{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T04:41:31Z","timestamp":1758343291774,"version":"3.44.0"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"7","license":[{"start":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T00:00:00Z","timestamp":1700438400000},"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":[[2025,9,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>By making use of three IBM case studies involving the author and colleagues, this paper is about applying theory to practice. In the first case study, the system builders (or practitioners) initiated the interaction. This interaction led to the following problem. Assume that there is a set of objects, each with multiple attributes, and there is a numerical score assigned to each attribute of each object. In the spirit of real-valued logics, there is a scoring function (such as the min or the average), and a ranking of the objects is obtained by applying the scoring function to the scores of each object\u2019s attributes The problem is to find the top $k$ objects, while minimizing the number of database accesses. An algorithm is given that is optimal in an extremely strong sense: not just in the worst case or the average case, but (up to a constant factor) in every case! Even though the algorithm is only 8 lines long (!), the paper containing the algorithm won the 2014 G\u00f6del Prize, the top prize for a paper in theoretical computer science. The interaction in the second case study was initiated by theoreticians, who wanted to lay the foundations for \u2018data exchange\u2019, in which data is converted from one format to another. Although this problem may sound mundane, the issues that arise are fascinating, and this work made data exchange a new subfield, with special sessions in every major database conference. This work won the 2020 Alonzo Church Award, the highest prize for research in logic and computation. The third case study, specifically on real-valued (or \u2018fuzzy\u2019) logic, arose as part of a large \u2018Logical Neural Nets\u2019 (LNN) project at IBM. The inputs to, say, an \u2018and\u2019 gate could each be any numbers in the interval [0,1]. The system builders of LNN wanted a sound and complete axiomatization for real-valued logic, so that they could arrive at truth values given other truth values whenever possible. This recent work provides a sound and complete axiomatization for a large class of real-valued logics, including the most common ones. It also allows weights, where the importance of some subformulas can be greater than that of other subformulas. This paper is aimed at both theoreticians and system builders, to show them the mutual benefits of working together. This is via the three case studies mentioned above: two initiated by the system builders, and one by the theoreticians. The moral for the theoreticians is to show by example how to apply theory to practice, and why applying theory to practice can lead to better theory. The moral for the system builders is the value of theory, and the value of involving theoreticians. This paper is written in a very informal style. In fact, it is based closely on a talk on \u2018Applying theory to practice\u2019 that the author has presented a number of times.<\/jats:p>","DOI":"10.1093\/logcom\/exad066","type":"journal-article","created":{"date-parts":[[2023,11,22]],"date-time":"2023-11-22T12:21:39Z","timestamp":1700655699000},"source":"Crossref","is-referenced-by-count":0,"title":["Applying Theory to Practice"],"prefix":"10.1093","volume":"35","author":[{"given":"Ronald","family":"Fagin","sequence":"first","affiliation":[{"name":"IBM Almaden Research Center , San Jose, CA"}]}],"member":"286","published-online":{"date-parts":[[2023,11,20]]},"reference":[{"key":"2025091917092375700_ref1","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1145\/320083.320091","article-title":"The theory of joins in relational databases","volume":"4","author":"Aho","year":"1979","journal-title":"ACM Transactions on Database Systems (TODS)"},{"key":"2025091917092375700_ref2","first-page":"1","article-title":"Composition with target constraints","volume-title":"Logical Methods in Computer Science","author":"Arenas","year":"2011"},{"article-title":"New foundations of reasoning via real-valued first-order logics","year":"2023","author":"Badia","key":"2025091917092375700_ref3"},{"key":"2025091917092375700_ref4","first-page":"149","article-title":"On the analytic formalism of the theory of fuzzy sets","volume-title":"Information Sciences","author":"Bellman","year":"1973"},{"key":"2025091917092375700_ref5","first-page":"124","article-title":"Towards heterogeneous multimedia information systems: the garlic approach","volume-title":"RIDE-DOM \u201995 (5th Int\u2019l Workshop on Research Issues in Data Engineering: Distributed Object Management)","author":"Carey","year":"1995"},{"key":"2025091917092375700_ref6","first-page":"209","article-title":"Criteria aggregation and ranking of alternatives in the framework of fuzzy set theory","volume-title":"Framework of Fuzzy Set Theory, in Fuzzy Sets and Decision Analysis","author":"Dubois","year":"1984"},{"key":"2025091917092375700_ref7","first-page":"627","article-title":"Fuzzy logics with enriched language","volume-title":"Chapter VIII of the Handbook of Mathematical Fuzzy Logic","author":"Esteva","year":"2011"},{"key":"2025091917092375700_ref8","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1145\/320557.320571","article-title":"Multivalued dependencies and a new normal form for relational databases","volume":"2","author":"Fagin","year":"1977","journal-title":"ACM Transactions on Database Systems (TODS)"},{"key":"2025091917092375700_ref9","first-page":"1","article-title":"Fuzzy queries in multimedia database systems","volume-title":"ACM Symposium on Principles of Database Systems (PODS)","author":"Fagin","year":"1998"},{"key":"2025091917092375700_ref10","first-page":"207","article-title":"Data exchange: semantics and query answering","volume-title":"International Conference on Database Theory (ICDT)","author":"Fagin","year":"2003"},{"key":"2025091917092375700_ref11","first-page":"83","article-title":"Composing schema mappings: second-order dependencies to the rescue","volume-title":"ACM Symposium on Principles of Database Systems (PODS)","author":"Fagin","year":"2004"},{"key":"2025091917092375700_ref12","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/S0022-0000(03)00026-6","article-title":"Optimal aggregation algorithms for middleware","volume":"66","author":"Fagin","year":"2003","journal-title":"Journal of Computer and System Sciences"},{"article-title":"Foundations of reasoning with uncertainty via real-valued logics","year":"2023","author":"Fagin","key":"2025091917092375700_ref13"},{"key":"2025091917092375700_ref14","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1023\/A:1008023416823","article-title":"Relaxing the triangle inequality in pattern matching","volume":"30","author":"Fagin","year":"1993","journal-title":"International Journal of Computer Vision"},{"key":"2025091917092375700_ref15","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1006\/jcss.1998.1600","article-title":"Combining fuzzy information from multiple systems","volume":"58","author":"Fagin","year":"1999","journal-title":"Journal of Computer and System Sciences"},{"key":"2025091917092375700_ref16","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-5300-3","volume-title":"Metamathematics of Fuzzy Logic","author":"H\u00e1jek","year":"1998"},{"key":"2025091917092375700_ref17","doi-asserted-by":"crossref","DOI":"10.1145\/375663.375767","article-title":"Clio: a semi-automatic tool for schema mapping","volume-title":"System Demonstration. 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