Introduction

Doesn't exist in reality

concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics.

Formal systems are an abstract structure and formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules.[1]

Because of their non-empirical nature, formal sciences are construed by outlining a set of axioms and definitions from which other statements (theorems) are deduced. For this reason, in Rudolf Carnap's logical-positivist conception of the epistemology of science, theories belonging to formal sciences are understood to contain no synthetic statements, instead containing only analytic statements.[2][3]

Formal language