Tag Archives: Equational Inference

The 16 boolean functions on two variables are shown in the following Table. As before, all boolean functions on proper subsets of the current variables are subsumed in the Table at hand.  In particular, we have the following inclusions. The … Continue reading →

A good way to illustrate the action of the conjunction and surjunction operators is to show how they can be used to construct the boolean functions on any finite number of variables.  Though it’s not much to look at let’s … Continue reading →

If one takes the view that PARCEs and PARCs amount to a pair of intertranslatable representations for the same domain of objects then denotation brackets of the form can be used to indicate the logical denotation of a sentence or … Continue reading →

Last time we reached the threshold of a potential codomain or target space for the kind of semantic function we need at this point, one able to supply logical meanings for the syntactic strings and graphs of a given cactus … Continue reading →

Words spoken are symbols or signs (symbola) of affections or impressions (pathemata) of the soul (psyche);  written words are the signs of words spoken.  As writing, so also is speech not the same for all races of men.  But the … Continue reading →

The task before us is to specify a semantic function for the cactus language in other words, to define a mapping from the space of syntactic expressions to a space of logical statements which “interprets” each expression of as an … Continue reading →

It is common in formal settings to speak of interpretation as if it created a direct connection from the signs of a formal language to the objects of the intended domain, in effect, as if it determined the denotative component … Continue reading →

Alas, and yet what are you, my written and painted thoughts!  It is not long ago that you were still so many‑coloured, young and malicious, so full of thorns and hidden spices you made me sneeze and laugh — and … Continue reading →

Re: Cactus Language • Mechanics 4 The following Table summaries the mechanics of the parsing rules given in the previous post. A substructure of a painted and rooted cactus is defined recursively as follows.  Starting from the root node of … Continue reading →

To develop a parser for cactus languages in a functional programming style takes a way to express the description of a PARC in terms of its nodes, by recursion from the root up.  That requires each node to be specified … Continue reading →