Strength (mathematical Logic)
The relative strength of two systems of formal logic can be defined via model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat .... Specifically, a logic \alpha is said to be as strong as a logic \beta if every elementary class in \beta is an elementary class in \alpha. Heinz-Dieter Ebbinghaus ''Extended logics: the general framework'' in K. J. Barwise and S. Feferman, editors, ''Model-theoretic logics'', 1985 page 43 See also * Abstract logic * Lindström's theorem References Model theory Mathematical logic Concepts in logic {{mathlogic-stub ...
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Formal 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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