Generalized Definitional Reflection and the Inversion Principle
نویسندگان
چکیده
منابع مشابه
Generalized Definitional Reflection and the Inversion Principle
The term inversion principle goes back to Lorenzen who coined it in the early 1950s. It was later used by Prawitz and others to describe the symmetric relationship between introduction and elimination inferences in natural deduction, sometimes also called harmony. In dealing with the invertibility of rules of an arbitrary atomic production system, Lorenzen’s inversion principle has a much wider...
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The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister (1990, 1991) proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by...
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This paper discusses two rules of definitional reflection: The “logical” version of definitional reflection as used in the extended logic programming language GCLA and the “ω”-version of definitional reflection as proposed by Eriksson and Girard. The logical version is a Left-introduction rule completely analogous to the Left-introduction rules for logical operators in Gentzen-style sequent sys...
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We show how lattice paths and the reflection principle can be used to give easy proofs of unimodality results. In particular, we give a “one-line” combinatorial proof of the unimodality of the binomial coefficients. Other examples include products of binomial coefficients, polynomials related to the Legendre polynomials, and a result connected to a conjecture of Simion.
متن کاملExternal Inversion , Internal Inversion , and Reflection Invariance
Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by the application of internal space inversion or time reversal is generally a different particle. From this point of view the intrinsic parity of a nuclear pa...
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ژورنال
عنوان ژورنال: Logica Universalis
سال: 2007
ISSN: 1661-8297,1661-8300
DOI: 10.1007/s11787-007-0018-7