Material dialogues for first-order logic in constructive type theory: extended version

Dominik Wehr, Dominik Kirst

Research output: Contribution to journalArticlepeer-review


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 regard to intuitionistic material dialogues fails in both constructive and classical settings. As an alternative, we propose material dialogues played over Kripke structures. These Kripke material dialogues exhibit constructive completeness when restricting to the negative fragment. The results concerning classical material dialogues have been mechanized using the Coq interactive theorem prover.

Original languageEnglish
JournalMathematical Structures in Computer Science
StateAccepted/In press - 1 Jan 2023
Externally publishedYes


  • Dialogue games
  • completeness theorems
  • constructive type theory
  • first-order logic
  • game semantics

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Computer Science Applications


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