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CS322/lectures/semiotics.md

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Semiotics

Semiotics is the study of signs and symbols and their use or interpretation. What is a sign? A sign is a token that represents something. What a sign represents depends upon the interpreter of that sign. The intended meaning is often referred to as the value of the sign. A symbol likewise is a token that represents something. (Interesting side note is to explore the entymology of the word.)

3 Points of view of semiotics

**syntax** - the grammar or structure of a language
**semantics** - the meaning of a language
**pragmatics** - the effective use of a language

Duality, in mathematics, principle whereby one true statement can be obtained from another by merely interchanging two words. It is a property belonging to the branch of algebra known as lattice theory, which is involved with the concepts of order and structure common to different mathematical systems. A mathematical structure is called a lattice if it can be ordered in a specified way (see order). Projective geometry, set theory, and symbolic logic are examples of systems with underlying lattice structures, and therefore also have principles of duality.

The development of symbolic logic led to the development of programming languages. Programming languages depend upon the duality that exists between a language and the machine that recognizes that language.