Abstract
We give two characterizations for dense intervals consisting of grammatical families. These results are general enough to cover the eases of context-free grammar forms, general grammar forms and synchronized EOL forms. By means of the characterizations it is proved that denseness is undecidable for context-free forms. The characterization theorems also enable us to investigate the maximality of dense intervals. The paper is divided into two parts. The results mentioned above are presented in Part II. This first part contains definitions and preliminary results. Also in Part I, we investigate language families defined by subregular forms and clarify the role of the empty word in form theory.
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