Logic studies valid forms of
inference like modus ponens.
Logic
Logic is the study of correct reasoning. It includes both formal and
informal logic. Formal logic is the study of deductively valid
inferences or logical truths. It examines how conclusions follow
from premises based on the structure of arguments alone,
independent of their topic and content. Informal logic is associated
with informal fallacies, critical thinking, and argumentation
theory. Informal logic examines arguments expressed in natural
language whereas formal logic uses formal language. When used
as a countable noun, the term "a logic" refers to a specific logical
formal system that articulates a proof system. Logic plays a
central role in many fields, such as philosophy, mathematics,
computer science, and linguistics.
Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the
argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the
conclusion "I don't have to work".[1] Premises and conclusions express propositions or claims that can be
true or false. An important feature of propositions is their internal structure. For example, complex
propositions are made up of simpler propositions linked by logical vocabulary like  (and) or 
(if...then). Simple propositions also have parts, like "Sunday" or "work" in the example. The truth of a
proposition usually depends on the meanings of all of its parts. However, this is not the case for logically
true propositions. They are true only because of their logical structure independent of the specific
meanings of the individual parts.
Arguments can be either correct or incorrect. An argument is correct if its premises support its
conclusion. Deductive arguments have the strongest form of support: if their premises are true then their
conclusion must also be true. This is not the case for ampliative arguments, which arrive at genuinely new
information not found in the premises. Many arguments in everyday discourse and the sciences are
ampliative arguments. They are divided into inductive and abductive arguments. Inductive arguments are
statistical generalization—such as inferring that all ravens are black, based on many individual
observations of black ravens.[2] Abductive arguments are inferences to the best explanation—for
example, when a doctor concludes that a patient has a certain disease, as the best explanation for the
symptoms that they are observed to suffer.[3] Arguments that fall short of the standards of correct
reasoning often embody fallacies. Systems of logic are theoretical frameworks for assessing the
correctness of arguments.
Logic has been studied since antiquity. Early approaches include Aristotelian logic, Stoic logic, Nyaya,
and Mohism. Aristotelian logic focuses on reasoning in the form of syllogisms. It was considered the
main system of logic in the Western world until it was replaced by modern formal logic, which has its
roots in the work of late 19th-century mathematicians such as Gottlob Frege. Today, the most commonly
used system is classical logic. It consists of propositional logic and first-order logic. Propositional logic
only considers logical relations between full propositions. First-order logic also takes the internal parts of