The science that systematically studies the function of signs is known as

The correct option is Semiology.

To understand why this is the correct answer, let us break down the definition and origin of the terms:
1. Semiology (or semiotics) is the systematic study of signs, symbols, and how they function to convey meaning. Coined by Ferdinand de Saussure, a founder of modern linguistics, it explores how signs are created, interpreted, and used to communicate within societies.
2. Semantics, while related, is specifically the branch of linguistics and logic concerned with the study of meaning in language, rather than the broader study of all signs and symbol systems.
3. Scriptoria refers to the rooms in medieval monasteries where scribes copied manuscripts.
4. Sismography (seismography) is the science of measuring and recording earthquakes.

Therefore, Semiology is the precise scientific term for the systematic study of the function of signs.