On Thu, Jul 12, 2012 at 2:31 PM, And Rosta <= span dir=3D"ltr"><and.rosta@gmail.com> wrote:

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 a= rgument of more than one predicate, it gets repeated. And every bound varia= ble is notated at least twice, once where it is shown bound by quantifier a= nd once where it is argument of a predicate. But this is one and the same v= ariable; 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 wri= te variables at all. For simplicity's sake, I'll describe a notatio= n 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 pla= ce. Each argument place symbol is placed on the appropriate row for the var= iable 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 structur= e ergonomically, in such a way that it is not so verbose or so taxing on th= e memory that the advantages of its logical explicitness and unambiguousnes= s 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 d= iffers 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 prece= dents in terminology). This is a feasible structure, easily realized in two= (and simply in three) dimensions, without anaphora. The case of existentia= l graphs and general topological considerations, however, suggest that anap= hora will be needed in one-dimensional speech. The usual problems with that= are simplified by the canonical location of topics. Multiple topics increa= se the complexity of this but not its basic simplicity. Comments come and g= o (naturally) while topics run on and on (and so are always available for c= onnection).
2. Comments have no inherent places, which need to be filled implicitly whe= n not explicitly, but have only those which are explicitly filled. This mea= ns, 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 bu= t probably a simplification in learning (and possible a reduction in the ne= ed for compounds, many of which are just to add a place to an existing pred= icate or rearrange those places). The bareness of comments means that comme= nt words can be raised to topics directly to do business as properties or e= vents, 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 feasibl= e so far.
**

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