@inproceedings{65fbe2d71dd942a991d30ef9e55214cd,
title = "Material Dialogues for First-Order Logic in Constructive Type Theory",
abstract = "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.",
keywords = "Constructive Type Theory, Dialogue Games, First-Order Logic, Game Semantics",
author = "Dominik Wehr and Dominik Kirst",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 28th International Workshop on Logic, Language, Information and Computation, WoLLIC 2022 ; Conference date: 20-09-2022 Through 23-09-2022",
year = "2022",
month = jan,
day = "1",
doi = "10.1007/978-3-031-15298-6_22",
language = "English",
isbn = "9783031152979",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "344--361",
editor = "Agata Ciabattoni and Elaine Pimentel and {de Queiroz}, {Ruy J.G.B.}",
booktitle = "Logic, Language, Information, and Computation - 28th International Workshop, WoLLIC 2022, Proceedings",
address = "Germany",
}