Chaining

When two predicates are strung one after the other they form a new predicate, which has the same arguments as the left predicate.

Every predicate has a default chaining behavior which dictates how two predicates are connected together. If the left predicate has intransitive behavior, then its E place will interact with the right predicate. Otherwise if the left predicate has transitive behavior, then the A place is used.

For root words, they have transitive behavior if they end with a vowel, while they have intransitive behavior if they end with n, r or l.

This place can expect either an atom/generic, or a predicate. As this can greatly impact the structure of sentences, this is encoded in root words with the following rules:

  • if the root is a form CCV, the A place is a predicate place.
  • if the root ends with an -i, the A place is a predicate place.
  • otherwise the place is an atom/generic place.
  • an intransitive root shouldn’t have a E predicate place, as it will be chained to as if it was an atom/generic place. If a predicate have a single predicate place, it should be transitive with a single A predicate place. A predicate with many predicate places can have a E predicate place but it must be transitive.

Particles acting as predicates have different rules which will be explained later.

When chaining predicates the new predicate inherits the chaining behavior of the left predicate.

Atom argument chaining

If the chaining argument is an atom argument, then the variable filling this argument also fills the E argument of the right predicate. The context argument is automatically shared between left and right predicates.

mian blan

\[ \begin{align} \text{mian}(c,e) &= \text{[$e$ is a cat]} \\ \text{blan}(c,e) &= \text{[$e$ is beautiful]} \\ \ \\ \text{blan}_1(c,e) &= \text{blan}(c,e) \\ \ \\ \text{mian}_1(c,e) &= \text{mian}(c,e) \wedge \text{blan}_1(c,\color{magenta}{e}) \end{align} \]

Given $(c),$(e):
$(e) is a cat and is beautiful.

If the right predicate has more than one explicit argument, then it is wrapped in a predicate having only one explicit argument and every other argument is filled with existential variables. The process of wrapping the predicate and creating existential variables to have the correct arity is called arity mismatch resolution and it is a key aspect of Eberban grammar to reduce verbosity in simple cases.

mian bure

\[ \begin{align} \text{bure}(c,e,a) &= \text{[$e$ eats $a$]} \\ \ \\ \text{bure}_1(c,e,a) &= \text{bure}(c,e,a) \\ \color{magenta}{\text{bure}^w_1(c,e)} &= \color{magenta}{\exists a. \text{bure}_1(c,e,a)} \\ \ \\ \text{mian}_1(c,e) &= \text{mian}(c,e) \wedge \text{bure}^w_1(c,e) \end{align} \]

Given $(c),$(e):
$(e) is a cat and there exists an $(a) such that $(e) eats $(a).
$(e) is a cat that eats something.

Predicate argument chaining

If the chaining argument is a predicate argument, then the right predicate is stated to be equivalent to the predicate represented by the argument. If the predicate argument and right predicate don’t match in arity, then the arity mismatch resolution is performed. The right predicate is not stated as is, and will be instantiated by the left predicate (according to its definition). The right predicate is able to be instantiated multiple times and with any (correctly typed) arguments, and with a different context argument.

tce mian

\[ \begin{align} \text{tce}(c,e,A) &= \text{[$e$ is a set of things that satisfies $A$ (1-ary)]} \\ \ \\ \text{mian}_1(c,e) &= \text{mian}(c,e) \\ \ \\ \text{tce}_1(c,e,A) &= tce(c,e,A) \color{magenta}{\wedge A \Leftrightarrow \text{mian}_1} \end{align} \]

Given $(c), $(e), $(A):
$(e) is a set of things that satisfies $(A), and $(A) is equivalent to mian.
$(e) is a set/group of cats.

gli mian

\[ \begin{align} \text{gali}(c,e,A) &= \text{[$e$ is happy about $A$ (0-ary) being true]} \\ \ \\ \text{mian}_1(c,e) &= \text{mian}(c,e) \\ \text{mian}^w_1(c) &= \exists e. \text{mian}_1(c,e) \\ \ \\ \text{gali}_1(c,e,A) &= gali(c,e,A) \wedge A \Leftrightarrow \text{mian}^w_1 \end{align} \]

Given $(c), $(e), $(A):
$(e) is happy about $(A) being true, and $(A) is equivalent to \(\text{mian}^w_1\).
$(e) is happy that there exist a cat.

Longer chains

When more than two predicates are strung one after the other they are chained in right-grouping order (A (B (C D))).

mi dona tcu mian

\[ \begin{align} \text{mi}(c,e) &= \text{[$e$ is a speaker]} \\ \text{dona}(c,e,a) &= \text{[$e$ likes $a$]} \\ \text{tcu}(c,e,A) &= \text{[$e$ is the set of all things that satisfy $A$ (1-ary)]} \\ \ \\ \text{mian}_1(c,e) &= \text{mian}(c,e) \\ \ \\ \text{tcu}_1(c,e,A) &= \text{tcu}(c,e,A) \wedge A \Leftrightarrow \text{mian}_1 \\ \text{tcu}^w_1(c,e) &= \exists A. \text{tcu}_1(c,e,A) \\ \ \\ \text{dona}_1(c,e,a) &= \text{dona}(c,e,a) \wedge \text{tcu}^w_1(c,a) \\ \text{dona}^w_1(c,e) &= \exists a. \text{dona}_1(c,e,a) \\ \ \\ \text{mi}_1(c,e) &= \text{mi}(c,e) \wedge \text{dona}^w_1(c,e) \end{align} \]

Given $(c), $(e):
$(e) is a speaker who likes all cats.