On Thu, Jul 12, 2012 at 6:44 PM, And Rosta <and.rosta@gmail.com><= /span> wrote:

.arpis., On 12/07/2012 23:09:

The common way (speaking as a computer scientist) of avoiding variable repe= tition (and variable naming issues) in formal methods is to use De Bruijn i= ndices (https://en.wikipedia.org/wiki/De_Bruijn_index), but thi= s fails the requirement of fitting in human memory.

Can you give an example of how it would work if applied to a predicate--arg= ument structure? I can't follow the wikipedia article enough to see how= it would work (-- setting aside the memory limitation problem you mention)= .

On Thu, Jul 12, 2012 at 2:31 PM, And Rosta <and.rosta@gmail.com <mailto:and.rosta@gmail.com>&g= t; wrote:

=A0 =A0 Let me try harder to explain:

=A0 =A0 Take a variety of predicate logic consisting of predicates, quantif= iers and variables. In normal predicate logic notation, if a given variable= is an argument of more than one predicate, it gets repeated. And every bou= nd variable is notated at least twice, once where it is shown bound by quan= tifier and once where it is argument of a predicate. But this is one and th= e same variable; the repetition is a mere notational device necessary to li= nearize the string.

=A0 =A0 If the notation could be two dimensional, then you wouldn't nee= d to write variables at all. For simplicity's sake, I'll describe a= notation for only predicates and variables:
=A0 =A0 Use a 2 dimensional grid, infinite in both dimensions.
=A0 =A0 Each 'row' corresponds to a variable.
=A0 =A0 Each 'column' corresponds to a predicate.
=A0 =A0 Predicates are notated by sets of symbols, one symbol for each argu= ment place. Each argument place symbol is placed on the appropriate row for= the variable that fills the argument place.

=A0 =A0 That's the basic data structure for predicate--argument structu= re. A 2-dimensional notation can notate it without redundancy. But spoken l= anguage 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 taxi= ng on the memory that the advantages of its logical explicitness and unambi= guousness are not outweighed?

=A0 =A0 --And.

=A0 =A0 John E Clifford, On 12/07/2012 17:17:

=A0 =A0 =A0 =A0 As far as I can figure from the limited information, &&= #39;s language differs from Logjam in two significant respects.
=A0 =A0 =A0 =A0 1. Instead of a predicate with various arguments dripping f= rom it, the core utterance is an argument (topic, say) with dangling predic= ates (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 ca= se of existential graphs and general topological considerations, however, s= uggest that anaphora will be needed in one-dimensional speech. The usual pr= oblems with that are simplified by the canonical location of topics. Multip= le topics increase the complexity of this but not its basic simplicity. Com= ments come and go (naturally) while topics run on and on (and so are always= available for connection).
=A0 =A0 =A0 =A0 2. Comments have no inherent places, which need to be fille= d implicitly when not explicitly, but have only those which are explicitly = filled. This means, apparently, that the nature of the connection of a comm= ent to its topic has to be specified in (almost) every case, an added nuisa= nce in speech but probably a simplification in learning (and possible a red= uction 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.
=A0 =A0 =A0 =A0 These points are too sketchy to give any notion of the rela= tive size, ease or clarity of an &lang as here conceived, but at least = it looks feasible so far.
=A0 =A0 =A0 =A0 **

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mu'o mi'e .arpis.

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