Hilbert-style Deductive Systems
In logic, more specifically proof theory, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of formal proof Proof calculus, system attributed to Gottlob FregeMáté & Ruzsa 1997:129 and David Hilbert. These deductive systems are most often studied for first-order logic, but are of interest for other logics as well. It is defined as a deductive system that generates theorems from axioms and inference rules, especially if the only postulated inference rule is modus ponens. Every Hilbert system is an axiomatic system, which is used by many authors as a sole less specific term to declare their Hilbert systems, without mentioning any more specific terms. In this context, "Hilbert systems" are contrasted with natural deduction systems, in which no axioms are used, only inference rules. While all sources that refer to an "axiomatic" logical proof system characte ...
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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 wor ...
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