Category Archives: Mathematics

We now have the materials in place to formulate a definition of our subject. The painted cactus language with paints in the set is the formal language defined as follows. In the idiom of formal language theory, a string is … Continue reading →

Defining the basic operations of concatenation and surcatenation on arbitrary strings gives them operational meaning for the all‑inclusive language   With that in hand it is time to adjoin the notion of a more discriminating grammaticality, in other words, a … Continue reading →

The array of syntactic operators may be put in more organized form by making a few additional conventions and auxiliary definitions. Concatenation The conception of concatenation permits extension to its natural prequel, the corresponding operator on zero operands. From that … Continue reading →

The definitions of the syntactic connectives can be made a little more succinct by defining the following pair of generic operators on strings. Concatenation The concatenation of the sequence of strings is defined recursively as follows. Surcatenation The surcatenation of … Continue reading →

The easiest way to define the language is to indicate the general run of operations required to construct the greater share of its sentences from the designated few which require a special election. To do that we introduce a family … Continue reading →

The informal mechanisms illustrated in the preceding discussion equip us with a description of cactus language adequate to providing conceptual and computational representations for the minimal formal logical system variously known as propositional logic or sentential calculus. The painted cactus … Continue reading →

A few definitions from formal language theory are required at this point. An alphabet is a finite set of signs, typically, A string over an alphabet is a finite sequence of signs from The length of a string is just … Continue reading →