Category Archives: Equational Inference

Perhaps I ought to comment on the differences between the present and the standard definition of a formal grammar, since I am attempting to strike a compromise with several alternative conventions of usage, and thus to leave certain options open … Continue reading →

Before the capacity of a language to describe itself can be evaluated, the missing link to meaning must be supplied for each of its expressions.  That means opening a dimension of semantics to be navigated by means of interpretation, topics … Continue reading →

The present patch of discussion is concerned with describing a family of formal languages whose typical representative is the painted cactus language   Once we have the abstract forms of cactus languages well enough in hand to grasp their application, … Continue reading →

As a rough illustration of the difference between rhetorical and logical orders, consider the contrasting types of order appearing in the following conjunction of conditionals. The formula exhibits a happy conformity between its rhetorical form and its logical content, in … Continue reading →

In looking at what seems like an incidental issue, the discussion arrives at a critical point.  The question is:  What decides the issue of style?  Taking a given language as the object of discussion, what factors enter into and determine … Continue reading →

As a result, we can hardly conceive of how many possibilities there are for what we call objective reality.  Our sharp quills of knowledge are so narrow and so concentrated in particular directions that with science there are myriads of … Continue reading →

Derivations An immediate derivation in is an ordered pair of sentential forms in such that the following conditions hold. As noted above, it is usual to express the condition by writing The immediate derivation relation is indicated by saying that … Continue reading →

Characterizations Recall that a formal grammar is defined by a 4‑tuple where is the initial, special, start, or sentence symbol, is a finite set of intermediate symbols, is a finite set of terminal symbols, also known as the alphabet of … Continue reading →

It is fitting to wrap up the foregoing developments by summarizing the notion of a formal grammar which appeared to evolve in the analysis of cactus languages.  For the sake of future reference and further application it is useful to … Continue reading →

Grammar 6 Grammar 6 has the intermediate alphabet with the set of covering rules listed in the next display. Our exploration of the grammar space for the language shows how an initially effective and succinct definition of a formal language … Continue reading →