CycL sentences combine terms into meaningful expressions.
Every sentence has the structure of a Lisp list. It is enclosed in parentheses, and consists of a list of objects which are commonly designated ARG0, ARG1, ARG2, etc. The object in the ARG0 position may be a predicate, a logical connective, or a quantifier. The remaining arguments may be constants, non-atomic terms, variables, numbers, English strings delimited by double quotes (“), or other sentences.
This is the class of well-formed sentences in CycL. If a CycL sentence satisfies all the constraints on the number and types of arguments to the relations that appear in it, the system will recognize it as an instance of the collection #$CycLSentence-Assertible.
The simplest kind of sentence is an atomic sentence: a sentence in which the ARG0 position is occupied by a predicate, and all the other argument positions are filled with terms:
(#$likesAsFriend #$MattDamon #$BenAffleck) (#$skillCapableOf #$LinusVanPelt #$PlayingAMusicalInstrument #$performedBy) (#$colorOfObject ?CAR ?COLOR)
The first two of the atomic sentences above are ground atomic formulas (GAFs), since none of the terms filling the argument positions ARG1, ARG2, etc. are variables. Here the word “formula” is used to mean a term composed of other terms; e.g. either a NAT or a sentence. Ground atomic sentence, or GAS, would be a more precise name, but GAF is the more common usage.