Typically, a logic consists of a formal or informal language together with a deductive system or a model-theoretic semantics. The language is, or corresponds to, a part of a natural language like German, English or Chinese. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions, or possible truth conditions, for at least part of the language.

Logic can be defined as the study of consistent sets of beliefs Hodges 2001, this will be kept in mind, however to define logic as the study of valid arguments or valid reasoning is closer to the root meaning of ''Logo'' and is preferred here.

Logic is of practical importance in underpinning the main concern of this site; appliction and development of:

  • Mathematics
  • Science
  • Technology.

Logic proper, as a system of reasoning, starts with Aristotle Gabbay 2004. However the mathematical arguments and the attempts at critical reasoning of the Presocratic Philosophers Barnes 1982, followed by Socrates himself then Plato form an important cultural context and body of argumentation that was necessary before Aristotle could provide his formalisation.

Logic comes in a number of variants describes in the sub-pages.