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Jorge Llamb�as, On 03/08/2012 02:37:
On Thu, Aug 2, 2012 at 2:10 PM, And Rosta<and.rosta@hidden.email> wrote:2. Create a loglang that satisfies the key requirement of unambiguously encoding explicit logical forms in a way that is no less concise than the corresponding natlang or Lojban sentences (which are not unambiguous and explicit).How about using only consonants for predicates and vowels and vowel strings (a, e, i..., a'a, a'e ..., a'a'a, ...) as the variables. Hopefully you would rarely need more than five variables at a time. So for example if "r" is the universal quantifier, "mlt" means "x1 is a cat" and "xkr" means "x1 is black", then "ra mlta xkra" means "every cat is black". If "s" is the existential quantifier, "ntrl" means "x1 is a natural number" and "flw" means "x1 follows x2", then we have "ra ntrla se ntrle flweka" (where "k" is the argument separator for predicates with two arguments): "For every natural number x, there's a natural number y such that y follows x". If "l" is the quantifier "the", then "la mlta xkra", "the cat is black". Connectives and unary operators such as negation would be of CV form where the vowel is not a variable, so if "je" is "and", we have: "la djna le mrye je prmake prmeka": "John loves Mary and Mary loves John".
You'd want to add some mechanism for omitting the variable when it would correspond to Lojban {zo'e}. Since the scheme already allows for the omission of terminal arguments (i.e. "love(x,y)" can be "lvake" or "lva" with the second argument implicit), one solution would be to have different versions of the predicate for each possible ordering of the arguments, tho that's not a very economical use of morphological predicate space: you'd need two versions of each dyadic predicate, six of each triadic, 24 of each tetradic, 120 of each pentadic; and various of the contrasts would often be redundant (e.g. for a triadic predicate with two implicit args, there'd be a redundant two-way choice of predicate; for a triadic predicate with no implicit args, there'd be a redundant six-way choice of predicate). There are more economical schemes, but I think they'd all entail using up a bit of predicate space in order to provide the marking sufficient to allow for implicit arguments.
--And.