About: System L

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System L is a natural deductive logic developed by E.J. Lemmon. Derived from Suppes' method, it represents natural deduction proofs as sequences of justified steps. Both methods are derived from Gentzen's 1934/1935 natural deduction system, in which proofs were presented in tree-diagram form rather than in the tabular form of Suppes and Lemmon. Although the tree-diagram layout has advantages for philosophical and educational purposes, the tabular layout is much more convenient for practical applications.

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dbo:abstract	System L is a natural deductive logic developed by E.J. Lemmon. Derived from Suppes' method, it represents natural deduction proofs as sequences of justified steps. Both methods are derived from Gentzen's 1934/1935 natural deduction system, in which proofs were presented in tree-diagram form rather than in the tabular form of Suppes and Lemmon. Although the tree-diagram layout has advantages for philosophical and educational purposes, the tabular layout is much more convenient for practical applications. A similar tabular layout is presented by Kleene. The main difference is that Kleene does not abbreviate the left-hand sides of assertions to line numbers, preferring instead to either give full lists of precedent propositions or alternatively indicate the left-hand sides by bars running down the left of the table to indicate dependencies. However, Kleene's version has the advantage that it is presented, although only very sketchily, within a rigorous framework of metamathematical theory, whereas the books by Suppes and Lemmon are applications of the tabular layout for teaching introductory logic. (en)
dbo:wikiPageExternalLink	https://www.sfu.ca/~jeffpell/papers/pelletierNDtexts.pdf http://gdz.sub.uni-goettingen.de/dms/resolveppn/%3FPPN=GDZPPN002375508 http://gdz.sub.uni-goettingen.de/dms/resolveppn/%3FPPN=GDZPPN002375605%7Cdoi=10.1007/bf01201363
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rdfs:comment	System L is a natural deductive logic developed by E.J. Lemmon. Derived from Suppes' method, it represents natural deduction proofs as sequences of justified steps. Both methods are derived from Gentzen's 1934/1935 natural deduction system, in which proofs were presented in tree-diagram form rather than in the tabular form of Suppes and Lemmon. Although the tree-diagram layout has advantages for philosophical and educational purposes, the tabular layout is much more convenient for practical applications. (en)
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