{"type":"ScholarlyArticle","title":"On the Decidability of Intuitionistic Tense Logic without Disjunction","authors":[{"name":"Fei Liang","slug":"fei-liang","given":"Fei","family":"Liang","affiliation":"School of Philosophy and Social Development , Shandong University , China; Institute of Concept and Reasoning , Shandong University , China"},{"name":"Zhe Lin","slug":"zhe-lin","given":"Zhe","family":"Lin","affiliation":"Department of Philosophy , Xiamen University , China"}],"abstract":"Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.","doi":"10.24963/ijcai.2020/249","url":"https://ijcai.org/proceedings/2020/249","pdf":"https://ijcai.org/proceedings/2020/0249.pdf","markdown":"https://ijcai.org/proceedings/2020/249.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/249","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":249,"pages":{"first":1798,"last":1804},"keywords":["Knowledge Representation and Reasoning: Non-monotonic Reasoning, Common-Sense Reasoning","Knowledge Representation and Reasoning: Other","Knowledge Representation and Reasoning: Qualitative, Geometric, Spatial, Temporal Reasoning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25311/file_25311.m3u8","length_sec":279,"provider":"hls"}],"references":[{"position":1,"raw":"[Balbiani and Diéguez, 2016] Philippe Balbiani and Martín Diéguez. 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