Some ideas about minimal grammar and predicate logic


In this article I present some of my ideas regarding simple constructed language grammar that I have called verb-based grammar in some contexts. Currently the presentation is in slight disorder, but I hope that it is intelligible nonetheless.

I began to apply predicate expressions to language planning in late 2003 inspired by a logic course held in the university of Oulu. I wrote down some ideas in January 2004 and pretty much forget all about it later on. The ideas re-emerged in early 2006. Thanks to Florent Garet and Jens Wilkinson for giving feedback about these ideas in the Gaja project and beyond.

The purpose of this article is to show how a very simple grammar can be constructed in an organized manner. Formal predicate expressions are a useful tool in detecting and avoiding numerous grammatical redundancies of natural languages that tend to blind us as language designers.

-- Risto Kupsala, August 2006
(Some corrections and additions made in May 2008)

Introduction to predicate expressions

This presentation is loosely based on a subset of the notation that is used in predicate logic. It has nothing to do with logic or reasoning itself. The notation consists of:

Notation and word order

Normally in predicate logic all the attributes are placed inside a pair of parentheses after the predicate. That implies VSO or VOS word order.

H(m, b) = Has money bank.

It could be reversed. Then the word order would be more like SOV or OSV.

(b, m)H = Bank money has.

Here I will use unconventional notation with attributes on the both sides of the predicate. Also I will limit to only two attributes in maximum. That means SVO or OVS word order. I prefer SVO.

(b)H(m) = Bank has money.

Tree diagrams

This kind of formal expressions can be illustrated as expression trees where predicate is above and its attributes are below so that subject is in the left branch and object is in the right branch.

Bank has money.

b m

The topmost level in tree diagrams must be a predicate, and that predicate is the center (i.e. the core) of the expression.

Monadic and dyadic expressions

This notation permits two kind of expressions: monadic and dyadic. In a monadic expression there is only one attribute in either side of the predicate.

(l)G = Life is-good.
(h)E = He is-Elvis.
(e)L = Elvis lives.
C(h) = Come here!

Monadic expressions are drawn like this:

Life is-good.


The other type is dyadic expressions, which have two attributes.

(b)F(s) = Birds fly south.

Dyadic expressions are drawn like this:

Birds fly south.

b s

Some monadic expressions are in fact dyadic expression where one of the attributes is not mentioned.

(b)E() = Boy eats.
(b)E(s) = Boy eats something.
()C(h) = Come here!
(y)C(h) = You, come here!

Predicates as attributes

So far we have discussed first order expressions where attributes are always individual objects. That allows us to formulate simple expressions like the previous examples. In second order expressions attributes can be other predicates.

(c)L(P(s)) = Children like to-play soccer.
(t)S((b)F) = They saw birds flying.
(F(o))M((y)B(h)) = Forgiving others means you believe-in humanity.
((1)P(2))E((6)M(3) = 1 plus 2 equals 6 minus 3.

Here's the first expression from the previous lot as a tree diagram:

c   P

As you can see, second (and higher) order expressions provide plenty of new possibilities for making more complex expressions.

Parts of speech and their utility

Verb, verbal noun (gerund) and verbal adjective (participle)

Some expressions can be translated to plain English in more than one way.

1a. (c)L(P(s)) = Children like to-play soccer.
1b. (c)L(P(s)) = Children like playing soccer.
2a. (t)S((b)F) = They saw birds fly.
2b. (t)S((b)F) = They saw birds flying.
2c. (t)S((b)F) = They saw flying birds.

1a exhibits a verb construction and 1b exhibits a verbal noun called gerund. They cannot be differentiated in predicate expressions (as defined here) and thus one of them can be discarded as a needless grammatical complication.

2a exhibits verb, 2b gerund and 2c participle. Again they cannot be differentiated in predicate expressions.


Adpositions are prepositions and postpositions. Prepositions are placed before noun (Come before tomorrow.) and postpositions are placed after noun (He came two days ago.) They are predicates.

((f)S)I(w) = Fish swim in water.
((w)C(h))B((h)M(f)) = Wife came home before husband made food.

The difference between prepositions and postpositions is a matter of branching. If object occupies the right branch, then prepositions are used.

before tomorrow


Otherwise postpositions are used.

years ago



Similarly conjunctions can be seen as predicates.

((w)C(h))A((h)M(f)) = Wife came home and husband made food.
((w)C(h))I((h)M(f)) = Wife comes home if husband makes food.

Ambiguity and disambiguation

Simple expressions

In addition to attributes and predicates the example expressions have had parentheses. Are they needed? To test it, the English equivalents have to be expressed in plain, ungrammatical English. That's because the predicate expressions and the English expression should be grammatically equal. They should contain exactly the same amount of information.

lG = Life good.
eL = Elvis live.
BiE = Become irritate easy.
cSbF = Children see birds fly.
cLPs = Children like play soccer.
FoMyBh = Forgive others mean you believe-in humanity.
cLPsmTi = Children like play soccer more than ice-hockey.

Ambiguous expressions

Looks like the grammar is intelligible. Let's try some more complex expressions.

cNLPsBTIcwBiE = Children naughty like play soccer bad to irritate coach who become irritate easy.

This one is ambiguous, because it could be understood in two ways:

(1) cNLP(sB)TIcwBiE = Naughty children like to play bad soccer in order to irritate the coach who becomes irritated easily.
(2) (cNLPs)BTIcwBiE = Naughty children who like playing soccer are bad in order to irritate the coach who becomes irritated easily.

Controlling ambiguity by marking verbs

This kind of ambiguity can be avoided by marking either the main verb or the participal construction of the expression. In general, marking verb would be more convenient. Verb could be marked by re-introducing the subject.

cNLP(sB)TIcwBiE = Children naughty like play soccer bad to irritate coach who become irritate easy.
(cNLPs)BTIcwBiE = Children naughty like play soccer they bad to irritate coach who become irritate easy.

Another way to mark verbs is to use tense, aspect or mood markers, in case the grammar involves them.

cNLP(sB)TIcwBiE = Children naughty do-like play soccer bad to irritate coach who become irritate easy.
(cNLPs)BTIcwBiE = Children naughty like play soccer do-bad to irritate coach who become irritate easy.

Aspect markers in existing languages

Kituba (the creole based on Kikongo) employes particles to mark aspect. Swahili uses almost the same particles as verb prefixes. This kind of particles are used commonly in pidgins and creoles.

Here are some examples of the use of aspect marker in Kituba. Note that the aspect marker is comparable to some usage patterns of the verb "to be" of English, the main difference being that formation of different aspects requires less grammatical gimmickry in Kituba.

Mu ke muntu. = I am a person.
Mu ke mbote. = I am good. / I am well.
Mu ke muntu mbote. = I am a good person.
Mu ke katuka na Matadi. = I am (coming) from Matadi.
Mu me katuka na Matadi. = I have (come) from Matadi.
Mu ke zonzila nge. = I am talking to you.
Mu me zonzila nge. = I have talked to you.
Mu ta zonzila nge. = I will talk to you.

Left or right branching?

Motivation: Why should we care about branching?

Languages employ variable word orders. The table below shows the normal word order of "attributes" in some language families, where SVO word order is dominant.

Chinese languages:numeral-adjective-noun-postposition
Germanic languages:preposition-numeral-adjective-noun
Romance languages:preposition-numeral-noun-adjective
Bantu languages:preposition-noun-numeral-adjective

If the word order was variable, people could learn to formulate utterances in a way which is most convenient to them. That could be of great help in the early stages of learning. Only later, when the learners would be in communication with foreigners, they should be able to understand other kind of word order. For example, between an English and a Chinese speaker, the only difference would be the place of adposition, which would hardly disturb communication.

In my opinion variable word order would be very beneficial.

Monadic expressions


Adjectives, which correspond here to stative verbs, are monadic predicates. They can take only one attribute. SVO word order suggests attribute-predicate order, but in fact nothing stops us from using predicate-attribute order.

cB = Car blue.
Bc = Blue car.

On top of that, it's possible to define that stative predicates can take an attribute on either side. Why not? This way the whole branching issue can be forgotten as far as plain adjectives are concerned.


The same idea can be applied to adpositions, if it is decided that they are monadic predicates too.

cSOt = Cat sleep on table.
cStO = Cat sleep table on.
mWIh = Man walk inside house.
mWhI = Man walk house inside.

The significant difference between monadic and dyadic adpositions is that a dyadic adposition can be the only predicate in complete, non-fragmentary expressions.

sAh = She at home.

s h

With monadic adpositions such expressions become ungrammatical, because they lack the core predicate.

sAh = She at home.

s A

This could be fixed by a dummy copula. In English such function is usually filled by the verb "to be".

sIAh = She is at home.

s A

Passive constructions

There are two kind of passive constructions that relate to the grammar under discussion. One type involves unknown actor. The easiest way to handle this is to use some null actor.

oRb = One read book.
sRb = Someone read book.
uRb = Unknown read book.

The other is used to reverse word order from SVO to OVS. This could be handled on lexical level as in the following example.

sRb = Student read book.
bЯs = Book is-read-by student.

In addition to English this way is used in literary Indonesian. English uses "to be" with passive participle whereas Indonesian uses prefix "di".

bDB = Buku ini dibelinya. (literally: Book this is-buy-ed.)

Another way is to introduce subject later, but it would indicate OSV word order. Nonetheless this way is used commonly in spoken Indonesian.

bdB = Buku ini dia beli. (literally: Book this s/he buy.)

Yet another way is to use a special predicate or perhaps several predicates to communicate that the subject is the object of the phrase that follows.

sBd = Snake bite dog.
dEsB = Dog experience snake bite.
dGsB = Dog get snake bite.


In this article I have demonstrated a grammar where:

Risto Kupsala, 2006, 2008