VIRTUALLY all of the material from the writings of Peirce upon which we have drawn in this paper is contained in The Collected Papers of C. S. Peirce.(n1) In referring to these volumes we have adopted the method of reference in general use among Peirce scholars. Thus, "4.567" will mean paragraph 567 of Volume IV of the Collected Papers.

The principal aim of this paper is the study of Peirce's graphs as logics, employing in the study modern logical methods. "'he notations and abbreviations we employ are accepted as standard by contemporary logicians we shall mention specifically that we employ "iff" an an abbreviation for "If and only if." This abbreviation, although of fairly recent vintage, may now be considered standard in logical and mathematical literature, Also, we often use single quotes to a technical manner, not to be confused with their use in indicating a quotation within a quotation. The complex consisting of a sign enclosed by single quotes in this usage is the name of the sign; note that all sentence punctuation, including periods and commas, will be placed outside the quotes in this case, This usage of single quotes is well established in the literature of logic. Another sign we shall mention is ' '.  This symbol will be used to indicate the conclusion of the proof of a lemma, metatheorem, or corollary in this paper.

We have numbered in this paper the definitions, certain "rules of formation," and the lemmas, metatheorems, and corollaries. The numbering of definitions is consecutive throughout the paper; a 'D' followed immediately by an Arabic number indicates a definition. The numbering of rules of formation follows the numbering of sections throughout this paper; the number of a rule of formation will be the number of the section within which it occurs in Arabic numerals followed immediately by the number of the rule within that section in lower-case Roman numerals. Thus '1,21ii' would be the number of the second rule of formation in Section 1.21.

Lemmas, metatheorems, and corollaries are numbered consecutively in the chapter in which they occur, using a "decimal" notation, The number '2.092' would number the ninth lemma, metatheorem, or corollary of chapter II. Whether a number indicates a metatheorem, a lemma, or a corollary is indicated by prefixing to it either an asterisk, '*', the word 'lemma', or the word 'corollary', respectively,

Very special thanks are due to Professor A. N. Prior who originally put me on the track or the graphs and steered me through my first months of research on them, And to Professors Dudley Shapere, Sylvain Bromberger, Lars Svenoinus, and Manley Thompson I am indebted; their criticism and suggestions were of great aid in the preparation of this paper.

JJZ (September, 1964)