Material Dialogues for First-Order Logic in Constructive Type Theory

Dominik Wehr, Dominik Kirst

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Material dialogues are turn taking games which model debates about the satisfaction of logical formulas. A novel variant played over first-order structures gives rise to a notion of first-order satisfaction. We study the induced notion of validity for classical and intuitionistic first-order logic in the constructive setting of the calculus of inductive constructions. We prove that such material dialogue semantics for classical first-order logic admits constructive soundness and completeness proofs, setting it apart from standard model theoretic semantics of first-order logic. Furthermore, we prove that completeness with regards to intuitionistic material dialogues fails in constructive and classical settings. The results concerning classical material dialogues have been mechanized using the Coq interactive theorem prover.

Original languageEnglish
Title of host publicationLogic, Language, Information, and Computation - 28th International Workshop, WoLLIC 2022, Proceedings
EditorsAgata Ciabattoni, Elaine Pimentel, Ruy J.G.B. de Queiroz
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages18
ISBN (Print)9783031152979
StatePublished - 1 Jan 2022
Externally publishedYes
Event28th International Workshop on Logic, Language, Information and Computation, WoLLIC 2022 - Iaşi, Romania
Duration: 20 Sep 202223 Sep 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13468 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Workshop on Logic, Language, Information and Computation, WoLLIC 2022


  • Constructive Type Theory
  • Dialogue Games
  • First-Order Logic
  • Game Semantics

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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