Abstract$${ CatLog3}$$CatLog3 is a 7000 line Prolog parser/theorem-prover for logical categorial grammar. In such logical categorial grammar syntax is universal and grammar is reduced to logic: an expression is grammatical if and only if an associated logical statement is a theorem of a fixed calculus. Since the syntactic component is invariant, being the logic of the calculus, logical categorial grammar is purely lexicalist and a particular language model is defined by just a lexical dictionary. The foundational logic of continuity was established by Lambek (Am Math Mon 65:154–170, 1958) (the Lambek calculus) while a corresponding extension including also logic of discontinuity was established by Morrill and Valentín (Linguist Anal 36(1–4):167–192, 2010) (the displacement calculus). $${ CatLog3}$$CatLog3 implements a logic including as primitive connectives the continuous (concatenation) and discontinuous (intercalation) connectives of the displacement calculus, additives, 1st order quantifiers, normal modalities, bracket modalities, and universal and existential subexponentials. In this paper we review the rules of inference for these primitive connectives and their linguistic applications, and we survey the principles of Andreoli’s focusing, and of a generalisation of van Benthem’s count-invariance, on the basis of which $${ CatLog3}$$CatLog3 is implemented.

中文翻译：

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逻辑语法 CatLog3 的解析/定理证明

Abstract$${ CatLog3}$$CatLog3 是一个 7000 行的 Prolog 解析器/定理证明器，用于逻辑分类语法。在这种逻辑范畴文法中，句法是通用的，文法被简化为逻辑：当且仅当相关的逻辑语句是固定演算的定理时，表达式才是符合语法的。由于句法成分是不变的，作为微积分的逻辑，逻辑范畴文法纯粹是词汇主义的，特定的语言模型仅由词汇词典定义。连续性的基本逻辑是由 Lambek (Am Math Mon 65:154–170, 1958)（Lambek calculus）建立的，而包括不连续性逻辑的相应扩展是由 Morrill 和 Valentín（Linguist Anal 36(1–4) 建立的） :167–192, 2010)（位移演算）。$${ CatLog3}$$CatLog3 实现了一种逻辑，包括作为原始连接词的位移演算的连续（串联）和不连续（插值）连接词、添加剂、一阶量词、正常模态、括号模态以及通用和存在子指数。在本文中，我们回顾了这些原始连接词及其语言应用的推理规则，我们调查了 Andreoli 聚焦的原理，以及 van Benthem 计数不变性的概括，在此基础上 $${ CatLog3}$$ CatLog3 已实施。