Lexical, Literal, Logical
Theme One puts cactus graphs to work in three distinct but related ways, called lexical, literal, and logical uses, and these applications make use of three distinct but overlapping subsets of the broader species of cacti. Thus we may find ourselves speaking of expressions, graphs, or files of lexical, literal, or logical types, depending on our focus and point of view at a given moment.
Logical cacti are the most inclusive class, encompassing the whole species of structures described above, and so we have already seen a typical example of a logical cactus, in its avatars as an abstract graph, a pointer structure, and a string of characters suitable for storage in an external text file.
But being a logical cactus is not just a matter of syntactic form — it means being subject to meaningful interpretations as a sign of a logical proposition. From a logical perspective we expect our cactus expressions to express something, to represent a proposition that can be true or false of something.
For present purposes it will speed things along to skip the discussion of lexical and literal cacti and jump right to the logical and semantic interpretation of cactus graphs. Readers seeking immediate enlightenment about the details may peruse the outline of notes given below. My next post in this series will take up the discussion at Note 13.
- Lexical Cacti • Notes (6) • (7) • (8) • (9) • (10)
- Literal Cacti • Notes (11) • (12)
- Logical Cacti • Notes (13) • (14) • (15) • (16)