{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,20]],"date-time":"2024-01-20T15:10:32Z","timestamp":1705763432678},"reference-count":81,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T00:00:00Z","timestamp":1678492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,1,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Information present in any training set of vectors for machine learning can be interpreted in two different ways, either as whole states or as individual atomic units. In this paper, we show that these alternative information distributions are often inherently incongruent within the training set. When learning with a Boltzmann machine, modifications in the network architecture can select one type of distributional information over the other; favouring the activation of either state exemplar or atomic characteristics.<\/jats:p>\n               <jats:p>This choice of distributional information is of relevance when considering the representation of knowledge in logic. Traditional logic only utilises preference that is the correlate of whole state exemplar frequency. We propose that knowledge representation derived from atomic characteristic activation frequencies is the correlate of compositional typicality, which currently has limited formal definition or application in logic. Further, we argue by counter-example, that any representation of typicality by \u2018most preferred model semantics\u2019 is inadequate. We provide a definition of typicality derived from the probability of characteristic features; based on neural network modelling.<\/jats:p>","DOI":"10.1093\/logcom\/exac104","type":"journal-article","created":{"date-parts":[[2023,3,11]],"date-time":"2023-03-11T22:05:36Z","timestamp":1678572336000},"page":"33-74","source":"Crossref","is-referenced-by-count":0,"title":["Modelling Supra-Classical Logic in a Boltzmann Neural Network: II Incongruence"],"prefix":"10.1093","volume":"34","author":[{"given":"Glenn","family":"Blanchette","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Otago , Dunedin 9054, New Zealand"}]},{"given":"Anthony","family":"Robins","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Otago , Dunedin 9054, New Zealand"}]}],"member":"286","published-online":{"date-parts":[[2023,3,11]]},"reference":[{"key":"2024012014560516900_ref1","volume-title":"Simulated Annealing and Boltzmann Machines","author":"Aarts","year":"1990"},{"key":"2024012014560516900_ref2","first-page":"91","volume-title":"Local Search in Combinatorial Optimization, chapter Simulated Annealing","author":"Aarts","year":"1997"},{"key":"2024012014560516900_ref3","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1080\/00201746508601430","article-title":"The logic of conditionals","volume":"8","author":"Adams","year":"1965","journal-title":"Inquiry"},{"key":"2024012014560516900_ref4","doi-asserted-by":"crossref","first-page":"510","DOI":"10.2307\/2274239","article-title":"On the logic of theory change: Partial meet contraction and revision functions","volume":"50","author":"Alchourron","year":"1985","journal-title":"Journal of Symbolic Logic"},{"key":"2024012014560516900_ref5","volume-title":"Central limit theorem (summary)","author":"Annis","year":"2014"},{"key":"2024012014560516900_ref6","volume-title":"The Description Logic Handbook: Theory, Implementations and Applications","author":"Baader","year":"2003"},{"key":"2024012014560516900_ref7","first-page":"32","article-title":"Non-monotonic inferences in neural networks","author":"Balkenius","year":"1991","journal-title":"In Principles of Knowledge Representation and Reasoning, pages"},{"key":"2024012014560516900_ref8","first-page":"305","article-title":"Continuity of the conceptual system across species","volume":"9","author":"Barsalou","year":"1985","journal-title":"Trends in Cognitive Sciences"},{"key":"2024012014560516900_ref9","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1017\/S0140525X99002149","article-title":"Perceptual symbol systems","volume":"22","author":"Barsalou","year":"1999","journal-title":"Behavioural and Brain Sciences"},{"key":"2024012014560516900_ref10","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.ijar.2021.12.001","article-title":"Typicality: A formal concept analysis account","volume":"142","author":"Belohlavek","year":"2022","journal-title":"International Journal of Approximate Reasoning"},{"key":"2024012014560516900_ref11","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.ins.2019.12.022","article-title":"An evolving approach to data streams clustering based on typicality and eccentricity data analytics","volume":"518","author":"Bezerra","year":"2020","journal-title":"Information Sciences"},{"key":"2024012014560516900_ref12","volume-title":"Towards a representation of non-monotonic inference in an artificial neural network","author":"Blanchette","year":"2015"},{"key":"2024012014560516900_ref13","volume-title":"What does a boltzmann machine learn? 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