Sergey Slavnov - Making first order linear logic a generating grammar

lmcs:9727 - Logical Methods in Computer Science, November 17, 2023, Volume 19, Issue 4 -
Making first order linear logic a generating grammarArticle

Authors: Sergey Slavnov

    It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type calculus (ETTC). ETTC is a calculus of specific typed terms, which represent tuples of strings, more precisely bipartite graphs decorated with strings. Types are derived from linear logic formulas, and rules correspond to concrete operations on these string-labeled graphs, so that they can be conveniently visualized. This provides the above mentioned fragment of MLL1 that is relevant for language modeling not only with some alternative syntax and intuitive geometric representation, but also with an intrinsic deductive system, which has been absent. In this work we consider a non-trivial notationally enriched variation of the previously introduced ETTC, which allows more concise and transparent computations. We present both a cut-free sequent calculus and a natural deduction formalism.

    Volume: Volume 19, Issue 4
    Published on: November 17, 2023
    Accepted on: August 8, 2023
    Submitted on: June 22, 2022
    Keywords: Computer Science - Computation and Language,Computer Science - Logic in Computer Science,Mathematics - Logic

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