First-Order Tableaux with Unification for Henkin Quantifiers

16 pages•Published: October 23, 2026

Matthias Baaz, Mariami Gamsakhurdia, Anela Lolic and Stella Mahler

Abstract

First-order logic extended with Henkin quantifiers is not recursively enumerable, even for the simplest Henkin quantifier that is not definable in first-order logic. Despite this, such quantifiers arise naturally in the analysis of partially ordered quantification, motivating partial proof systems suitable for automated reasoning. We present a tableau-based proof system with unification for first-order logic extended by the simplest Henkin quantifier. The system is derived from a second-order function calculus but avoids second-order unification by internalizing dependency structure via side-variable and weak regularity constraints.

Keyphrases: eigenvariable conditions, henkin quantifiers, tableau methods

In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 348-363.

Links:	https://easychair.org/publications/paper/3Vr3
	https://doi.org/10.29007/hvv6

BibTeX entry

@inproceedings{LPAR-26:First_Order_Tableaux_with,
  author    = {Matthias Baaz and Mariami Gamsakhurdia and Anela Lolic and Stella Mahler},
  title     = {First-Order Tableaux with Unification for Henkin Quantifiers},
  booktitle = {Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning},
  editor    = {Erika Ábrahám and Nikolaj Bjørner and Michael Rawson},
  series    = {EPiC Series in Computing},
  volume    = {112},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/3Vr3},
  doi       = {10.29007/hvv6},
  pages     = {348-363},
  year      = {2026}}

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