Tag Archives: Propositional Calculus

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 →

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 →

Depending on whether a formal language is called by the type of sign it enlists or the type of object its signs denote, a cactus language may be called a sentential calculus or a propositional calculus, respectively. When the syntactic … Continue reading →

In the development of Cactus Language to date the following two species of graphs have been instrumental. Painted And Rooted Cacti (PARCAI). Painted And Rooted Conifers (PARCOI). It suffices to begin with the first class of data structures, developing their … Continue reading →

In order to facilitate the use of propositions as indicator functions it helps to acquire a flexible notation for referring to propositions in that light, for interpreting sentences in a corresponding role, and for negotiating the requirements of mutual sense … Continue reading →