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Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .
Computational logic is the branch of logic and computer science that studies how to implement mathematical reasoning and logical formalisms using computers. This includes, for example, automatic theorem provers , which employ rules of inference to construct a proof step by step from a set of premises to the intended conclusion without human ...
Peirce's revisions of logic's divisions Peirce in 1902, 1903: Logic (begins on general level with presuppositions of reason, logical conception of mind, nature of belief & doubt, etc.). A. Stechiology (classes of signs & their combinations). B. Critic (modes of argument). C. Methodeutic (methods of inquiry). Peirce in 1906: Logic.
A logic that extends first-order logic to allow for more nuanced expressions of quantifier scope and dependence, particularly in contexts of game-theoretical semantics. independent Referring to a pair of propositions that are not contrary , subcontrary , contradictory , logically equivalent , or implied one by the other (either the first by the ...
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
Logic (from Greek: λογική, logikḗ, 'possessed of reason, intellectual, dialectical, argumentative') [5] [6] [note 1] is the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions ().
Diagrammatic representation of computer logic gates. Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas: Theoretical foundations and analysis; Use of computer technology to aid logicians; Use of concepts from logic for computer applications
Mathematical logic is the study of formal logic within mathematics. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. Mathematical logic is divided into four parts: Model theory; Proof theory; Recursion theory, also known as computability theory ...