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The Explosion Calculus
Studia Logica ( IF 0.6 ) Pub Date : 2019-04-12 , DOI: 10.1007/s11225-019-09861-6
Michael Arndt

A calculus for classical propositional sequents is introduced that consists of a restricted version of the cut rule and local variants of the logical rules. Employed in the style of proof search, this calculus explodes a given sequent into its elementary structural sequents—the topmost sequents in a derivation thus constructed—which do not contain any logical constants. Some of the properties exhibited by the collection of elementary structural sequents in relation to the sequent they are derived from, uniqueness and unique representation of formula occurrences, will be discussed in detail. Based on these properties it is suggested that a collection of elementary structural sequents constitutes the purely structural representation of the sequent from which it is obtained.

中文翻译:

爆炸演算

引入了经典命题序列的演算,它由切割规则的受限版本和逻辑规则的局部变体组成。该演算采用证明搜索的风格,将给定的序列分解为其基本结构序列——由此构造的推导中的最顶层序列——其中不包含任何逻辑常数。将详细讨论基本结构序列的集合与它们所源自的序列、唯一性和式出现的唯一表示相关的一些性质。基于这些特性,建议基本结构序列的集合构成从中获得它的序列的纯结构表示。
更新日期:2019-04-12
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