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The paper builds on a previously developed game for G\u00f6del logic with projection operator in Ferm\u00fcller<jats:italic>et al<\/jats:italic>. (in: M.-J. Lesot, S. Vieira, M.Z. Reformat, J.P. Carvalho, A. Wilbik, B. Bouchon-Meunier, and R.R. Yager, (eds.),<jats:italic>Information processing and management of uncertainty in knowledge-based systems<\/jats:italic>, Springer, Cham, 2020, pp. 257\u2013270). This game is extended to cover G\u00f6del logic with involutive negations and constants, and then lifted to a provability game using the concept of disjunctive strategies. Winning strategies in the provability game, with and without constants and involutive negations, turn out to correspond to analytic proofs in a version of<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\text{ SeqGZL } $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mspace\/><mml:mtext>SeqGZL<\/mml:mtext><mml:mspace\/><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>(A. Ciabattoni, and T. Vetterlein,<jats:italic>Fuzzy Sets and Systems<\/jats:italic>161(14):1941\u20131958, 2010) and in a sequent-of-relations calculus (M. Baaz, and Ch.G. Ferm\u00fcller, in: N.V. Murray, (ed.),<jats:italic>Automated reasoning with analytic tableaux and related methods<\/jats:italic>, Springer, Berlin, 1999, pp. 36\u201351) respectively.<\/jats:p>","DOI":"10.1007\/s11225-021-09966-x","type":"journal-article","created":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T14:03:55Z","timestamp":1635170635000},"page":"429-456","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["From Semantic Games to Provability: The Case of G\u00f6del Logic"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1877-1167","authenticated-orcid":false,"given":"Alexandra","family":"Pavlova","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8251-4272","authenticated-orcid":false,"given":"Robert","family":"Freiman","sequence":"additional","affiliation":[]},{"given":"Timo","family":"Lang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,25]]},"reference":[{"key":"9966_CR1","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BF01531058","volume":"4","author":"A Avron","year":"1991","unstructured":"Avron, A., Hypersequents, logical consequence and intermediate logics for concurrency, Annals of Mathematics and Artificial Intelligence 4:225\u2013248, 1991.","journal-title":"Annals of Mathematics and Artificial Intelligence"},{"key":"9966_CR2","doi-asserted-by":"crossref","unstructured":"Baaz, M., Infinite-valued g\u00f6del logics with 0-1-projections and relativizations, in P. 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