me try harder to explain:


Take a variety of predicate logic consisting of predicates, quantifiers and variables. In normal predicate logic notation, if a given variable is an argument of more than one predicate, it gets repeated. And every bound variable is notated at least twice, once where it is shown bound by quantifier and once where it is argument of a predicate. But this is one and the same variable; the repetition is a mere notational device necessary to linearize the string.

If the notation could be two dimensional, then you wouldn't need to write variables at all. For simplicity's sake, I'll describe a notation for only predicates and variables:
Use a 2 dimensional grid, infinite in both dimensions.
Each 'row' corresponds to a variable.
Each 'column' corresponds to a predicate.
Predicates are notated by sets of symbols, one symbol for each argument place. Each argument place symbol is placed on the appropriate row for the variable that fills the argument place.

That's the basic data structure for predicate--argument structure. A 2-dimensional notation can notate it without redundancy. But spoken language is 1-dimensional. Is there a way of linearizing predicate-argument structure ergonomically, in such a way that it is not so verbose or so taxing on the memory that the advantages of its logical explicitness and unambiguousness are not outweighed?

--And.

John E Clifford, On 12/07/2012 17:17:
> As far as I can figure from the limited information, &'s language differs from Logjam in two significant respects.
> 1. Instead of a predicate with various arguments dripping from it, the core utterance is an argument (topic, say) with dangling predicates (comments -- not the standard usage quite but Logjam is not famous for following precedents in terminology). This is a feasible structure, easily realized in two (and simply in three) dimensions, without anaphora. The case of existential graphs and general topological considerations, however, suggest that anaphora will be needed in one-dimensional speech. The usual problems with that are simplified by the canonical location of topics. Multiple topics increase the complexity of this but not its basic simplicity. Comments come and go (naturally) while topics run on and on (and so are always available for connection).
> 2. Comments have no inherent places, which need to be filled implicitly when not explicitly, but have only those which are explicitly filled. This means, apparently, that the nature of the connection of a comment to its topic has to be specified in (almost) every case, an added nuisance in speech but probably a simplification in learning (and possible a reduction in the need for compounds, many of which are just to add a place to an existing predicate or rearrange those places). The bareness of comments means that comment words can be raised to topics directly to do business as properties or events, without a lot of extra detail.
> These points are too sketchy to give any notion of the relative size, ease or clarity of an &lang as here conceived, but at least it looks feasible so far.
> **
>
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