MONOTONICITY, HEADEDNESS, AND REVERSIBLE GRAMMAR 
Martin Kay 
Xerox Palo Alto Research Center 
3333 Coyote Hill Road 
Palo Alto, CA 94304 
ABSTRACT 
The notion of reversibility that is salient for grammars rests on the idea that grammars are trans- 
ducers between strings of words and some more abstract meaning representation. The grammar 
is reversible if the transducer will work in both directions. The notion was important in driving 
the evolution from procedural grammar formalisms, like ATN, to declaritive formalisms, like 
LFG and HPSG. The key was to replace the setting of registers with the unification of logical 
variables. The aim was to base grammars entirely on 'monotonic' operations. An issue has 
arisen more recently has to with the various notions of 'head of a construction'. After an attempt 
to place reversible grammars in their historical perspective, I will discuss the relation between 
mon0tonicty and headedness. 
