It is useful to examine the relation between syntactic production and logical implication with one eye to what they have in common and another eye to how they differ.

The production says the appearance of the symbol in a sentential form implies the possibility of replacing with   Although that sounds like a possible implication, to the extent that implies a possible or that possibly implies the qualifiers possible and possibly are essential to the meaning of what is actually implied.  In effect, those qualifications reverse the direction of implication, making the best analogue for the sense of the production.

One way to understand a production of the form is to realize non‑terminal symbols have the significance of hypotheses.  The terminal strings form the empirical matter of the language in question while the non‑terminal symbols mark the patterns or types of substrings which may be recognized in the linguistic corpus.  If one observes a portion of a terminal string which fits the pattern of a sentential form then it is an admissible hypothesis, according to the theory of the language afforded by the formal grammar, that the piece of string not only fits the type but even comes to be generated under the auspices of the non‑terminal symbol

Resources

• Cactus Language • Pragmatics
• Survey of Animated Logical Graphs
• Survey of Theme One Program

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