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In addition, traditional logic inference methods are effective in solving problems that are based on logic, but not suitable for general tasks such as recommendations.<\/jats:p>\n                  <jats:p>In response to these challenges, this article introduces a Logical Large Language Model (L3M) that integrates the strengths of logical reasoning and LLMs. The data in L3M are represented in logical expressions, and the model uses logical constraints to learn the rules of basic logical operations such as And, Or, and Not. We conduct experiments on both theoretical tasks (solving logical equations) and practical tasks (recommender systems). The results of our theoretical experiments demonstrate that L3M is highly effective in solving logical expressions and variables. Additionally, L3M outperforms the state-of-the-art recommendation models in sequential recommendation tasks.<\/jats:p>","DOI":"10.1145\/3729238","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T13:18:26Z","timestamp":1744723106000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Probing the Symbolic Logical Reasoning Ability of Large Language Models"],"prefix":"10.1145","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0712-3527","authenticated-orcid":false,"given":"Jianchao","family":"Ji","sequence":"first","affiliation":[{"name":"Department of Computer Science, Rutgers University, New Brunswick, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3110-4481","authenticated-orcid":false,"given":"Zelong","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Rutgers University, New Brunswick, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0865-5223","authenticated-orcid":false,"given":"Shuyuan","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Rutgers University, New Brunswick, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2043-2704","authenticated-orcid":false,"given":"Wenyue","family":"Hua","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Rutgers University, New Brunswick, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3646-933X","authenticated-orcid":false,"given":"Juntao","family":"Tan","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Rutgers University, New Brunswick, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0353-3571","authenticated-orcid":false,"given":"Haoming","family":"Gong","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Rutgers University, New Brunswick, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2633-8555","authenticated-orcid":false,"given":"Yongfeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Rutgers University, New Brunswick, New Jersey, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2026,4,28]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"Josh Achiam Steven Adler Sandhini Agarwal Lama Ahmad Ilge Akkaya Florencia Leoni Aleman Diogo Almeida Janko Altenschmidt Sam Altman Shyamal Anadkat et al. 2023. 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