Logic is a field of science that teaches and researches the reasonable conclusion.For this purpose, so-called logical systems are defined and investigated. A logical system is a formal system with an underlying formallanguage, a set of truth values, and an illustrationcalled semantics.
Semantics assigns a truth value to each word of formal language. In addition, semantic and syntactic inference relationships can be defined.The semantic inference relationship is defined solely by the semantics and their definition of an “if, then” operator.For the syntactic inference relationship, an axiomand final rulesystem must be determined, which behaves according to the semantics.Often a logical system is simply referred to as “logic”.
Language, truth values and semantics of logical systems can also be defined mathematically at will.The logical system, for example, does not have to have anything to do with nature. The essential characteristic of a logical system is that its syntactic inference relationship is independent of semantics or Meaning works: Statements are examined only in terms of their structure with regard to truth values, regardless of the content of the statements.Therefore, a logical system is also a “formal” system, because it considers the form, not the content. This makes it possible for arguments written as formal evidence to be objectively verifiable: a simple tool (e.g. computer program) can perform the computational steps without the susceptibility to error of thinking. The fact that we are not aware of any other scientific method that is even close to error-resistant shows how high-quality and important the logic or formal methods for the sciences. Especially since the support of computers through their enormous computing power greatly accelerates scientific progress.
Although the natural sciences use specific logical systems of so-called “mathematical logic”, the field of logic encompasses much more, namely the study of all logical systems whose concepts of truth are not at all compatible with must be the concept of truth in mathematical logic.Popular examples include trivalent logic, fuzzy logic, and paraconsistentlogic.