the layered stream method, which is an efficient mechanism for search prob-
lems based on parallel logic programming languages. Basically, PAX employs 
a chart parsing algorithm. Our type judgment processing formalism is quite 
the same as PAX, but the usage of process and data is completely opposite. 

EXAMPLE OF GRAMMATICAL AND LEXICAL DESCRIPTION 

The grammar rules below show how the adequacy of the semantic category 
of the grammatical object can vary dynamically depending on the subject. 


             {np,[sem=Subj]} < ({vp,VP}  {s,VP=[agent=Subj]}) 


This grammar rule shows that the superordinate type of the type "np" is 
a function of type "vp  s" and that an object which is judged as the type 
"np" is also a function which, if applied to an object of type "vp", results in 
an object of type "s". In this rule, all the descriptions of "vp" are merged to 
those of "s", and the value of the feature "sem" of "np" is unified with the 
value of feature "agent" of the type "s". 

Now we also show some lexicon entries to go with these rules. 


   eats: {np,[sem=Obj]}  {vp,[agent=Ag:{animal,[eat_obj=Obj]}]} 
   john: {np,[sem={human,Id,[name='John']}]} 
   the_tiger: {np,[sem={tiger,Id,[]}]} 

In the lexicon the object "eats" has function type "np  vp" added with 
the description that says the value of the feature "agent" is a typed variable 
and the type of the variable is sorted "animal" and the value of the feature of 
"eat_obj" is unified with the value of the feature of "sem" of type "np". The 
rules specifying semantic categories look as follows. 


                    {tiger,[]} < {animal,[eat_obj=E:{animal,[]}]} 
                    {human,[]} < {animal,[eat_obj=E:{food,[]}]} 


These rules mean that a tiger is an animal which eats animals and a human 
is an animal which eats food, respectively. 

Although, under these rules of grammar, lexicon and semantic categories, 
'john' and 'the_tiger' are both animals, the judgment (the_tiger,eats,john):s 
succeeds but (john,eats,the_tiger):s fails, because John is a human and a hu-
man is an animal which eats food but a tiger cannot be judged as food from 
the rules governing semantic categories. 


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