Logic

Overview

Logic is the study of deductively valid inferences or logical truths.

Formal Systems

In general, this is formalized via formal systems which consist of a formal language and a proof system. A formal system endowed with semantics is called a logical system. Confusingly, this is sometimes also referred to as a formal system.

Formal Languages

A formal language comprises of an alphabet and a formal grammar. An expression is any sequence of symbols found in the alphabet. The grammer has associated rules describing how symbols of the alphabet are manipulated to create well-formed formulas (WFFs).

The syntax of a language describes the set of possible expressions that are valid utterances. An associated semantics of a language describe how these valid utterances should be interpreted.