The following notations will be used:

(a) Aux)iliary), the complex of elements which represents the obligatory choices of tense, number, person, modal auxiliary, assertion, etc. of the verb, is for simplicity symbolized by the simple third-person singular present tense of the verb.

(b) X, Y, Z are syntactic variables standing for any string of symbols in the syntactic representation of a sentence.

(c) Single quotes enclose meanings such as components, definitions, glosses, translations, or interpretations.

(d) For simplicity, A, B, C are used to represent variables or the syntactic position of noun phrase, rather than the more usual indexed NP₁ NP₂, NP₃. Al-noun or A-noun phrase refers to the actual morpheme (string) occurring in the position A. When enclosed in single quotes, e.g. ‘A' or ‘A has B ’, the letter represents the referent of a token of the A-noun type.¹

(e) Similarly, P,  , R, or ‘ P ’, ‘ Q ’, ‘ R ’, rather than S₁, S₂, S₃, stand for sentences, schematic sentences, or semantic components in sentence form.

(f) Pj, Pj are tokens of P.

(g) AF symbolizes a function with variable A. This order, rather than the more usual f(x) or Fx, is used to simplify reading in the subject-predicate order of English. ARB, with variables A and B, stands for a relation between ‘A’ and ‘B’.

(h) The existential quantifier ‘ there is a... ’ is indicated in a definition by prefixing the indefinite article a- (an-) to the first occurrence of the quantified variable in the definition.

(i) Not- is prefixed to a whole sentence to indicate negation with wide scope and directly to a specific item in the sentence for negation with narrow scope. Thus, with narrow scope: ‘ he not-has every one ’, corresponding to ‘ he lacks every one ’; with wide scope: ‘ not- (he has every one) ’, which can mean ‘ not-he has every one ’ or ‘ he not-has every one ’ or ‘ he has not-every one’.

¹ Symbol tokens are separate observable occurrences in speech. An abstract symbol type is the class of its tokens. A referent is the given thing, event, etc., real or hypothetical, that a given token is made to refer to or stand for by the symbol-using organism as utterer or hearer of the token.