Tag Archives: Mathematics

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 →

As a temporary notation, let the relationship between a particular sign and a particular object , namely, the fact that denotes or the fact that is denoted by , be symbolized in one of the following two ways. Now consider … Continue reading →

Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually … Continue reading →