English

On a Second-Order Version of Russellian Theory of Definite Descriptions

Logic in Computer Science 2025-08-20 v1

Abstract

Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of Russell's theory of definite descriptions. While full second-order logic is incomplete, its fragment defined by Henkin's general models admits completeness. We develop our theory within this fragment and formalize it using a cut-free sequent calculus.

Keywords

Cite

@article{arxiv.2508.13928,
  title  = {On a Second-Order Version of Russellian Theory of Definite Descriptions},
  author = {Yaroslav Petrukhin},
  journal= {arXiv preprint arXiv:2508.13928},
  year   = {2025}
}