Linear logic: Difference between revisions
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(Created page with "'''Linear logic''' is a refinement of classical logic and intuitionistic logic. Instead of emphasizing truth, as in classical logic, or proof, as in intuitionistic logic, linear logic emphasizes the role of formulas as resources. To achieve this focus, linear logic does not allow the usual structural rules of contraction and weakening to apply to all formulas but only those formulas marked with certain modals. Linear logic contains a fully involutive negation...") Β |
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'''Linear logic''' is a refinement of [[classical logic]] and [[intuitionistic logic]]. Instead of emphasizing [[truth]], as in classical logic, or proof, as in intuitionistic logic, linear logic emphasizes the role of formulas as resources. To achieve this focus, linear logic does not allow the usual structural rules of contraction and weakening to apply to all formulas but only those formulas marked with certain modals. Linear logic contains a fully involutive negation while maintaining a strong constructive interpretation. Linear logic also provides new insights into the nature of proofs in both classical and intuitionistic logic. Given its focus on resources, linear logic has found many applications in Computer Science. | '''Linear logic''' is a refinement of [[classical logic]] and [[intuitionistic logic]]. Instead of emphasizing [[truth]], as in classical logic, or proof, as in intuitionistic logic, linear logic emphasizes the role of formulas as resources. To achieve this focus, linear logic does not allow the usual structural rules of contraction and weakening to apply to all formulas but only those formulas marked with certain modals. Linear logic contains a fully involutive negation while maintaining a strong constructive interpretation. Linear logic also provides new insights into the [[nature]] of proofs in both classical and intuitionistic logic. Given its focus on resources, linear logic has found many applications in Computer Science. | ||
[[Category:Definitions]] | [[Category:Definitions]] | ||
Revision as of 17:10, 17 February 2023
Linear logic is a refinement of classical logic and intuitionistic logic. Instead of emphasizing truth, as in classical logic, or proof, as in intuitionistic logic, linear logic emphasizes the role of formulas as resources. To achieve this focus, linear logic does not allow the usual structural rules of contraction and weakening to apply to all formulas but only those formulas marked with certain modals. Linear logic contains a fully involutive negation while maintaining a strong constructive interpretation. Linear logic also provides new insights into the nature of proofs in both classical and intuitionistic logic. Given its focus on resources, linear logic has found many applications in Computer Science.