\section{Three Regimes}
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In semantical as well as syntactical terms the problem in 
understanding a sentence is to know which of the words is 
the head or functor and which of the others are which 
arguments of the functor. This problem can be looked at in 
two ways: as a {\it coding problem\/} or as a {\it decoding 
problem}. If looked at as a decoding problem, we will talk of 
{\it strategies}. A {\it strategy\/} is a way to find out how 
the words hang together. If looked at as a coding problem we 
will talk of {\it regimes}. A {\it regime\/} is a fixed way of 
expressing things so that they can be decoded. Strategies and 
regimes are of course closely connected. A regime is what is 
fixed by the language systematically, while a strategy is what 
hearers may employ in addition to disambiguate. Let us illustrate
the problem with a thought experiment. Imagine a language with 
only three words, {\sf eg}, which means `cat�, {\sf ag}, 
which means `dog�, and the word {\sf um}, which means 
`to chase�. There are no determiners, so {\sf eg} may mean, 
depending on circumstances, either `a cat� or `the cat�. 
But this will hardly matter. 
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\\[2mm]
\begin{tabular}{ll}
(\thesection.1) & {\sf The cat chases the dog.} \\
   & 
$\mbox{\sf chase}�(x,y) \und \mbox{\sf cat}�(x) and 
	\mbox{\sf dog}�(y)$
\end{tabular}
\\[2mm]
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What regimes can language implement to help identify 
the subject and the object? There are three basic choices. 
%%
\begin{enumerate}
\item
Inferential Regime. Subject and Object must be inferred 
from their meaning and the context. {\sl Examples.} 
Guarani (Paraguay), Dakota. 
\item
Positional Regime. It is agreed that the elements follow 
in a certain order, for example subject first. 
{\sl Example.} English. 
\item
Marking Regime. The words get markers that allow to 
dismabiguate the sentence. 
%%
\begin{enumerate}
\item
Head Marking. The head is marked for some quality of the 
subject and the object. We write as follows 
%%
$$N_1 \quad N_2 \quad \mbox{\it V--}n_1\mbox{--}n_2$$
%%
Here $n_1$ and $n_2$ are markers (which we write as prefixes, 
even though they may also be suffixes or clitics etc) 
that reflect a property of $N_1$ and $N_2$ (gender, class etc). 
We call these markers also {\it agreement markers}. Also, 
$n_1$ is the {\it reflex\/} of $N_1$ in $V$. Some 
agreement markers may be absent. Note that the order of subject 
and object marker must be fixed for this to disambiguate the 
sentence. {\sl Examples.} Mohawk, Bantu languages. 
%%
\item 
Dependent Marking. The head identifies subject by a subject 
marker and the object by an object marker. These markers 
are called {\it cases}. We write as follows. 
%%
$$N_1\mbox{--}\gamma_1 \quad N_2\mbox{--}\gamma_2 \quad V$$
%%
Note that $\gamma_1$ and $\gamma_2$ must be distinct in order 
for this to disambiguate the sentence. {\sl Example.} 
Tagalog.
\end{enumerate}
\end{enumerate}
%%
Let us illustrate this with our language. If it uses the inferential 
regime, then any permutation of the sequence {\sf eg ag um} will 
mean the same, all circumstances being equal. In the positional 
regime it is declared, for example, that the subject precedes the 
object (this is in fact all that is needed in the present case). 
Then the sentences are unique in meaning. {\sf eg ag um} means 
`the cat chases the dog', while {\sf ag eg um} means `the dog 
chases the cat�. When the marking regime is employed, we may 
either have cases, say {\sf su} for subject and {\sf ob} for 
object. Then any permutation of the sequence {\sf eg-su ag-ob 
um} will mean `the cat chases the dog�, and any permutation 
of the sequence {\sf eg-ob ag-su um} will mean `the dog chases 
the cat�. If we finally choose the head marking regime, we 
shall have certain prefixes, say {\sf e-} for cats and {\sf a-} 
for dogs, and then any permutation of {\sf eg ag e-a-um} means 
`the cat chases the dog�, while any permutation of 
{\sf eg am a-e-um} means `the dog chases the cat�. So much 
for an illustration of the basic regimes.

Some notes are in order. First, languages usually use a  
mixture of these regimes. Indo--European languages usually 
have subject verb agreement in addition to case marking (if 
present). Furthermore, as we shall see, in languages the systems 
are never pure enough to guarantee full disambiguation (for example, 
in German there is no distinction between nominative and 
accusative in feminine and neuter nouns as well as all plural 
nouns). In that case some other regime jumps in. Second, 
a marker is to be understood in an abstract sense. For 
example, intonation is also added as a cue for disambiguation. 
In the German case, the subject--first preference jumps in as soon 
as the cases fail to distinguish nominative from accusative. 
This can be overruled by adding intonation. Also, the context 
may help (then we are in Regime 1). In what is to follow, 
we will exclude both possibilities. Third, the markers can 
be suffixes or words or clitics. To keep matters simpley, 
we assume them to be part of their host word, so they are 
neither clitics nor separate words. 

Before we go on, we note some direct consequences. The 
head marking regime and the dependent marking regime 
are very distinct in the following sense. If the head 
marking regime is chosen, the reflex $n_1$ of $N_1$ 
depends on the actual choice of $N_1$. This can be a 
semantic property or what we call a {\it ritualized\/} 
property. Here by {\it ritualized\/} we mean roughly 
{\it must be learnt by heart}. These two, semantic and 
ritualized head marking, are not sharply distinguished. 
Gender systems in Indo--European languages are semantically 
motivated but to a large extent ritualized. 
If the reflex is semantic it can be inferred from the 
meaning of $N_1$. It may well be that the reflex depends 
on the phonetic form of $N_1$, but we ignore that choice 
as it makes no difference in principle. A neutral term 
in place of {\it semantic\/} is {\it inferential}. 
In contrast to head marking, dependent marking languages 
need to record in the lexicon what the cases of the 
actants must to be. Again, this can be inferential 
(i.~e. mainly semantic) or ritualized. The first 
option is realized in Manipuri (a Tibeto--Burman language, 
see \cite{dixon:ergativity}) and the second in Indo--European 
languages. Mixtures do occur. In Finnish, the case of 
the direct object varies between accusative and partitive 
depending on the meaning of the sentence and whether the 
object is entirely affected by the action etc. 

Let us close with a remark on the first regime. It has 
an obvious problem. Namely, only one of the meanings below 
will be expressed by the sentence (\thesection.2), which is 
rendered into English by either (\thesection.2a) or by 
(\thesection.2b). 
%%
\\[2mm]
\begin{tabular}{ll}
(\thesection.2) & {\sf eg ag um.}  \\
(\thesection.2a) & {\it The dog chases the cat.} \\
(\thesection.2b) & {\it The cat chases the dog.} 
\end{tabular}
\\[2mm]
%%
To generate the other meaning some other sentence must be 
used. An obvious possibility is to have a marker on the verb 
(let it be {\sf inv}) that exchanges the role of subject and 
object. So, if (\thesection.2) expresses (\thesection.2a), 
(\thesection.3) will express (\thesection.2b), and if 
(\thesection.2) expresses (\thesection.2b) then (\thesection.3) 
will express (\thesection.2a). 
%%
\\[2mm]
\begin{tabular}{ll}
(\thesection.3) & {\sf eg ag um-inv.} 
\end{tabular}
\\[2mm]
%%
In principle the problem could be solved also by marking an 
argument as being `demoted'. So, assume that the suffix {\sf dem} 
means `is demoted' (which is attached to the subject and says that 
it becomes the new object). Then if (\thesection.2) expresses 
(\thesection.2a), (\thesection.4) now expresses (\thesection.2b), 
and if (\thesection.2) expresses (\thesection.2a) then 
(\thesection.5) expresses (\thesection.2b).
%%
\\[2mm]
\begin{tabular}{ll}
(\thesection.4) & {\it ag-dem eg um.} \\
(\thesection.5) & {\it ag eg-dem um.}
\end{tabular}
\\[2mm]
%%
A note of clarity. If regimes other than the Positional 
Regime are employed, the sentence above may in principle 
be replaced by any permutation of its words with identical 
meaning. 

The list above is not entirely complete. We could in principle 
invent a new word {\sf per} (for permuted) which functions 
just like {\sf inv}, which however can appear anywhere 
in the sentence. (See also the discussion surrounding 
the reflexes, whether they are separate words.) We know of 
no language where this option is chosen. There are obvious 
shortcomings of this regime, though it is of course not 
prima facie excluded. 

Some of the regimes discussed earlier have some gaps in them. 
Here to contain a {\it gap\/} means that there exist sentences 
which are semantically ambiguous if that regime is used alone. 
We shall use the term {\it ambiguous\/} in a rather strict sense 
here: the sentence is counted as ambiguous if it can have two 
meanings, judging from the mere string alone. Though it may mean 
one thing in one context and another in a different context, it 
has two meanings, if the context is not specified. This allows us 
to measure the disambiguating potential of the regime alone. The 
higher the disambiguating potential of the regime, the less context 
dependent the language is. We begin with the inferential regime. 
Here matters are clear: any sentence where a verb has two arguments 
is ambiguous. 

Now consider the case of head--marking. Suppose that there are 
two NPs with identical reflex. Then it is not possible to decide 
which of the two is subject and which of the two is the object.
We summarize this in the following theorem. 
%%
\begin{thm}
The Inferential Regime has gaps if there exists different 
arguments. The Head Marking Regime has gaps if there exist 
argument with identical reflex on the head.  
\end{thm}
%%
The conditions of the theorem are always satisfied. There 
exist transitive verbs in any language we know of. Furthermore, 
head marking languages typically use some classification 
system that distiguishes a few types of things. These are 
gender or class systems. A more elaborate case are noun 
incorporation languages. In such languages, the object 
agreement is realized by a noun of the language rather than 
an agreement marker of the usual sort. If we would make our language 
into a noun incorporation language, we get the following 
sentences: 
%%
\\[2mm]
\begin{tabular}{ll}
(\thesection.6) & {\sf eg ag-um} \\
		& the cat dog-chase \\
		& {\it the cat chases the dog} \\
(\thesection.7) & {\sf ag eg-um} \\
		& the dog cat-chase \\
		& {\it the dog chase the cat}
\end{tabular}
\\[2mm]
%%
However, even this is not enough even though it surrounds most 
of the problems. It so happens in these languages that there is 
no incorporation when there is talk of people with names. So, 
we do not say in such languages {\sf John Paul-hit}, rather 
we say {\sf John hit Paul}. Mohawk, for example, has a gender 
system for such cases. But gender systems will not do, as we have 
just seen. 

What about the other two regimes? We will see shortly that in both 
cases there exist idealized languages which have no gaps, 
that is, in which every sentence is unambiguous! For languages 
with word order regime this has been shown already in the 20ies. 
It was noted that terms can be written down unambiguously without 
using brackets, if the functor is always initial (or always 
final) and the argument are given in their canonical order. 

It is often said that head marking languages tend to have freer word 
order than case marking languages. To the extent that I 
know this is not true. The languages which have the most 
freedom in word order are case marking languages (Latin, 
Finnish, Hungarian). Free word order is used often somewhat 
misleadingly.  The problem is that word order restrictions 
must be made immediately when the constituents of the sentence 
are complex. 

