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Boolean proportions ...
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Abstract:
Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper studies analogical proportions between booleans of the form `$a$ is to $b$ what $c$ is to $d$' called boolean proportions. Technically, we instantiate an abstract algebraic framework of analogical proportions -- recently introduced by the author -- in the boolean domain consisting of the truth values true and false together with boolean functions. It turns out that our notion of boolean proportions has appealing mathematical properties and that it coincides with a prominent model of boolean proportions in the general case. In a broader sense, this paper is a further step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity. ... : arXiv admin note: text overlap with arXiv:2006.02854 ...
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Keyword:
Artificial Intelligence cs.AI; Discrete Mathematics cs.DM; FOS Computer and information sciences; Logic in Computer Science cs.LO
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URL: https://dx.doi.org/10.48550/arxiv.2109.00388
https://arxiv.org/abs/2109.00388
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Polynomial Graph Parsing with Non-Structural Reentrancies ...
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The Linear Arrangement Library. A new tool for research on syntactic dependency structures ...
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| 5 |
Complete Variable-Length Codes: An Excursion into Word Edit Operations
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In: LATA 2020 ; https://hal.archives-ouvertes.fr/hal-02389403 ; LATA 2020, Mar 2020, Milan, Italy (2020)
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The relationship between word complexity and computational complexity in subshifts
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In: https://hal.archives-ouvertes.fr/hal-02063174 ; 2019 (2019)
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Avoiding or limiting regularities in words
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In: Sequences, Groups and Number Theory ; https://hal-lirmm.ccsd.cnrs.fr/lirmm-02083655 ; Sequences, Groups and Number Theory, pp.177-212, 2018, 978-3-319-69151-0. ⟨10.1007/978-3-319-69152-7_5⟩ (2018)
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| 12 |
Tools for the analysis of noisy discrete curves ; Outils pour l'analyse des courbes discrètes bruitées
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In: https://tel.archives-ouvertes.fr/tel-01947024 ; Géométrie algorithmique [cs.CG]. Université de Lorraine, 2018. Français. ⟨NNT : 2018LORR0159⟩ (2018)
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| 14 |
K4-free Graphs as a Free Algebra
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In: 42nd International Symposium on Mathematical Foundations of Computer Science ; https://hal.archives-ouvertes.fr/hal-01515752 ; 42nd International Symposium on Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmark (2017)
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Matroids Hitting Sets and Unsupervised Dependency Grammar Induction ...
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Parsing with Traces: An $O(n^4)$ Algorithm and a Structural Representation ...
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| 19 |
Palindromic language of thin discrete planes
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In: ISSN: 1879-2294 ; EISSN: 0304-3975 ; Theoretical Computer Science ; https://hal.archives-ouvertes.fr/hal-01262289 ; Theoretical Computer Science, Elsevier, 2016, pp.101-108. ⟨10.1016/j.tcs.2015.11.023⟩ (2016)
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Synchronizing Relations on Words
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In: ISSN: 1432-4350 ; EISSN: 1433-0490 ; Theory of Computing Systems ; https://hal.archives-ouvertes.fr/hal-01778459 ; Theory of Computing Systems, Springer Verlag, 2015, 57 (2), pp.287 - 318. ⟨10.1007/s00224-014-9584-2⟩ (2015)
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