Archive for the ‘grammar’ Category

Betascript Mathematical Notation

Wednesday, September 6th, 2017
Betascript got a mathematical notation. I tried to shed off traditional math notation as well as I could from a lifetime of indoctrination. Things that specifically got to go were fractional notation, representing equations as, well, equations, zero, and all the shenanigans with logarithms. The latter was heavily inspired by the Triangle of Power, a very useful notation that helps (YMMV) unify exponentiation, taking roots, and logarithms. So here goes.

The number system is duodecimal (base 12, dozenal) and the digits are slightly uncomfortably simple. 12 would have been small enough of a set to have completely different glyphs, but let's say Beta culture was developed by the kind of people that develop number systems.



The system is bijectional, meaning every numeral corresponds with exactly one number, unlike our system that has has redundancies like 1 = 01 = 001 etc. This is a rather roundabout way of saying that the system doesn't use zero, like Ancient Klingon . This should clear out any confusion, things to pay attention to are underlined:


Decimals are expressed by basically using the equivalent of scientific notation to shift the 'point'


Sums and products can be expressed in a variety of ways, with binary operators or surrounding with different kinds of brackets, or both. Simply stringing symbols together is considered summation.


There is no separate symbols for the reverses, ie. subtraction and division, nor for equalness. The relation is expressed just by writing the result next to the operation. (This probably leads to problems, but let's call this notation a draft...)


The same principle of stating a relation is used to combine exponentiation, taking a root, and logarithms. The default form is <base>⊥<exponent> over <result>, and some additional notation allows you to write the result on the same line, left or right, optionally enclosed in brackets.


If the need arises to refer to one of the variables (ie. as in 'selecting' one of the three types of operation), one can use a dot to denote what is considered the result. The same can be used to denote division and subtraction.


The symbol for e is a square, and it forms a ligature with the exponentiation sign.


Minus one, the ubiquitous unsung constant, has its own symbol. Used with different operations it yields useful things like negative numbers, reciprocals, and another useful constant, namely zero. Ligatures get formed, and the imaginary unit gets a further simplified symbol.


Trigonometry tries to make sense with the circle constant and functions that hint at their meaning. Zero degrees is y-axis, not our x. This might be a bad idea. Again using the idea of expressing a relation, the reverse operations are expressed by omitting the argument of the forward version.


Finally, some familiar formulas rendered in Betascript. The last example adds a simple notation for summing series and a sign for infinity. As I'm a beginner in this notation, there might be mistakes or ambiguities.


I can't say anything about the practicality of this system in actually doing mathematics, but creating it certainly was interesting. Some things like the role of -1 fell nicely into place. I have a hunch that similar clicking might happen if one were to go further with this, like with learning any new way of looking at things, like the aforementioned Triangle of Power, reverse Polish notation, or Haskell.

The logical next steps from here would be a) to test the system on actually doing maths, and b) extending it to calculus. My understanding of the latter is, however, probably too shallow to see clearly enough to be able to create anything interestingly different or logical.
 Comments welcome.

(The font was done in Fontforge, equations typeset in Libreoffice and tweaked in Inkscape.)

(Hello to readers of Conlang Blog Aggregator, first post here!)

Betascript Mathematical Notation

Wednesday, September 6th, 2017
Betascript got a mathematical notation. I tried to shed off traditional math notation as well as I could from a lifetime of indoctrination. Things that specifically got to go were fractional notation, representing equations as, well, equations, zero, and all the shenanigans with logarithms. The latter was heavily inspired by the Triangle of Power, a very useful notation that helps (YMMV) unify exponentiation, taking roots, and logarithms. So here goes.

The number system is duodecimal (base 12, dozenal) and the digits are slightly uncomfortably simple. 12 would have been small enough of a set to have completely different glyphs, but let's say Beta culture was developed by the kind of people that develop number systems.



The system is bijectional, meaning every numeral corresponds with exactly one number, unlike our system that has has redundancies like 1 = 01 = 001 etc. This is a rather roundabout way of saying that the system doesn't use zero, like Ancient Klingon . This should clear out any confusion, things to pay attention to are underlined:


Decimals are expressed by basically using the equivalent of scientific notation to shift the 'point'


Sums and products can be expressed in a variety of ways, with binary operators or surrounding with different kinds of brackets, or both. Simply stringing symbols together is considered summation.


There is no separate symbols for the reverses, ie. subtraction and division, nor for equalness. The relation is expressed just by writing the result next to the operation. (This probably leads to problems, but let's call this notation a draft...)


The same principle of stating a relation is used to combine exponentiation, taking a root, and logarithms. The default form is <base>⊥<exponent> over <result>, and some additional notation allows you to write the result on the same line, left or right, optionally enclosed in brackets.


If the need arises to refer to one of the variables (ie. as in 'selecting' one of the three types of operation), one can use a dot to denote what is considered the result. The same can be used to denote division and subtraction.


The symbol for e is a square, and it forms a ligature with the exponentiation sign.


Minus one, the ubiquitous unsung constant, has its own symbol. Used with different operations it yields useful things like negative numbers, reciprocals, and another useful constant, namely zero. Ligatures get formed, and the imaginary unit gets a further simplified symbol.


Trigonometry tries to make sense with the circle constant and functions that hint at their meaning. Zero degrees is y-axis, not our x. This might be a bad idea. Again using the idea of expressing a relation, the reverse operations are expressed by omitting the argument of the forward version.


Finally, some familiar formulas rendered in Betascript. The last example adds a simple notation for summing series and a sign for infinity. As I'm a beginner in this notation, there might be mistakes or ambiguities.


I can't say anything about the practicality of this system in actually doing mathematics, but creating it certainly was interesting. Some things like the role of -1 fell nicely into place. I have a hunch that similar clicking might happen if one were to go further with this, like with learning any new way of looking at things, like the aforementioned Triangle of Power, reverse Polish notation, or Haskell.

The logical next steps from here would be a) to test the system on actually doing maths, and b) extending it to calculus. My understanding of the latter is, however, probably too shallow to see clearly enough to be able to create anything interestingly different or logical.
 Comments welcome.

(The font was done in Fontforge, equations typeset in Libreoffice and tweaked in Inkscape.)

(Hello to readers of Conlang Blog Aggregator, first post here!)

ANADEWs: Complications in Nominal Marking with Numerals

Tuesday, September 5th, 2017
In many languages around the world, numbers beyond 'one' are followed by plurals, because obviously, two, three, four etc are semantically plural. Likewise, in many languages, numbers beyond 'one' are followed by singulars, because a plural marking is superfluous. In some languages, two, and maybe other small numbers are followed by some form of paucal or dual or whatever.

However, some languages mess this up a bit, and I figure it might be of some interest to describe two examples.

1. Finnish
The Normal Noun
If the noun phrase is any other case than nominative or accusative, the noun is in the singular and its expected case, while the number likewise is marked for that case. With the nominative or accusative, the noun itself is in the partitive case (which also is the case when the number is in the partitive), and the number is in the nominative form (or rather, numbers have identical nominatives and accusatives, except for 'one').

The Abnormal Noun
Some nouns lack singular forms, and can thus not abide by the rules laid forth above. Instead, the number adjusts, and is marked for the plural. This even goes for the number 'one', giving us monstrosities like
'yksissä häissä' - 'one-plur-inessive wedding-plur-inessive' - at one wedding
but also
yhde-t bilee-t
one-plur party-plur
a party ("ones parties")
This is even more sick, as ordinals too get this treatment, giving us ugly monstrosities like
kolm-ans-i-ssa festare-i-ssa
three-ORD-plur-inessive festival-plural-inessive
at the third festival
Of course, in Finnish each element of the numeral (except 'toista', roughly "-teen" as in thirteen and such) is inflected for the case of the NP, and each element of a numeral is also inflected for ordinality, etc.

Further, the comitative case lacks formally singular forms, and thus whenever that is used, the numeral also needs to be plural - even if that plural is one.

2. Russian
Russian has a peculiarity going on, whose origin is the defunct dual form. The dual was identical for some nouns in the nominative to the genitive singular (but not for all nouns, e.g. feminines had a distinct dual). This has generalized so almost all nouns, when following the numbers two, three and four, take the genitive (when the numeral is in the nominative, mind you!). With other cases, the noun and the numeral are in the same gender.

With accusatives, inanimates behave like in the nominative example above. Animates, however, take the plural genitive from two onwards.

Certain numbers - thousand, million, billion - are really nouns, and the "real noun" is in the genitive plural.

3. Hebrew
In Biblical Hebrew (maybe in modern too; I don't know and will not try to find it out today - no diss of modern Hebrew, but Biblical just is so much more cool) the numbers three to ten take the opposite gender's congruence marker. Thus, 'five lads' would be five-fem.sg lad-masc.plur

There is also a 'construct'-number, which signifies 'n of', but has no gender congruence. These construct numerals can also take possessive suffixes for 'two of us' and the like.

Finally, in modern Hebrew, there is still a dual, but this is used only with:
  • nouns that naturally occur in pairs, even for genuinely plural numbers of the noun, and with some pluralia tantum (that also naturally occur in pair-like structures, I guess?)
  • units of time

Detail #354: Complete Omission of some low Numerals

Monday, September 4th, 2017
Consider a language in which the use of a singular pretty much implies exactly one, and never a 'generic' referent. In such a language, the number 'one' could be entirely omitted in favour of always using a noun instead, much like how Russian sometimes uses 'raz' ('a time, one time') instead of 'odin'.

Now, in such a language, one can imagine that mathematical notation would not develop very well, since the idea of a symbol for 'one' might be less obvious if there's no word for it.

If the language also has explicit duals, we could even consider dropping 'two' out of it as well.

EDIT: This post was renumbered due to previous omission of #354.

Conlangery #132: Coptic (natlang)

Monday, September 4th, 2017
This episode, we discuss Coptic, the last descendant of thousands of years of Ancient Egyptian, now spoken mainly as a liturgical language in Coptic Christian churches in Egypt. Top of Show Greeting: Nalathis Special Mention: Go watch Conlanging: The Art of Crafting Tongues! Links and Resources: Plumley, Martin (1948) An Introductory Coptic Grammar. London: Home... Read more »

Every Word is a Portal: Conlanging at the Crossroads of Art, Mystery and Science

Friday, September 1st, 2017

James E. Hopkins received a BA in French from Hofstra University in 1974 and an MS in Metaphysics from the American Institute of Holistic Theology in 1998. He is a published poet, Eden’s Day (2008), and has a novel which features five of his conlangs, Circle of the Lantern, with the publisher as of this writing. He has been involved in language construction since 1995 with the birth of his first conlang, Itlani (then known as Druni). Although Itlani is his first and foremost love, since that time he has been developing Semerian (Pomolito), Djiran (Ijira), Djanari (Nordsh) and Lastulani (Lastig Klendum), the other languages spoken on the planet Itlán. One further language project, Kreshem (Losi e Kreshem), is also under development. His primary interest in language construction is from an aesthetic and artistic perspective.

Abstract

The roles played by art and metaphysics may sometimes go unnoticed and underappreciated in today’s growing, busy and scientifically oriented conlanging world. This article explores these roles and the essential balance of art, mystery and science that informs and inspires so many involved in the constructed language scene.

Version History

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#506

Tuesday, August 29th, 2017

Create a conscript inspired by complicated road intersections - some of the ones here may be a good example.

Update on the Grammar Writing Process IV

Saturday, August 26th, 2017

Grammar writing has gone slowly again for the past couple of weeks, which is mostly due to reading up on things. I have now arrived at discussing verbs, which are the most complex part of speech since they are at the head of clauses—not just structurally, but also functionally. Important questions right now are:

  • What evidence is there for a constituent S which holds all the verb’s arguments besides the fact that verbless clauses exist complete with predication?
  • Is there a VP in hiding? This requires performing tests on constituency as well (there is a way to say does so as well, so there should be a VP even if the verb word itself is the head of the superordinate IP).

I assume that Ayeri’s basic sentence structure looks essentially like this:

The sentence 'Ang konja Yan pahiley' ('Yan eats a cookie') charted in terms of LFG

And then, there are some further questions which I’d like to answer:

  • Austronesian alignment gave the impetus for Ayeri’s strategy of marking one certain NP on the verb, however, after reading Kroeger (1991) it became clear to me that there are strong differences between the real thing and what I have. This is mostly due to not consistently following the original model but falling back on structures familiar from German and English. Thus: what is a so-called ‘trigger conlang’ of which Ayeri is supposedly a prominent example,1 and how is Ayeri actually positioned in this regard?
  • In consequence, how does Ayeri deal with more complex sentence structures, for instance, involving raising and control, as opposed to what Kroeger (1991) describes?
  • Ayeri basically grammaticalizes topic marking by way of agreement morphology. How (un)typical is this with regards to typology? (e.g., see Li and Thompson 1976 for something very old and basic)
  • Does the way in which Ayeri deals with topicalization have any effects on binding? Topics are supposed to operate outside of the functional hierarchy which Bresnan et al. (2016) propose as an important factor in pronominal binding.
  • Since I’ve been trying my hands on an LFG-based analysis, how do verbs behave regarding assigning roles in argument structure? (Dalrymple 2001: 203–215, Bresnan et al. 2016: 329–348)

To be honest, when I started working on Ayeri in 2003, I would not have understood a word of what Kroeger (1991) writes, so it was basically clear from the beginning that there’d be large inconsistencies with regards to the intention of playing around with Austronesian alignment. The thing is, besides Tagalog’s infamous marking of the ang phrase’s role on the verb (actor, goal, direction, beneficiary, etc.), whatever that phrase is syntactically, It also has effects on raising, control, and binding, which I have long ignored out of a lack of knowledge and awareness of these grammatical processes. Even when I tried to come to terms with Ayeri’s syntactic alignment in an often-clicked blog article in 2012, I applied some of the tests discussed there only mechanically, without actually understanding what they’re about.

It also may be noted that Kroeger (1991) analyzes It as the subject because of consistencies with syntactic traits usually associated with subjects, though with the added complication that it’s not fixed to its conventional position as the specifier of VP.2 You can also see It variously analyzed as focus or topic, which is terribly confusing especially when you don’t know a lot, and this confusion was a major impact on what I ended up with in Ayeri. It will also be necessary, thus, to look at whether the logical subject and the syntactic subject in Ayeri coincide. My gut feeling is that they do, which would make Ayeri more similar, in fact, to analyses of the basic clause structure of Celtic languages such as Welsh or Irish (compare, for instance, Chung and McCloskey 1987, Sadler 1997, Dalrymple 2001: 66, Bresnan et al. 2016: 130–138).

  • Bresnan, Joan et al. Lexical-Functional Syntax. 2nd ed. Chichester: Wiley Blackwell, 2016. Print. Blackwell Textbooks in Linguistics 16.
  • Chung, Sandra, and James McCloskey. “Government, Barriers, and Small Clauses in Modern Irish.” Linguistic Inquiry 18.2 (1987): 173–237. Web. 11 Aug. 2017. ‹http://www.jstor.org/stable/4178536›.
  • Dalrymple, Mary. Lexical Functional Grammar. San Diego, CA: Academic Press, 2001. Print. Syntax and Semantics 34.
  • Kroeger, Paul R. Phrase Structure and Grammatical Relations in Tagalog. Diss. Stanford University, 1991. Web. 17 Dec. 2016. ‹http://www.gial.edu/wp-content/uploads/paul_kroeger/PK-thesis-revised-all-chapters-readonly.pdf›.
  • Li, Charles N. and Sandra A. Thompson. “Subject and Topic: A New Typology of Language.” Subject and Topic. Ed. Charles N. Li. New York: Academic P, 1976. 457–485. Print.
  • Sadler, Louisa. “Clitics and the Structure-Function Mapping.” Proceedings of the LFG ’97 Conference, University of California, San Diego, CA. Ed. by Miriam Butt and Tracy Holloway King. Stanford, CA: CSLI Publications, 1997. Web. 12 Aug. 2017. ‹https://web.stanford.edu/group/cslipublications/cslipublications/LFG/2/lfg97sadler.pdf›.
  1. The oldest message on Conlang-L (itself the oldest conlanging group on the internet I’m aware of) which uses the term ‘trigger’ to refer to case/voice marking I could find is by John Cowan, dated December 16, 1995. The archives 1991–1997 seem to only survive archived by the Wayback Machine anymore. Search for the time stamp, “Sat Dec 16 13:09:06 1995”, on the linked archive page to read the message.
  2. This is probably not much of a problem for the likes of LFG or HPSG, but likely more of a problem for generative grammar.

A Question of Attestation

Friday, August 25th, 2017
Does anyone happen to know of any split-S language, where it is the noun, rather than the verb, that decides what case the intransitive subject takes?

Unrelated idea: split-S-like with regards to dechtichaetiativity.

Detail #355: Nouns with Inconsistent Gender

Wednesday, August 23rd, 2017
Consider a typical IE-style gender-case fusional system. In such a system, individual words could be exceptional and behave as members of one gender with regards to some forms, but another with regards to other forms. This might lead to any number of interesting consequences down the line.

In many languages, the case system is inconsistent between genders: different genders or numbers may conflate some cases; alternatively we can think of this as one gender distinguishing more cases than another. Sometimes, however, multiple genders overlap in such a way that over some 'area' of the case system, no particular gender has more case distinctions than another, they just split the case system in different ways, e.g.

gender 1gender 2gender 3
case 1-A-C-E
case 2-A-D-F
case 3-B-D-E

Here, we have a clear three-case system, with only two distinctions ever made. In fact, even if we eliminated one of the genders from this system, there'd imho be a sufficient reason to consider there to be three underlying cases in this language.

Now, a noun could exceptionally manage to behave like gender 1 with regards to case 1, like gender 2 with regards to case 2, and like gender 1 with regards to case 3. Maybe there's a whole slew of cases where it behaves exceptionally. Maybe it's only a certain combination of number and case that triggers the exception.

However, let's consider a different part of this: pronouns. Consider a language that has different roots for different gender referents. Potentially, we could have, say, gender 1 roots taking gender 2 morphology with nouns like these (or vice versa).