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Effective and Complete Discovery of Order Dependencies via Set-based Axiomatization [article]

Jaroslaw Szlichta, Parke Godfrey, Lukasz Golab, Mehdi Kargar, Divesh Srivastava
2016 arXiv   pre-print
This is based on a novel polynomial mapping to a canonical form for ODs, and a sound and complete set of axioms (inference rules) for canonical ODs.  ...  Hence, proposals for automatic discovery have been made for some classes of ICs, such as functional dependencies (FDs), and recently, order dependencies (ODs).  ...  Set-based Axiomatization. We introduce axioms for set-based canonical ODs and prove these are sound and complete (Section 3.2).  ... 
arXiv:1608.06169v2 fatcat:dmctyt75xnfehbrhacji6x7pre

Effective and complete discovery of order dependencies via set-based axiomatization

Jaroslaw Szlichta, Parke Godfrey, Lukasz Golab, Mehdi Kargar, Divesh Srivastava
2017 Proceedings of the VLDB Endowment  
Hence, proposals for automatic discovery have been made for some classes of ICs, such as functional dependencies (FDs), and recently, order dependencies (ODs).  ...  We present a new OD discovery algorithm enabled by a novel polynomial mapping to a canonical form of ODs, and a sound and complete set of axioms (inference rules) for canonical ODs.  ...  Set-based Axiomatization. We introduce axioms for set-based canonical ODs and prove these are sound and complete (Section 3.2).  ... 
doi:10.14778/3067421.3067422 fatcat:s5dwqctbtrdzxh5xkco4io2n3e

Relational Models of Microarchitectures for Formal Security Analyses [article]

Nicholas Mosier, Hanna Lachnitt, Hamed Nemati, Caroline Trippel
2021 arXiv   pre-print
Second, we develop a static analysis tool based on LCMs which automatically identifies Spectre vulnerabilities in programs and scales to analyze realistic-sized codebases, like libsodium.  ...  First, we demonstrate that our leakage definition faithfully captures a sampling of (transient and non-transient) microarchitectural attacks from the literature.  ...  ACKNOWLEDGEMENTS We would like to thank John Mitchell and Clark Barrett for their valuable discussions and feedback on this work.  ... 
arXiv:2112.10511v1 fatcat:ylcaex3mxfatrl2sezl5hl2iha

Efficient Discovery of Ontology Functional Dependencies [article]

Sridevi Baskaran, Alexander Keller, Fei Chiang, Golab Lukasz, Jaroslaw Szlichta
2017 arXiv   pre-print
We lay out theoretical and practical foundations for OFDs, including a set of sound and complete axioms, and a linear inference procedure.  ...  We then develop effective algorithms for discovering OFDs, and a set of optimizations that efficiently prune the search space.  ...  [28] for Order Dependency (OD) discovery since OFDs subsume FDs and ODs subsume FDs.  ... 
arXiv:1611.02737v3 fatcat:fgwha6wvznaixet4etqh4bxi5u

Do Not Claim Too Much: Second-order Logic and First-order Logic

STEWART SHAPIRO
1999 Philosophia Mathematica  
The purpose of this paper is to apply the moral to the contrast between first-order logic and second-order logic, as articulated in my Foundations without foundationalism: A case for second-order logic  ...  the author to step into the role of a lawyer or salesman for Second-Order, Inc., and this approach leads to some exaggerated and tendentious formulations.  ...  A fortiori, there is no effective deductive system that is both sound and complete for second-order languages. To see this, let $ be a (first-order) sentence in the language of arithmetic.  ... 
doi:10.1093/philmat/7.1.42 fatcat:m2spad6v3rb4hnt6jzpqo4jscy

Application of Axiomatic Design for Project-based Learning Methodology

Gabriele Arcidiacono, Kai Yang, Jayant Trewn, Luca Bucciarelli
2016 Procedia CIRP  
effect on its quality and outcomes.  ...  In this study, the Axiomatic Design method is applied to link learning outcomes of Lean Six Sigma training with all the teaching processes and the availability of resources.  ...  Project-Based Learning changes the teachers' role from instructor to facilitator in order to develop the learners' technical proficiency as well as critical thinking, team collaboration and a set of attributes  ... 
doi:10.1016/j.procir.2016.08.003 fatcat:uans6mspu5e75bwl2r2efodefm

On the psychology of mathematical problem solving by gifted students

Sándor M. Veres
2015 Teaching Mathematics and Computer Science  
First the meta-mathematical background is outlined in order to present problem solving as a well defined search problem and hence as a discovery process.  ...  Finally, non-procedural aspects of the psychology of problem solving are summarized, such as the role of persistence, teacher-pupil relationship, the amount of experience needed, self-confidence and inspiration  ...  Divide-andconquer is the principle of solving a whole problem via decomposing it into a set of sub-problems.  ... 
doi:10.5485/tmcs.2015.0405 fatcat:wuenh2dhn5bi3oa2cm2aq242qi

Discovery and Contextual Data Cleaning with Ontology Functional Dependencies [article]

Zheng Zheng, Longtao Zheng, Morteza Alipour Langouri, Fei Chiang, Lukasz Golab, Jaroslaw Szlichta
2022 arXiv   pre-print
Towards enabling OFDs as data quality rules in practice, we study the problem of finding minimal repairs to a relation and ontology with respect to a set of OFDs.  ...  We explore dependency-based data cleaning with Ontology Functional Dependencies(OFDs), which express semantic attribute relationships such as synonyms and is-a hierarchies defined by an ontology.  ...  These results are in line with previous FD [25] , inclusion dependency [42] , and order dependency [48] discovery algorithms.  ... 
arXiv:2105.08105v4 fatcat:s2lsv5ce3reo7bmsah4mdruroy

How does this interaction affect me? Interpretable attribution for feature interactions [article]

Michael Tsang, Sirisha Rambhatla, Yan Liu
2020 arXiv   pre-print
We propose an interaction attribution and detection framework called Archipelago which addresses these problems and is also scalable in real-world settings.  ...  There are a number of methods that extract feature interactions in prediction models; however, the methods that assign attributions to interactions are either uninterpretable, model-specific, or non-axiomatic  ...  In (c), the attribution of (bad, awful) should be negative via φ (2), but Shapley Taylor Interaction Index uses the positive δ. Note that φ depends on a and d whereas δ depends on a, b, c, and d.  ... 
arXiv:2006.10965v1 fatcat:xh2kexnhkjemni5tj2mblkeucq

Cats vs. Spectre: An Axiomatic Approach to Modeling Speculative Execution Attacks [article]

Hernán Ponce-de-León, Johannes Kinder
2021 arXiv   pre-print
Due to the axiomatic approach, our models can be rapidly extended to allow our framework to detect new types of attacks and validate defenses against them.  ...  Approaches based on operational speculative semantics have made initial inroads towards finding vulnerable code and validating defenses.  ...  ACKNOWLEDGMENTS We would like to thank our anonymous shepherd and the anonymous reviewers for their comments and feedback.  ... 
arXiv:2108.13818v2 fatcat:dkatpfjvcfgg3oafh2epi3lj7i

The Post‐Modern Transcendental of Language in Science and Philosophy [chapter]

Gianfranco Basti
2017 Epistemology and Transformation of Knowledge in Global Age  
That is, from the standpoint of the "completion of the linguistic turn" in the foundations of logic and mathematics using Peirce's algebra of relations.  ...  This allows the development of a new class of quantum computers based on coalgebras.  ...  dual as to the usual induction principle (↑) of set 'orderings' (≤) for an 'initial Boolean algebra', but equally effective as method of set definition and proof [15, 43] .  ... 
doi:10.5772/intechopen.68613 fatcat:zisvl3hvmbdahfu2hu4vvzgopy

Logics for Dependence and Independence (Dagstuhl Seminar 15261)

Erich Grädel, Juha Kontinen, Jouka Väänänen, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
This report documents the programme and outcomes of Dagstuhl Seminar 15261 'Logics for Dependence and Independence'.  ...  A key objective of the seminar was to bring together researchers working in dependence logic and in the application areas so that they can communicate state-of-the-art advances and embark on a systematic  ...  Our main result shows that the satisfiability and validity problems of the extensions of propositional independence and inclusion logic by the classical negation are complete for alternating exponential  ... 
doi:10.4230/dagrep.5.6.70 dblp:journals/dagstuhl-reports/GradelKVV15 fatcat:wqkpzm2ywbcjdke2zyvvw4dlny

A New Style of Proof for Mathematics Organized as a Network of Axiomatic Theories [article]

William M. Farmer
2018 arXiv   pre-print
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms.  ...  Traditional and formal proofs do not adequately fulfill all the purposes that mathematical proofs have, and they do not exploit the structure inherent in a theory graph.  ...  Introduction An axiomatic theory (theory for short) is a set of axioms that specifies a set of mathematical structures.  ... 
arXiv:1806.00810v2 fatcat:nkwqk4mzknbvlpjaygkgepay5y

Page 7146 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
, in particular, do not admit an effective axiomatization [S.  ...  Instead of looking for a complete axiomatization of the predicate provability /ogic, the authors consider particular first-order theories enriched by the provability operator.  ... 

Embracing a mechanized formalization gap [article]

Antal Spector-Zabusky, Joachim Breitner, Yao Li, Stephanie Weirich
2019 arXiv   pre-print
If a code base is so big and complicated that complete mechanical verification is intractable, can we still apply and benefit from verification methods?  ...  Concretely, we translate core parts of the Haskell compiler GHC into Coq, using hs-to-coq, and verify invariants related to the use of term variables.  ...  Thanks to Josh Cohen, Christine Rizkallah, and John Wiegley for assistance with the development of hs-to-coq and the theory of the containers library.  ... 
arXiv:1910.11724v1 fatcat:iancabvl3nbrxi2coyol7c4iie
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