منابع مشابه
Hypothetical Reasoning and Definitional Reflection in Logic Programming
This paper describes the logical and philosophical background of an extension of logic programming which uses a general schema for introducing assumptions and thus presents a new view of hypothetical reasoning. The detailed proof theory of this system is given in [7], matters of implementation and control of the corresponding programming language GCLA with detailed examples can be found in [1, ...
متن کاملBasic Logic: Reflection, Symmetry, Visibility
We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant ...
متن کاملRules of Definitional Reflection
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...
متن کاملGeneralized 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...
متن کاملInversion by Definitional Reflection and the Admissibility of Logical Rules
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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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2013
ISSN: 0168-0072
DOI: 10.1016/j.apal.2012.10.010