[1]

Unker Non-Linear Writing System[2] 

Grammatical sketch (under active revision; some parts may be deprecated)

by Alex Fink & Sai

"I understood from my parents, as they did from their parents, etc., that they became happier as they more fully grokked and were grokked by their cat."[3]

Our conlang relay 19 entry (the most major text to date written in UNLWS)
Interpretation of the Prayer of St. Francis (a more subtle text in poetic form)
A small love poem  (has another meaning when zoomed out, a UNLWS-native poetic feature)
Our LCC5 relay entry

Contents

Salient links

Premise

Grammar

Metalanguage markup

High-level concepts

Reading order

Linearity in discourse

Rotation and reflection

Glyphs

Binding points, lines and relations

A first example

Relating to relations

Cartouches

Abbreviative devices

Line decorations

Domain emblems

Pronouns

Names

Time pronouns

Modality

Counterfactuals and worlds

Collectivity and distributivity

Collectives

Distributives

Measure glyphs and numbers

Articles

Tense and aspect

Aspect marking

Time marking

Aspects of stage

Micrographs

Scalar families

Location and motion

Lexicon of glyphs

Examples

Salient links

Our active UNLWS design sketchpad

Sai’s early language design essay, NLWS design essay and talk about it

Schuyler Duveen’s Ouwi language and LCC3 presentation

Jim Rosenberg’s diagram poems

The linguistic diagrams from the Palo Alto CARET laboratory

Academic precedents for two-dimensional notations for predicative content:

Frege’s Begriffsschrift

Conceptual dependency, a program of research in classical AI

Our other joint conlang, the Gripping Language

If you’re unfamiliar with linguistic terms like “irrealis”, SIL’s glossary of linguistic terminology may help.

Premise

Non-linear languages have as their aim to exploit the syntactical possibilities that are opened up by writing in an ambient space of more than one dimension.  An utterance in a spoken language is a succession of tokens, each next to just two others.  By contrast, in a non-linear language, any number of tokens may be connected to any others, making any shape of network.  

The non-linear language described here, named UNLWS[4], is a pilot implementation of this ideal, meant primarily to help hash out the understanding of the design space of non-linear language through bottom-up design.

UNLWS is intended to be written by hand, with a pen or the like.  Accordingly, shading and stroke heaviness have roles, but the role of color is at best marginal.  We have completely excluded from our palette such things as complex precise graphics, widely varying zooms, animation, interactivity, etc., which cannot reasonably be drawn by hand.  This is a (mostly[5]) simplifying assumption to make thinking about and designing this language easier; it does not reflect a bias against computer-native media.  In the future, we may design variant non-linear languages to take full advantage of a native computer medium, and they may contain such features.

Grammar

Metalanguage markup

The following metasymbols belong to the description language, not UNLWS.  Note that they are filled in in light blue: a circle that is white on the inside is a real circle.  UNLWS avoids solid regions as finicky to draw by hand (although cartouches may in fact be distinguished by a background color).

binding point

[ ... ]

(in glosses) subunit; ~= syntactic constituent

glyph

needs work

line decoration

deprecated

arbitrary amount of UNLWS text

derived form

cartouche

variant form

High-level concepts

Reading order

In keeping with our renunciation of linearity, reading order is intentionally not defined in UNLWS texts.  Non-linear texts can often be rendered in multiple ways in linear language, depending on where one starts and how one traverses the graph.  As one consequence, UNLWS lacks voice; indeed, it lacks syntactic relations (“subject”, “object”, …), as reified notions different from the grammatical relations of each individual word.  One sentence could be read indifferently as “I bought a muffin from Bob”, “Bob sold me a muffin”, etc.

However, one should not take away from this that information structure has no place in a non-linear language.  Languages frequently have different sentences with the same truth conditions, whose difference is information-structural: the different sentences call out different participants as topical or in focus (which in turn can exert influence on “real meaning”, e.g. perception of agentivity). Many natlangs use fronting and backing transformations for information structure, which is a well-motivated technique in view of human retention / recall / salience biases on time-sequenced items.

A non-linear language optimized for human cognition could be designed to exploit the same biases to the same ends, e.g. by prompting certain reading orders. One shaped by centuries of native usage might even be likely to. At the very least, a completely hands-off approach to the effects of reading order is not necessarily an unalloyed boon.

At present, our nods to information structure in UNLWS are only weak: e.g. focus is indicated by bolding lines. Perhaps this will change in the future.

All the subtleties of reading order and its effects are only compounded when one looks at larger scales, on which discourse structure is relevant. 

We presume that all texts exist on an infinite 2D plane.  We view pagination as a misfeature of books and similar media — computers bring us closer to the ideal — and we do not yet have a workaround (aside from heavy pronoun use).

Linearity in discourse

As far as possible, we extend non-linearity to the overall discourse structure of texts.  We expect that many discourse structures which are presumed to be necessarily unidimensional have serviceable alternatives that aren't. Ceteris paribus, we prefer nonlinear representations.

The main truly linear thing we must deal with is Time (supposing no wacky chronophysics). UNLWS has several linear elements which are temporally derived. For example, tense/aspect markers and micrographs both treat time as an axis (radial and polar, respectively).

There are some things — like conversation and narrative — that are severely affected by fully adopting a nonlinear ethic[6].

We have only started to develop how to hold a conversation in UNLWS itself. As we currently have it, it's a very, very different kind of thing than linear atomic turntaking. Rather, it's a sort of ongoing mutual edit of a shared structure, where revision history playback (or live observation) expresses the 'conversational' tone expected by linear conversation, and the fixed form expresses the integrated totality of what the participants have expressed. Different ink colors help to distinguish participants, but there are no boundaries preventing one participant from using another's ink as part of their own expressions.  Indeed, there are a few special conversational variants of glyphs which are meant to be easier to drop in to an already-drawn passage than the normal forms; these are recognizable by their use of two ink colors. (It’s a pity that it’s so fiddly to edit pencil or pen drawings.)

Stories, likewise, could well be nonlinear if one isn't fixated on the temporal sequence of events. Nonlinearity frees one from excessive focus on the history of a single actor in a story, some particular way of reading the whole, etc. Instead, the focus can be on the structural interrelationship of the events and actors; on similarity between higher and lower level structure; etc.

That said, these are our cognitive-aesthetic aims, and we don't really know whether they will turn out to be feasible. UNWLS is a philosophical language sine qua non, meant to pose these kinds of questions, and so far we can only speculate about their answers.  

Rotation and reflection

In UNLWS, overall orientation is not phonemic, so to speak.  That is, turning the page on which an UNLWS text is written does not change the meaning.

Within a text, the orientations of the glyphs are chosen for syntactic reasons of layout, to avoid sharp bends in the connecting lines, to make these lines shorter, or just to improve aesthetics.  If we refer in this grammar to absolute directions on the page (“up”, “right”, …) we’re just talking about the way we drew the example in question.

Relative orientation of glyphs with respect to other elements of the same text, for example what points at what, may be significant.  In other words, UNLWS does not use absolute left-right / up-down axes; rather, it uses local radial / polar axes, relative to each element.

Mirror reflection is also phonemic: flipping things over makes a difference.  Like most phonemic contrasts it makes sometimes more systematic differences (flipping a graph inverts the sense of an axis), sometimes less (“be next to” becomes “be in” when flipped).

Glyphs

A glyph is the basic lexical element of UNLWS, though it might not always be possible to tell where one glyph ends and another begins.  A glyph expresses a predicate, more or less.

Glyphs are a single lexical class.  There is no syntactic difference between ‘nouns’ and ‘verbs’ and whatnot.  Some glyphs (like "X be cat") might be implied by their gloss to be ‘more nouny’ than others (like "X be happy" or "X eat Y"), but this distinction does not exist in UNLWS itself, nor does the implied voice or first-argument focus that the linear gloss is forced to express.

Some things to keep in mind regarding the form of glyphs are that

  1. glyphs have binding points (drawn ) that expose semantic relations
  2. glyphs may have derivational morphology — structurally integrated modifiable components that alter their meaning
  3. glyphs may have violable boundaries, and other glyphs can be contained within them or otherwise interact with their form; the form may be designed to accommodate this
  4. glyphs may be visually iconic of their semantic or syntactic structure

Binding points, lines and relations

Every glyph includes a number of binding points, one for each of its arguments, the semantic roles involved in its meaning.  For instance, the glyph glossed as eat has two binding points—one for the thing consumed and one for the consumer.  The glyph glossed as (be) fish has only one, the fish. Often we give glosses more like “X eat Y”, so as to give names for the binding points (X is eater, Y is eaten).   

A basic utterance in UNLWS is put together by writing out a number of glyphs (without overlaps) and joining up their binding points with lines.  When two binding points are connected, this means the entities filling those semantic roles of the glyphs involved coincide.  Thus when the ‘consumed’ binding point of eat is connected to the only binding point of fish, the connection refers to an eaten fish.  

This is the main mechanism by which UNLWS clauses are assembled.  To take a worked example, here are four glyphs:

“A is me”

“B eats C”

“D is a fish”

“E is large”

Putting A and B together, and C, D, and E together, assembles the text

  “I eat a large fish.”

The way we prefer to think of this is that we have stretched out the lines on each glyph that the binding points dangle on, and brought the binding points themselves into direct contact.  The stretched lines are imbued with the meaning of the relation that the referent of its binding point has to the meaning of the glyph.  For instance, the relations expressed by the two lines of eat are (approximately) being consumed and consuming.  The relation of an arbitrary line is called rel in this grammar.  

These lines are the subject of many operations in UNLWS.  As three examples, lines are the position of articles; their thickness can be varied to indicate focus; and other lines may be drawn to them to achieve the effect of embedded clauses (see just below).

Lines may be lengthened arbitrarily, for reasons of style or layout.  They can freely curve somewhat to allow for syntactic rearrangement, but should not make needlessly large curves, let alone sharp bends, as these may look like elements of glyphs. When the binding points of just two lines meet they should come together smoothly, with no kink or discontinuity.  In this case the binding point is more abstract, and is not a visible element with a precise location.

Lines may also be crossed for layout reasons, though we don’t like to.  A four-way meeting of binding points should be drawn with angles that make it obviously not a crossing.

Relating to relations

To bind a binding point to a relation itself (as opposed to one of its participants), it is placed slightly off the line of that relation.  A similar gap can be used to bind to a glyph in the action nominalization style (as in “I disapprove of eating glass”), or in fact to a whole cartouche.  

Binding type

Gloss

Notes

X rel [A rel B]

This gap is called the rel gap. It is distinct from the irrealis gap, below, in that it sits on a rel and not a line.

X rel [a gestalt of the situation ▷]

A rel gap on a glyph.

For quoting literal speech and similar purposes, one wants instead a mention construction.  (By default, relations are by use, not mention.)

Binding type

Gloss

Notes

X is a signal of meaning “Y” (as mention)

This is for indirect quotation.  It’s typically used with a cartouche.  But there is a binding point at Y, and so is legitimate for “X is a signal referring to Y”.  

X is (a signal of) form “Y” (possibly transcribed)

This is for direct quotation, whether of material in UNLWS or other written languages, colours, pictures, ...

In UNLWS text being quoted for form, it is generally assumed that the layout of the glyphs and lines doesn’t matter, but everything else does (though this is convention, not a law of grammar).  In any event, no semantic interpretation is carried out on such text.  

The two glyphs above can be composed to yield  “a signal with form N has referent Y”, that is “Y is called N”, “Y has name N”.  N can easily be text in a written language other than UNLWS, or a symbol of any sort, for foreign names.  (If the quoted name is being semantically translated into referential UNLWS text, there would be a binding point at N.)  However, this is not the normal way to refer to someone by name in UNLWS; it has more the force of “Y is called N”.  For native-style names, see the Pronouns section below.

One example of a relation which commonly has relations as its arguments is causality.

Construction

Gloss

Notes

[A rel A'] causes [B rel B']

While causality can take irrealis marking (see below) by putting a gap after the tip of the arrow, it cannot take a realis-hook, as the rels themselves specify their own reality. Irrealis causality is e.g. "I don't want to have gotten dessert only because I ate my vegetables".

A causes [B rel B'], i.e.

[A volitional rel ...] causes [B rel B’]

Causation fundamentally holds between relations.  When the causer A is not a relation, it stands in for “a volitional action of A.

A causes B / A makes B, i.e. [A volitional rel …] causes [B exists]

Likewise, when the causee B is not a relation, it stands in for “the existence of B”.

This example happens to use both contractions. Note that contractions bind directly, whereas the full version binds with a rel-gap.

Another is the relation of being evidence.

Z supports (the fact) [X rel Y]

This is how UNLWS handles evidentiality: one adjoins another clause Z as a support, indicating one’s source of the knowledge.  “I perceived [rel]” and “I perceived a mention of [rel]”  are common values of Z used to render direct and indirect evidentiality.  However, it’s probably a fairly pragmatically marked thing to indicate evidentiality in UNLWS (unlike in natlangs which grammaticalise it).

Cartouches

A cartouche is something that surrounds a section of text, to group it together.  The most ideal way to draw one in UNLWS is as a subtly shaded background behind the section of text.  Partial cartouches, where the shading fades on its inside to the same background color as the outside, are acceptable too.  That is, cartouche boundaries may be drawn as lines which shade off gradually on one side.  For practical pen-and-paper usage, cartouche boundaries may be drawn as lines of any other sort whose timbre is distinct from ordinary lines.  Drawing them identically to ordinary lines would be confusing and is to be avoided.  

Regardless of which kind of cartouche is used, it is perfectly acceptable to draw only whichever parts of the boundary are necessary for clarity.

It is frequent that lines penetrate the boundary of a cartouche, to make binding points inside and outside the cartouche coreferential.

One frequent use of cartouches is to provide a binding point for some text as a whole, rather than any particular element.  This is used, for example, by mentioned text.  In this case the line binding to the cartouche will terminate in a mention marker, and not physically connect.  

A second use of cartouches is to explicitly indicate scope for certain grammatical elements, for instance, quantifiers like “all”, or the irrealis marker.  (This can become rather important when there is coreference crossing the boundary of the scope.)

Abbreviative devices

Line decorations

A line decoration is a type of glyph with a binding point which isn’t connected by any stroke to the rest of the glyph, like  “X be good”.  When a line decoration takes a rel-gap on this binding point, no line need be drawn at all.  For example, “it is good that X rel Y” is typically written as , though it can also be explicitly written as .

Line decorations can take the stroke denoting negation across their body (see “Modality”, below).

Semantically, line decorations express broadly mood-like notions, such as a positive or negative attitude towards, expectation of, or evidence for a relation.

Decoration

Gloss

Notes

X rel Y, expectedly

… unexpectedly

… which is good

… which is bad

To attribute these attitudes to a particular holder (e.g. “... which the president expects“), use the glyph think, which can incorporate a line decoration.  E.g. is “A expects X rel Y”.  “Think good” and “think bad” are particularly frequent; they are used, in various mode and tense/aspect categories, to express “(not) want”, “(dis)like”, etc.

Line decorations can take micrographs to indicate variation over time. For example, “I was hungry [= “wanted to eat”] but was mostly sated once I ate” would be expressed with this device.

Domain emblems

Sometimes, a family of glyphs will all frequently collocate with themselves and each other.  For instance, UNLWS’ kin-terms are built up of chains of the glyphs “be a parent of” and “be in a relationship with” and a few others, like gender indications.  On a broader scale, most texts, if they use technical terms at all, draw them from only one or a few fields of study.

In UNLWS, a domain is a collection of glyphs like this that furthermore share a graphic element, the domain’s emblem.  For instance, the basic kin terms are a domain, whose emblem is a figure eight.  Domain emblems can be partially or wholly omitted in regions composed of glyphs from the domain, as long as the emblem is retained near the boundary of the cluster in order to delimit it. Also, glyphs from outside the domain can intrude into the region, where this is unambiguous.  

For instance, “A be a niece or nephew of B” would be fully written , but is usually abbreviated via domains as .  (As an aside, the compositional meaning of this sequence would include “A be a child of B”; that is only excluded by implicature.)

Pronouns

As a rule, pronouns in UNLWS can be thought of as merely a layout device: each set of coreferential pronouns is interpreted as though it was a single binding point.  (We exclude first and second person pronouns, which are ordinary glyphs with deictic meaning, from this class of “pronouns”.)

Pronouns are equilateral triangles.  Here are three examples:   As many different pronouns as necessary can be made by filling the triangles differently (including color fillings, if the medium supports color).  Semantically meaningful fillings, or fillings otherwise reminiscent of words, are encouraged: for instance,  would be a good choice of pronoun for an animal.

As a rule of thumb, the more intricate the filling of the triangle is, the longer is its spatial range.  An unfilled triangle is meant for short-term local uses: in a text with two widely separated pairs of empty triangles, the pairs would likely be read as having two unrelated referents.  If the triangles had instead been (say) densely cross-hatched, they would likely be read as four references to one thing.

Often multiple pronouns are needed in the same place.  For compactness in this case, UNLWS provides multiple-bound pronouns, which have the same function as multiple separate pronouns.  Their form is .  

It is not yet clear how the filling namespace of multiple-bound pronouns relates to that of single-bound ones.

Names

UNLWS-native names are a special class of pronoun, to wit, pronouns whose range exceeds the confines of the particular text they occur in, and are coreferential among many texts[7].  

Formally, the hint that a pronoun is a name is that its “filling” transgresses the boundary of the triangle.  For personal names, a default form for this outer filling are epaulets of the form  .  For other sorts of names, one can express a broad semantic classification with the epaulets: for instance, names of cities TODO

Time pronouns

Time pronouns refer to a time, which can be a point or an interval, or framed as either in different contexts.  They appear in the following constructions:

  1. In conjunction with an aspect marker, as the time part of tense-aspect marking (q.v.).
  2. Alongside a temporal micrograph, identifying a point or interval on that line as the referent of the pronoun.

The time pronouns include three with fixed syntactic or deictic meaning, plus a family of freely-assignable ones, like the ordinary pronouns.  

Time pronouns have alloglyphs when they are being used to mark a region.

Point

Region

the focal time, i.e. the implicit time of all relations involving this binding point, and others joined directly to it

the time of writing, i.e. now

[TODO: the time of reading]

[TODO: other time pronouns, related to ordinary pronouns.  I would like a wedge, decorable as pronouns are]

Modality

The forms glossed as questions below do not have the illocutionary force of questions baked in.  They can thus be used e.g. in embedded questions: “I don’t want to know what (if anything) the cat ate” would bind the object of “know” loosely, with a gap, to the “what” in “the cat ate what”.  

Relation

Gloss

Notes

(real) X rel (irrealis) Y

This irrealis gap indicates an irrealis relation. The (optional) hook indicates the side that is realis.  Without a hook it is understood that both sides are realis, and it’s only this single relation which is not being asserted.

The hook can fuse with the expected line decoration, and possibly others. See e.g. food in the lexicon.

Also see the next subsection for a more elaborate mechanism for irreality.

X not rel Y

X not rel (irrealis) Y

A contraction of negation and irrealis.  

This is used for negations in which one doesn’t want to even assert the referentiality of one side of the rel. E.g. “I’m not eating fish” should use this, unless “someone’s eating fish but it’s not me” is meant.  

Is X rel Y true?  -or-

(embedded question) Whether X rel Y [is focal].

X rel what? -or-

(embedded question) What X rel [is focal].

“Nothing” is an acceptable answer to “X rel what?”, i.e. the question shouldn’t be taken as presupposing some answer exists.

Counterfactuals and worlds

UNLWS has a facility for expressing possible and/or counterfactual worlds, which is used, for instance, to handle “if”.  This is along the lines of work such as Lewis’ counterpart theory [there are probably better citations].

A world is expressed as a double-lined cartouche, with an outer dashed line with long inter-dash separation surrounding an inner cartouche boundary of any valid sort.  Binding points and relations taking place inside the cartouche are interpreted in the world.  Lines may also cross the cartouche boundaries, e.g. to state something hypothetical of a real referent (for Lewis, its counterpart).  

“If X, Y” is analyzed as “in worlds where X holds, Y holds”.  The bare plural “worlds” here glosses the generic article (see below).  [TODO: pictures]

The gap in a rel line for irrealis modality can be taken as creating a world, too.  The question of whether it really does, I think, is academic.  

Collectivity and distributivity

Collectives

UNLWS has two related constructions for handling various sorts of multiple-hood. (Cf. also the generic, though from a language-internal perspective it is unrelated.)

For collectives, multiple referents engaging in a relation as a group, UNLWS has the following:

Y be a group of A and B

Can have more lines in the join (i.e. A,B,C,D,....)

Y be a group of Xs (of size/measure M)

M is optional.  It can be a number; we haven’t decided whether it can be a measure of another sort.

With M unspecified, this is UNLWS’ most basic analogue of a plural.

Y be a group of M1 A1s and M2 A2s and … and Mn Ans

Most general form.  

If the measure M is omitted, it is often taken to be one.  This happens when there are multiple As: for any A which is explicitly mentioned but has no measure specified, the number is interpreted as one.  But sometimes an omitted measure is taken to be unspecified: this is the case if the corresponding A itself is unspecified.  Thus , with no measure on the bottom line, means “Y be a group containing (one) A (and any number of other things)”.  This is the construction used for “A be a part of Y”: e.g.  “I have two hands”.  (There is a derivation, below, to make a part-whole interpretation explicit.)

Another useful deployment of this latter form is  “A be a member of the group consisting of A1 and A2”, that is, “A be either A1 or A2”.  This is the usual UNLWS rendering of “or”.  It also serves for clausal “or”, with A bound to “be true” and A1 and A2 bound via rel-gaps to irrealis relations.

Here are some derivational variants of the collective.

Y be a gestalt mass of As

E.g. “sand” can be ‘a gestalt mass of tiny rocks’.

Here the default number is indefinite, and expected to be large.  The form intentionally occupies the spot where a number would otherwise be written.  

Substances whose lexically basic form is not countable (e.g. “water”) have a family resemblance to Y here, with a line bound on the top crossing near the binding point.

Y be a whole including part A

There may freely be more than one A in the grouping construction in either of these.

...

[its ‘small’ analogue]

Y be a group of many … few As

This is a scalar family.

Distributives

For distributives, referents engaging separately in parallel relations, analogues of the basic collective constructions exist, lacking the middle bar.  Thus means “A rel Y, and B rel Y too”.

Distributives should really be thought of as abbreviations for multiple utterances that share some of their material, with the shared pieces drawn but once.  We tend to visualize these as stacks.  

For example,  “I eat fish and so do you” represents the stack [8].

One can make some glyph coreferential across all the layers in a distributive with a binding point.  The construction  would compositionally be read as a stack of A and A; by convention it is in fact a stack of whatever size consisting entirely of A.  See the “separately eat the same fish” example at the end.

If there are several distributives in a text, they may be interpreted with the sense of “respectively”.  Below is a simple case.

A and B (separately) ... D and C respectively;

that is, A … D and B … C

It might seem unnatural that we have glossed this as “D and C respectively”, with the pairings crossed, rather than “C and D”.  To be honest, this ordering is merely strongly suggested; either is possible.  The principal convention for how to line up the elements of multiple stacks is rotational (jibing with global rotation not being phonemic): the clockwise-most element of one stack should be matched with the clockwise-most element of the other.

A and B ... D and C respectively

A respective marker is an angle of around 30° placed near a set of stacks, to show whether they are to be interpreted respectively or independently (that is, as a programmer might say, as a Cartesian product or as a zip).  

Like pronouns, the insides of respective markers can be given a filling.  Stacks with identical fillings are respective, and stacks with different fillings are independent.  (The degree of filledness has the same heuristic interpretation too.)  

The directions the respective markers are pointing indicates how the two sets of ends in the stack should be matched up in: they should be matched tip to base on both sides.  

In the examples below we have placed the markers at the ends of the stacks, but for long stacks it is better to put them in matching positions near the middle, or even repeated, for ease of reading.

A … C and B … D

A … C and A … D and B … C and B … D

There is a special syntax for breaking up collective and distributive constructions among instances of a pronoun, so that not all the members of a group or stack have to be mentioned in physical proximity.  Below they are demonstrated for two-member collections.

equivalent to

equivalent to

Broken distributive triangles share a filling namespace with respective markers.  That is, if the broken triangles are filled, then respective markers with the same filling refer to the same stack.

Collectives and distributives both have conversational variants.  The red material is drawn by the later participant.

equivalent to

equivalent to

Measure glyphs and numbers

The table below shows some measure glyphs in blue set in a one-item collective construction in green.  These glyphs have generally simple forms, and are made distinctive by their placement on a collective or a distributive or similar frame.  For instance, in  “be (a group of) two cats”, “two” is conveyed by the red stroke.  See the bottom of this Conlang list post for discussion of how fractions behave within a measure glyph.

The measure can be the indefinite article to explicitly mark it as arbitrary.  This is one UNLWS analogue of a plural.  On the collective it has a special ligated binding, .  On a distributive it does not imply coreference, in contrast to the  construction (and accordingly it is not very useful).

Numbers are a kind of measure glyph.  A given number doesn’t have a single canonical expression; there are various possible ways to build it.

Small enough primes (likely more than those shown here), and a few other elementary things, are monomorphemic.

The plural is the indefinite article explained above.  –1 and 0 are both inspired in form by negation.  The primes p are loosely and irregularly inspired in form by p1.  

 

Left-to-right juxtaposition multiplies.

Top-to-bottom juxtaposition exponentiates.  Stacks may contain products, and may themselves be multiplied; exponentiation has precedence over top-level multiplication.  (How to handle deeper groupings isn’t decided yet.  Cartouches?)

The stacks themselves are bottom-associative.  

Top-to-bottom stacks with a dot above the line are instead power series, i.e. base constructions.  The base is placed to the left, and takes a default value if there is nothing to the left.  

A double dot is a decimal (or whateverimal) point, i.e. comes above the zeroth term of a Laurent series.

To discuss a number as an independent mathematical object, as opposed to the quantity of a group, use the above forms with a binding point on the lower end of the vertical green line: e.g.  “be the number 13”.

Our current proposal for ordinals is compositional: for instance, “be the sixth time I eat” can be rendered , i.e. “be an instance of my eating temporally after five such”, with the usual Gricean implicature that “five” means “only five”.  The highlighted “be temporally after” can easily be replaced by a mini-graph  to get “sixth Adj-est”.  Note that where ordinals are being used merely as handles (“19th Street”, “Room 101”), UNLWS would rather use a name consisting of the number.

Articles

Articles are placed on rel lines, and act like quantifiers. If no article is specified, which one is meant is (as usual) determined by pragma; mostly it’s the indefinite.

A  B

indefinite

A  B

correlate
obsolete meaning: indefinite

A  B

generic

A  B

universal (“all”)

A rel with an indefinite article means “some A is B”, with an existential quantifier.  Its form is meant to suggest the number 1.  The indefinite is the only article which is symmetric (“some A is B” and “some B is A” are equivalent), and it is the only article free of scoping problems.

A rel with a correlate article means “a greater proportion of As are B than members of the population from which As are drawn“.  For instance, it’s true that a correlate American is a baseball fan: even though a generic American might not be a baseball fan, more are, proportionally, than residents of other lands.  Another gloss is “being an A is [possibly weak] Bayesian evidence for being a B”.

A rel with a generic article has the meaning of the English bare plural construction in “As are B”, e.g. “birds fly” -- that is, “the A you think of by default, if I don’t say anything else about it, is B“.  Whether these statements are true is determined by the availability heuristic in the cognitively normal way.  (The generic doesn’t really have anything to do with quantity.  When humans try to think about proportions, they’re usually actually applying the availability heuristic.  The correlate is available for one form of actual proportion statement.)

A rel with a universal article means “all A are B”, in the strict sense.  We consider the generic less marked than the universal.

It is possible to put an article on each side of the same rel line; this means the conjunction of the individual meanings.  For instance, a double universal means “being an A and being a B are equivalent”.  A double correlate means “being an A correlates with being a B”.  A double generic might be appropriate on “women have breasts”.  A universal-cum-indefinite would be “all A are B, and (to be sure) there is at least one A”.

The non-indefinite articles have scopes on the A side.  It is not decided how to make these scopes explicit, but perhaps a cartouche can be used, with the generic marker straddling its boundary.  

One might expect to see a definite article among these, but UNLWS lacks a definite category.  Most definite NPs in a linear language are coreferential with an earlier NP, but the preferred strategy for coreference in UNLWS is simply connecting two binding points, even when one of them was written by one’s interlocutor; this has no good linear analogue.  Pronouns are also available for coreference, where direct connections are inconvenient.  Referents which are essentially globally unique (“the moon”, “the President”) typically will not use an article in UNLWS.  Referents foregrounded by the situation (“hey, did you see the guy in the tree back there?”) will use a deictic expression.  Referents foregrounded by an earlier referent (“I went to Applebee’s last night and the waiter was really rude to me”) will typically have some relation made explicit (in this example, likely “X serves Y”, or perhaps just colocation), though in several cases one can get by without.

Tense and aspect

Aspect marking

The construction of the (non-iterative) aspect markers is based on a segment, extending from the counterclockwise to the clockwise side, whose length is the duration for which the relation denoted is true.  Thus, marking the glyph as at a time inside this segment signifies the imperfective; marking it as at the whole segment (which collapses the segment to zero length!) signifies the perfective; etc.

The iterative imperfective is not to be understood as being in the middle of the gestalt of a repeating sequence of punctual relations, but merely as repeatedly being in the middle of some relation.  The iterative perfective is closer to this; the graphic similarity of the iterative perfective to the simple imperfective is intentional, and reflects this gestalt view.

Normal

Iterative

Perfective

Imperfective

Terminative

Inceptive

Note that, although tense and aspect markers bind to glyphs in all our examples, they can also bind to relations.

We have used the ad-hoc modification  of the imperfect aspect marker to mean “forevermore into the future”.  This needs enlarging into a flexible system; the question is probably the same one as micrograph axis labelling.  [In any event this precise form is surely obsolete; it should be a circle that means ‘all’.]

Time marking

One or more time pronouns, except for the focal time pronoun, can be placed on the aspect marker to relate their times to the time of the relation.  This is most commonly done with now, as in the following examples (accompanying the perfective aspect):

future

present

past

In general these placements locate the time referred to by a pronoun respectively before, at, or after the time of the decorated glyph (observe that later times are again the clockwise side).  Thus, the above future is literally “now is before this relation”.  Multiple different time pronouns may also be present, with the expected sense.

The line which forms the stem of the TA marker may be thought of as being the focal time pronoun, which indeed means “the time of this relation”.  In that sense, this pronoun is present in every TA marker.  (In fact, TA markers can be thought of as a lot like contractions of Y-axis-less micrographs, q.v. below.)

One can also use identity lines between time-pronoun binding spots on multiple TA markers, or a TA marker and a micrograph, to express more complex relationships, e.g.  (triangle, then hexagon).  

Aspects of stage

[These are old and may want revisiting on principle.]

Aspects of stage are aspects which relate the duration of a situation to the natural progress of a (telic) situation of its type.  This includes, for example, the contrast between “finish” and “stop” (without finishing).  

In UNLWS, aspects of stage are expressed on the aspect marker much like time is, treating the “natural” beginning and end points of the situation similarly to time pronouns.  These points are marked by the outward tip of a diagonal slash. The examples below use the terminative aspect marker, but any aspect marker (including the perfective) can be used.

  natural inception

  natural termination

after

 

terminate after (normally) beginning

stop late, stop overshooting the finish (!)

simultaneous

terminate at its beginning

finish

before

terminate before it began (!)

stop without finishing

The two boxes marked (!) don’t ordinarily attain for achievements, when the “natural” span of an event is a kind of whole — it’s hard to keep eating a muffin after the whole thing is gone — but pragmatics can justify them: perhaps one keeps picking crumbs off the muffin wrapper past the point when anyone else would have thrown it out.

Some combinations of these can express notions to do with the natural span of an event. For instance, having a natural termination after an inception means “begin something that will someday be completed”.

Here’s another set of examples of potential pragmatic values of these aspects.  If the base glyph is be alive, forms based on the terminative marker, like those in the table, could be interpreted thus (reading top to bottom in each column, columns left to right): die after birth (unremarkable); die during birth; be aborted; die too old; die at a natural age; and die too young.

With an inceptive marker, they could mean: born late; born naturally; born premature (perhaps by Caesarean?); reborn after being dead (zombie? coma remission?); reborn during death (ditto); and born mortal.

With an imperfective marker, they could mean: live after being born (unremarkable); be alive (already) during birth; be alive before birth (perhaps a claim about fetal sentience); be alive after death (more zombies?); be alive (even) at death (fighting to the last?); be alive as a mortal.

Micrographs

Micrographs are small, one- or two-dimensional graphs that compactly express the variance of some attribute(s).  One of their inspirations are the sparklines of Edward Tufte.  Our graphs share the property of full integration into the text, but are not necessarily of small size.  

The micrograph glyph in its most basic form is  which might be glossed “Y hold to the degree depicted in G”, or “Y vary as graphed in G”.  G is where the graph goes; the green point is not actually a binding point.  Y is the quantity varying on the vertical axis through the other two endpoints of the glyph.  The attribute Y increases going up the axis (in the orientation drawn here).  If Y binds with a rel-gap, the quantity being graphed is, by context, either the intensity of the rel or glyph it binds to, or the degree or phase of its completion.  

The variable on the other axis may be indicated with another instance of the same glyph, or else as the X in the form .  A frequent default is that the other variable is time (and behaves as an independent variable), with the future direction being further away from the glyph.  In this case, X is connected to a TA marker (usually the TA marker on the glyph Y is on, but possibly another one).

Micrographs may have scales and labels for their axes.  A bar on the outside of a graph parallel to an axis exposes a binding point for the length of that interval.  Thus in , M is the length of time depicted (its line emanates downward).  [How does this work in the case ?  How do we indicate the zero point, or other instants?]

There need not be a variable on the X axis.  For instance, the form  expresses “Y holds to a large degree / intensity”, and is the most general-purpose translation equivalent of “very”.  In this way, a single-point micrograph can effectively serve to make out of any glyph a scalar family for degree or intensity.  

[[Genuine one-axis graphs for degree, distribution, etc.  Sai’s standard-deviation widget.]]

The independent axis in a micrograph may also be a distributive stack (or a respective marker) to compare the extents to which individual things are Y.  This is how UNLWS handles comparatives.  For example:

 “I’m less asleep than you and as asleep as the cat.”

If it is clear, one can allow dots in this construction to align vertically, and label them from any side.  The dependent axis may also be a distributive stack or respective marker if the graph consists of multiple curves which can be clearly associated to the elements of the stack.

Another minor form of the micrograph glyph has the X axis only, and looks like .  This can be useful e.g. to compare the intervals of time that various processes run, without saying anything about their intensity or phase.  On the timeline, a tickmark indicates the time being asserted of X in the rest of the clause (the relative present tense), and a dot indicates the absolute present.

Scalar families

As a rule, glyphs which denote gradable properties, like “be large” and “be small”, tend to form scalar families.  These have a movable or stretchable or turnable or … element, whose situation can be continuously adjusted to refer to various points on the scale.  For example, here are glyphs for five different points along the continuum from “large” to “small”:

Location and motion

Glyphs which pertain to the positioning and motion of things in space have the feature that the relative positions and, especially, orientations of multiple such glyphs in them have an iconic semantic function.  The highest aim of this subsystem is to allow one to speak of spatial situations in as cleanly iconic a way as possible, amounting to drawing a map.  (One may bound this orientation context by a cartouche, if necessary).

all of these are yet to be drawn

be a figure object

be a ground object

positions of ground objects: outside and in.  both-sidedness.  boundaries.

have shape

be the direction of gravity

move

have facing

turn

If a direction indicator comes between the lines in a grouping construction, it indicates that the order of the elements in the group matches the orientation context.  For example,

 “A is the lower part of Y”.

Lexicon of glyphs

Many UNLWS glyphs share subregularities and family resemblances among their forms.  For instance, the  stroke in “cat” and “dog” is a base for, approximately, mammals.  It appears closed in “sapient”, and “fish” is built on a variation with sharper bend.  One might call such shared elements radicals.

The table includes select variants (related, but not by a regular process) and derivations (including compositional constructions).  

Glyph

Gloss

Notes

Etymology

X exist (incl. abstractly); (of a rel) X be true

TAM must be placed at an angle, so this is not confused with ‘be in a location’.

a simple shape

A be at B; A and B be colocated

Contrast with the figure-ground version, below; here, A and B have equal status.

A be a (physical) thing

be in (a location)

A (figure) be at, outside B (ground)

A be in(side) B

X have property, be characterised by Y

Frequently used in pairs with the Ys connected, rendering ‘X1 be like X2’.

X cause, make Y

X and Y are often rels.  Directly bound X means “a volitional action of X”, i.e. a relation involving X which X intended.  Directly bound Y means “the existence of Y”.

arrow of causality

X (act) in order to Y; X try to Y

[incorrectly formed]

Compositional.  Direct bindings as for ‘cause’.

Can have a ligature between the arrow and the tilde.

For a surer version, use ‘expected’ where this has ‘cause’.  Also consider ‘think’.

it would be good (for the actor in X) if X caused Y

X intend Y, Y happen through volition of X

Y is often a rel.  Directly bound Y means “the existence of Y”.

broken cause, as if irrealis

X intend that [X rel …]

ligature

X can, is capable of (causing) Y

This is not alethic possibility, but is specifically for planning-capable agents.

Y is usually an irrealis rel; direct binding works as in ‘cause’.

a form which sits on a line nicely

Z support, be evidence for [X rel Y]

Used for evidentials; see discussion above.

X be sapient

older sense “X be human”; sapience is usually the more important thing.

(human) head with hair on top, on legs

X be at least semisapient; X be the sort of thing which gets empathically attributed agency

older obsolete sense: "I [the author]"

reduction of sapient?  But the corner is unjustified.

X be cat

two cat ears over a nose

X be dog

panting tongue

X be pig

snout and tail

X be bird, flying creature

Our taxonomy of creatures is functional rather than phylogenetic.

vee-type bird

X be rodentoid

tooth

X be fish, swimming creature

The base stroke of this, more bent than mammals, serves as a family resemblance stroke in the below.

alphoid (e.g. early Christian) fish symbol

X be snake

 hieroglyph snake

X be plant

left leaf as family resemblance

stalk

X be tree

with a bushy part up top

X be flower(ing plant)

with petals [VM]

X be (zoomorphic) head, nexus of sense organs

head selected on the sentient base shape, but with the orientation of characteristic parts.  

Concentric circles are also good for ‘salient part’.

X be eye, visual organ

These are representative of a family of terms for sense organs, formed off the same elements seen as channels on ‘communicate’ (below).

inner circle of ‘head’ taken for ‘all’ senses

X be nosemouth, chemical-sensing organ

The hypotenuse of ‘communicate’ is the bottom of the loop as drawn here.

X be mind

‘head’ reflected.  The reflection is based on the one relating ‘in’ and ‘at’.

X be manipulator part

e.g. human hand, octopus arm, cat mouth, robot hand

hand

X manipulate Y

taking the base of “head” to be derived from “X is communicated to” by rounding and reflecting, this is backformed to “hand” similarly

A be a child of B,

B be a parent of A (socially)

Here begins a kinship / relationship domain whose emblem is a lemniscate, or in some cases simply a  or two.

a minimal composible shape, plus the lemniscate

A & B (& …) be in a long term relationship (marriage vel sim)

TODO: the commitment part of the sense should be factored out.

More lines can be added off the circle for polyadic relationships.  To express that the relationship has internal structure (it’s not just a clique) a graph can be drawn inside the circle.

Alternatively, the arguments can be groups of people.  (“Parent” and others can do the same.)

a shape that can take lots of undistinguished bindings

A & B (etc.) be in a formally recognised marriage-like relationship

This demonstrates a “formality” emblem.  Variations of it can be more specifically “religious”, “legal”, etc.

formality is phono-semantically square

A & B (& …) be (close) friends

passionate relationship stove in

A & B (& …) be acquaintances

The size of the gap can be varied continuously for degree of commitment.  The same can be done for the circle, above.

iconic

A be female (in gender)

These two are pretty poorly contrastive, except in probable ductus.

Their loops are still the kinship domain emblem.

the Venus sign

A be male (in gender)

All the terms of this domain are to be taken as defined by the individuals involved, and social rather than biological.  Thus this is ‘be of male gender’ aot ‘sex’, and e.g. adoptive parents count as parents.

the Mars sign, looserly (and adjusted for stroke convenience)

A be alive

It is not clear whether the ‘biological’ rams-horns is a (removable) domain emblem.

An allograph with the horns up against the circle probably exists.

exist, biologically

A be a child of B,

B be a parent of A (biologically)

[left] A be female (in sex)

[right] A be male (in sex)

A and B be (colocated) symbionts

An allograph with the horns up against the circle probably exists.

be biologically colocated

A eat, consume B; B fuel A

Pac-Man

X be food for Y

compositional

hypothetical expected eaten thing

X be water (mass)

mass family resemblance + 3/2 periods of a wave

X be (a) bread or similar food

cuneiform NINDA

X be a stone, rock

triangles for rigidity

X be large … small

Scalar family.

These can ligate onto the shape word, below.  In doing so, the vertical bar of this word gets omitted.  E.g.  ‘be big and flat’;

 ‘be big and compact’.

iconic

X be of specified shape: here

[0] compact

[1] long

[2] flat

The length of each line is the log of one dimension of the object, up to a global constant.  One line is always taken very small (phonemically a dot?).  

An orientation context may make the order of the lines meaningful.  Otherwise, the default is to order them by decreasing length.

(This family of glyphs has an obvious extension to numbers of dimensions other than three.)

a bar graph

X be ground, land

The line of this glyph is morphologically the same line appearing in the shape and position words.  So it can incorporate e.g. ‘depression’ or ‘protrusion’, as in the next entry.

solid surface which gravity is directed towards

Y be a depression in the ground

TODO

X be star

X be year

Perhaps a compositional path word except for the insertion of star.

instance of circling a star

[this is a member near the “rigid” end]

X be rigid … floppy

hand deforming an object

X be hot ... cold

flame

X

X sleep

Ki’s legs and tail as he slept

X have inebriation

Needs replacing with a more distinctive form.

swirly drunkenness icon in comics

X be good

These entries with disconnected binding points are line decorations.  Line decorations may take the negation stroke across their body.

X be expected

A give a to B and B gives b to A, in an exchange / transaction

a shape with the correct symmetry

A give a to B

unidirectional exchange

A think that X rel Y;

A think that it would be R that X rel Y

Position R may contain a line decoration, or a few other things.  The three next entries are selected examples.

If there is no R this simply means “A think that X rel Y”.  One may interpret an absent R as defaulting to “be true”.

built on the form of the irrealis

A expect that X rel Y

think expected that

A diswant that X rel Y

think ungood that

A think (X rel Y) is T, based on evidence B.  A thinks that the support of (X rel Y) by B is E.

think supported by B that

X think about, consider Y

X try to get Xself to think that Y is somehow [[maybe “is what” would be better.]]

Y communicate S to X, across modality / encoding C

Some particular modalities, and languages / encodings, can be specified by derivation as below.

(Is there a difference between channel and encoding?)

S is taken by use here, unless it bears a mention marker.  e.g. “Y said something scary”

In a conversation, all participants are bound as Y.

a simple shape

X perceive S

Y express S

communicate:

[left top] by light

[right top] by sound

[left middle] by chemical

[right middle] by physical contact

[left bottom] by perceiver’s internal sensations

[right bottom] by a gestalt

Incorporations of modalities into communicate.

These serve e.g. for the basic senses (“see, hear, taste/smell, touch, proprioceive“).

[bottom right] the arc of gestalt group

(the full forms of the others, if they have any, are yet undesigned)

X imagine, mentally model S [actually this should be ‘perceive via belief’, which isn’t very right.]

X perceive S by means of thinking (that things are somehow)

be I (the author)

In a conversation, refers to its original writer.

expresser

be we two (exclusive)

Pronouns may incorporate numbers in general.

be thou (the reader)

In a conversation, refers to its original intended recipient.

perceiver

be (a group of) I and thou, be we (inclusive)

ligature

???

participants converse, communicate back and forth

X be a language (as used in linguistics; excludes e.g. computer languages)

compositional

X be an encoding that can express anything

X be communication among the participants

Obsolete glyph.

has long regions on which to bind many participants

X know = remember, recall Y

e.g. “They know the formula for the determinant [this glyph], but don’t understand it [the “grok” glyph]”.  

Compositional, “X think [rel]” with [rel] in the realis.  Sai doesn’t want there to even be a ligated form for this.

cf. mind

X deeply / familiarly understand, grok Y.  Obsolete with the opposite binding, Y grok X.

psi for ψυχή, and resemblance to “recall” etc.

to be drawn

X teach Z to Y

X intend that Y grok Z

---

X have fluency / internalisedness / second-natureness

is there some broader sense this can have?

A wear B

aktionsart?

head & sleeves of a garment

A love B

close to be happy because of

X be happy

Emotion terms fall in an improductive 2D family, indicating valence and arousal.  [Do there exist scalar families?]

Duchenne lines

X be content

happy less one line

X be sad

to be drawn

[more emotions]

next slice: 49

Examples

Newer examples are at the bottom.  Many of the non-new examples are obsolete in various ways (though some have been updated).

Example

Gloss

Comments

A cat doesn’t eat.

Do I exist?

Are cats sentient?

“Sentient” = thinking.  Would be preciser to have an iterative here.

Cogito ergo sum.

For “R ergo S” this uses S, with good evidence R.  

So “That I think is good evidence for that I exist.”

I told the cat, “Food’s ready!”

I want (as an article of faith) that people would start thinking *in general* (not just this once)

“People” in generic (as opposed to some particular person) is indicated by the generic marker.

The center is “think good without evidence.

I want (ditto) that people would start *thinking* sometimes

Any communication from a fish is surprising.

Cat and human separately eat the same fish.

Think of the “eat” here (which is perfective) as representing a stack of two ‘eat’ symbols. The cat and human separately bind to each as consumer, and ‘fish’ binds to both.

J. Doe used to believe that I be a cat.

Line length is stylistic.

TA is unmarked on ‘I be a cat’.

A cat warms & falls asleep in synchrony.

These three examples use an old obsolete form of graph that has very little to do with the current one.

Cat falls suddenly asleep near the end of heating up.

(epsilon-time) = when X is awake (iterative);

*now* = last sleep

I opine, "mow is good!"

“Opine” = say and believe

“Believe” = think without evidence

“Mow” = typical cat-utterance

Note also that this is a case of both participating in and mentioning a relation.

I want to eat.

“X wants to Y” = X thinks Y good, and also X irrealis does Y

Like I told the Deep One, I think it's good for well-fed cats to purr to me (I know they do so because I’m drunk).
Somewhat forced; this was made explicitly to use all items created at the time.
 
“Deep one” = fish-human-thing

“Well-fed” = repeatedly finished eating

More out-of-date things: e.g. think should have something on its left, and the line from I *through* say doesn’t have a function (it doesn’t obviously bind).

Are you a conlanger?
Lit.: Do you create something that can be an encoding of any percept / communication?
I eat bread as though it were fish.
More closely, “... like I would eat fish”.
I intend to relate to other people in manner X more than vice-versa.

Old issues to think on

Vynce-era lexical things: bowtie-esque “law, legal” widget; “flower(ing plant)” shd maybe be “thing which is expected to blossom”; compositional “have the name”

(transplanted from the drawing document)

* scoping of the generic (how good is line-crossing?)

* things to facilitate global placement (“syntax”)

* a derivative for “have such-and-such conversation”: X said to Y S1, then Y said to X S2, then ...

* logic syntax

* giving "think" a 'nominal' object?


[1]UNLWS' autonym (lit. 'the language that this is rendered in'). Note that it has a binding point, like all UNLWS glyphs, and is entirely compositional. It uses the literal mention marker, rather than the more usual semantic one.

[2]Previously "An Untitled Non-Linear Writing System". "Unker" is the possessive of "wit", the hypothetical descendant of the old English 1st person dual pronoun.  UNLWS is in fact a full language, not just a writing system, but the name is kept for historical reasons.

[3]This example was created for Mark Rosenfelder (aka Zompist)'s forthcoming book on Advanced Language Construction.

[4]Arthaey suggests to read this Welshoidally, [ɪnˈluːs].  Alex approves, though in practice he reads [‘ʌnǝlz].

[5] A fully computer-native medium would avoid some problems of pen-written text — eg providing more possible graphemes, making graph relaxation easier, etc. For that matter, a 3D medium would have one fairly significant advantage, namely removing the problem of crossing lines entirely. But for now, narrowing the design space makes things easier overall.

[6]For more, see Schuyler Duveen's talk at the third Language Creation Conference (LCC3).

[7] Thanks to Vynce Montgomery for this suggestion.

[8] Thanks to Mark Rosenfelder for inspiring the design of this visualization.