{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T12:34:21Z","timestamp":1770294861027,"version":"3.49.0"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2021,3,17]],"date-time":"2021-03-17T00:00:00Z","timestamp":1615939200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"JSPS KAKENHI","award":["JP18H03288"],"award-info":[{"award-number":["JP18H03288"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,7,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by multiplying an interpretation vector and a program matrix. To optimize computation in vector spaces, we provide a method of partial evaluation of programs using linear algebra. Partial evaluation is done by unfolding rules in a program, and it is realized in a vector space by multiplying program matrices. We perform experiments using artificial data and real data, and show that partial evaluation has the potential for realizing efficient computation of huge scale of programs in vector spaces.<\/jats:p>","DOI":"10.1093\/logcom\/exab010","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T12:31:57Z","timestamp":1614083517000},"page":"1298-1316","source":"Crossref","is-referenced-by-count":13,"title":["An efficient reasoning method on logic programming using partial evaluation in vector spaces"],"prefix":"10.1093","volume":"31","author":[{"given":"Hien D","family":"Nguyen","sequence":"first","affiliation":[{"name":"Faculty of Computer Science, University of Information Technology, Ho Chi Minh City 700000, Vietnam, and Vietnam National University, Ho Chi Minh City 700000, Vietnam"}]},{"given":"Chiaki","family":"Sakama","sequence":"additional","affiliation":[{"name":"Department of Systems Engineering, Wakayama University, 930 Sakaedani, Wakayama 640-8510, Japan"}]},{"given":"Taisuke","family":"Sato","sequence":"additional","affiliation":[{"name":"Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan"}]},{"given":"Katsumi","family":"Inoue","sequence":"additional","affiliation":[{"name":"Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan"}]}],"member":"286","published-online":{"date-parts":[[2021,3,17]]},"reference":[{"key":"2021080400162691600_ref1","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0743-1066(99)00065-5","article-title":"Dynamic updates of non-monotonic knowledge bases","volume":"45","author":"Alferes","year":"2000","journal-title":"Journal of Logic Programming"},{"key":"2021080400162691600_ref2","first-page":"68","article-title":"Tensor-based abduction in Horn propositional programs","volume":"2206","author":"Aspis","year":"2018","journal-title":"Up-and-Coming and Short Papers of the 28th International Conference on Inductive Logic Programming (ILP 2018)"},{"key":"2021080400162691600_ref3","first-page":"59","article-title":"Stable and supported semantics in continuous vector spaces","volume-title":"Proc. 17th International Conference on Principles of Knowledge Representation and Reasoning","author":"Aspis","year":"2020"},{"key":"2021080400162691600_ref4","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1145\/2043174.2043195","article-title":"Answer set programming at a glance","volume":"54","author":"Brewka","year":"2011","journal-title":"Commun. 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