Mathematical logic and System of logic

Mathematical logic noun - Any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity.

System of logic and mathematical logic are semantically related. In some cases you can use "System of logic" instead a noun phrase "Mathematical logic".

System of logic noun - A system of reasoning.

Mathematical logic and system of logic are semantically related. Sometimes you can replace phrase "Mathematical logic" with "System of logic", this phrases are similar.