Xorban: commentary

Xorban is a project to build a loglang from scratch but keeping in mind both the ideals and the problems of Loglan and Lojban.  Among those ideals on the language side are the unique decomposability of the speech stream into words, the unique assignment of worlds to grammatical roles and the unique parsing of every utterance.  On the logic side, the chief goal is that the logical structure of each sentence -- and of the discourse as a whole -- be obvious at a glance.  In all of this, the aim is not to be significantly longer than say raw English.  The inherited problems are many, but the ones that have come to be dealt with first include such core matters as the need for unambiguous anaphora, the uncertainty of the limits of the scope of quantifiers (and, perhaps, other operators), and, at the more peripheral, technical issues like "donkey sentences" and statistical claims and parallel arguments. What follows is an attempt to bring up to date all the definite points established in the roughly 600 messages on Engelang in the last month and a half (as of 9/14/12) and lay out some of the disputes that have arisen and some of the tasks that remain.

To provide for the unique decomposability, Xorban continues the tradition of unique phonological forms for each type of linguistic item.  Although phonology and morphology are not yet being worked on, temporary forms are being used in discussions and example.  Under the present scheme, predicates are strings of three or more consonants CCC*, either borrowings from Lojban with the vowels removed, or schematic forms like bcd and fgh.  Variable, the only terms, vowels or V'V sequences V('V)*.  Quantifiers and connectives and other special operators are CV and a few special predicates with mainly logical functions are CC only.  Again, many of these bear suggestive relations to Lojban words.

For unique parsability, the proven structure of FOPL is adhered to,  For efficiency (keeping things a short as possible), the propositional connective are used in Polish Notation form, each connective connects the following two (or, occasionally, one) sentences, so no parentheses are required to indicate grouping.  This requires thinking through what you are to say before you say it -- probably not a bad requirement for a logical language.  The sentential connectives are one usual set, AND (currently je) IOR (ja), and NOT (na), with a couple of interesting additons we will discuss directly.  The quantifiers are restricted, that is, the quantifier atttaches not merely to a variable but to a variable and a sentence containing that variable free and restricts the ran ge of that variable to those things which satisfy that sentence (more details on this later).  The quantifiers are the standard ALL (r followed by the vowel which represents the variable) and SOME  (s) and a third CERTAIN (say) (l) that is meant to form constants through a following context.  This last is controversial and will turn up prominently in the discussion of disputed topics later.  Finally, but importantly, every predicate has a fixed number of terms and all of those terms must be in place.  Various shortcuts have been and will no doubt be further introduced to reduce some of the redundancy of irrelevance of some of these requirements.

So, at the core of every Xorban utterance (so far) is a simple formula, an n-place predicate and n variable, separated, for now, by k: bcdakeki, say, Fxyz in familiar logical terms.  But such a unit is not strictly speaking a sentence, since variables don't designate things and thus this does not say anything about anything in particular.  To bring this into focus, then, we need to add quantifiers which bind the variables and restrict them to particular sorts of things.  So, a fully formed sentence would be like ra cdfa se dfg e li fghi bcdakeki , [AxGx][SyHy][\zJz]Fxyz.  "Each of the Gs stand in relation F to some of the Hs and certain of the Js".  It is worth noting that the position of the ALL and the SOME are fixed in these formulas, once set down, but that of CERTAIN is not, so that in the above case, the Hs which stand F to a particular G may be different from the one that are in that relation to another G, the Js are the same throughout -- what it means to say that l, CERTAIN, forms a constant.  It also means that the same claim could be written as  li fghi ra cdfa se dfge bcdakeki, [\z Jz][Ax Gx][SxHx] Fxyz.

Of course, the formula to which the quantifier attaches -- nor the restriction formula of the quantifier -- need not be a simple formula.  Simple formulae can be negated, na bcdakeki, or two can be joined together with sentential connectives, ja bcdakeki jkla'ake'eko'e.  Nor need all the variables be quantified at once.  Thus, any of these processes, quantifying, connecting, and negating, can be done in any order and any number of times, eventually creating sentences, but then going on to compound sentences from there.

So far, Xorban is a complete FOPL in a fairly efficient format, ignoring the things that are moving toward a language: predicates distinguished by form rather than type face, variables  and predicates that run on for several characters, and the need to separate the various variable that attach to a predicate with k.  The next few features of Xorban seem to be also moving in the language direction -- indeed, most of what will happen with Xorban (or any loglang) after this point is directed toward the language side.  The logic is (pretty much -- we may want to go beyond FOPL some, as Lojban does) done.  The trick will always be to add these language features without losing the parsing uniqueness of the logic.

Item 1.  In addition to na, negation, Xorban has two other unary sentential connectives, ni, affirmation< "it is the case that", and nu, tautology "whether or not it is the case that".  Since these behave syntactically just like na, they present no problems for parsing.  Their exact purpose is somewhat obscure at the moment, however.  ni is strictly redundant, apparently, since an unnegated declarative sentence declares itself to be the case.  One can imagine a rhetorical use, however, to reassert the correctness of a challenged claim.  The second, nu, doesn't seem to have a use on its own at all.  It might be used with je, however, to reproduce the effect of Lojban  binary ju and its variants (though those have never played much of a role).  These perhaps lay the groundwork for some effects later.  Right now they are merely curiosities.

Item 2.  In addition to the usual connectives noted, Xorban has ju.  This is AND with the additional twist that the two sentences connected describe two events that are inherently part of a single event.  The example, of a person reading a poem and another person hearing that poem being parts of the single event of one person reading that poem TO the other person, shows the idea well.  And also indicates the probable usefulness of the connective: keeping the number of separate predicates and the number of arguments for each predicate down by treating complex events as composed of partial events joined together (whether this is more efficient or not is just unclear, as is whether this line will be pursued in later developments).

Item 3.  On much the same line, Xorban now has unary operators which make new predicates from old formulae or sentences.  bV is the agentive marker: if cdfa has come to pass, be cdfa says that e made it come to pass.  Similarly, f makes a predicate true of the following state of affairs: if bcd a has come to pass, then fe bcda says that e is what has come to pass.

Item 4.  So far, terms have all been variables, bound ones at that.  The operator m takes a term and a word and claims that the referent of the term is called by the word: ma 'John' says that a is called 'John' (following the Lojbanic style, the example is usually 'djn'.  At the moment, however, this is just an interesting fact without any linguistic significance, because we are not allowed to replace a by John anywhere.  The best we can do is introduce la ma 'John' and then use this, bound, a ever after (this is, of course, standard Lojban la djan with the understanding that  la is a sort of lo).  While this looks counterproductive, it does point toward the development of an anaphora system, where names and other descriptions are introduced, followed up by their variables for a while and then refreshed with a new use of the description, exactly the same as before, say, to carry human memory on for a spell.  The new description can be viewed as the old one, since l moves smoothly over all manner of intervening objects (well, maybe not all, but more on that later) so all of them can be taken as occurring at the first point, where duplicated quantifiers reduce to a single one.  It is even possible that some s might be picked up in this process, matching the pattern of introductory "a man" and subsequent "the man".  But this has not been clearly developed yet.

Item 5.  The predicate making d is related to m, in that assigns a item rather arbitrarily to its argument.  In this case, the item is a predicate with a free space to take the term for d.  There is no requirement, however, that the argument have that property; it is merely a convenient indicator.  The effect of this mixed with l is, of course, the Lojban {le}.

Item 6.  However, some more or less constants have been fixed to work.  The personal pronouns I, you, we are always a'a, e'e, a'e. These are, however, official abbreviations for quantifier expressions, involving further new predicates.  For "I", the predicate is mslf ("myself"?), apparently only applicable to the speaker of the moment.  bcd a'a then expands to la'a mslf a'a bcd a'a, with the leftward exodus of l stopped at the change of speakers.  "You" is handled similarly with rslf ("yourself"?).  The inclusive "we" requires mn ("is a member of/among") and then as defined as la'e je mna'aka'e mne'eka'e, a bunch to which both I and you belong.   There is also a defined gap-filler, o'e, for those arguments that we don't care about but which have to be present so that a predicate has all its arguments.  This uses the vacuous restriction sm ("something"?) and is given as lo'e smo'e.  But this is clearly wrong, since that would make the gap filler the same everywhere, which is clearly not the intention.  It would be better as so'e smo'e with the understanding that this quantifier should be absolutely next to the predicate involved.  However, even this will not quite work, since two gap-fillers in the same predicate would still be equated, as is not generally the intention,  (These problems seem inheirited from Lojban {zo'e} and require a similar solution -- whatever that is.  Probably a separate set of V'V for this role.) [Even if there is only one sm -- and every other predicate, apparently -- the manner or mode or subspecies or whatever of that one is different in the two places and ought to be marked for ordinary, as opposed to transcendental or meta-, speech.]