Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Stratification in Approximation Fixpoint Theory and Its Application to Active Integrity Constraints

Stratification in Approximation Fixpoint Theory and Its Application to Active Integrity Constraints Approximation fixpoint theory (AFT) is an algebraic study of fixpoints of lattice operators that unifies various knowledge representation formalisms. In AFT, stratification of operators has been studied, essentially resulting in a theory that specifies when certain types of fixpoints can be computed stratum per stratum. Recently, novel types of fixpoints related to groundedness have been introduced in AFT. In this article, we study how those fixpoints behave under stratified operators. One recent application domain of AFT is the field of active integrity constraints (AICs). We apply our extended stratification theory to AICs and find that existing notions of stratification in AICs are covered by this general algebraic definition of stratification. As a result, we obtain stratification results for a large variety of semantics for AICs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Stratification in Approximation Fixpoint Theory and Its Application to Active Integrity Constraints

Download PDF
19 pages

Loading next page...
 
/lp/association-for-computing-machinery/stratification-in-approximation-fixpoint-theory-and-its-application-to-3mjf8USl0I
Publisher
Association for Computing Machinery
Copyright
Copyright © 2021 ACM
ISSN
1529-3785
eISSN
1557-945X
DOI
10.1145/3430750
Publisher site
See Article on Publisher Site

Abstract

Approximation fixpoint theory (AFT) is an algebraic study of fixpoints of lattice operators that unifies various knowledge representation formalisms. In AFT, stratification of operators has been studied, essentially resulting in a theory that specifies when certain types of fixpoints can be computed stratum per stratum. Recently, novel types of fixpoints related to groundedness have been introduced in AFT. In this article, we study how those fixpoints behave under stratified operators. One recent application domain of AFT is the field of active integrity constraints (AICs). We apply our extended stratification theory to AICs and find that existing notions of stratification in AICs are covered by this general algebraic definition of stratification. As a result, we obtain stratification results for a large variety of semantics for AICs.

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Jan 5, 2021

Keywords: Active integrity constraints

References

  • Updates, a new frontier
    Abiteboul, Serge
  • Hex semantics via approximation fixpoint theory
    Antic, Christian; Eiter, Thomas; Fink, Michael
  • Groundedness in Logics with a Fixpoint Semantics
    Bogaerts, Bart
  • Fixpoint semantics for active integrity constraints
    Bogaerts, Bart; Cruz-Filipe, Luís
  • Grounded fixpoints and their applications in knowledge representation
    Bogaerts, Bart; Vennekens, Joost; Denecker, Marc
  • Partial grounded fixpoints
    Bogaerts, Bart; Vennekens, Joost; Denecker, Marc
  • On well-founded set-inductions and locally monotone operators
    Bogaerts, Bart; Vennekens, Joost; Denecker, Marc
  • Safe inductions and their applications in knowledge representation
    Bogaerts, Bart; Vennekens, Joost; Denecker, Marc
  • Declarative semantics of production rules for integrity maintenance
    Caroprese, Luciano; Greco, Sergio; Sirangelo, Cristina; Zumpano, Ester
  • Active integrity constraints and revision programming
    Caroprese, Luciano; Truszczyński, Mirosław
  • Approximation fixpoint theory and the well-founded semantics of higher-order logic programs
    Charalambidis, Angelos; Rondogiannis, Panos; Symeonidou, Ioanna
  • Negation as failure
    Clark, Keith L.
  • Optimizing computation of repairs from active integrity constraints
    Cruz-Filipe, Luís
  • Grounded fixpoints and active integrity constraints
    Cruz-Filipe, Luís
  • repAIrC: A tool for ensuring data consistency
    Cruz-Filipe, Luís; Franz, Michael; Hakhverdyan, Artavazd; Ludovico, Marta; Nunes, Isabel; Schneider-Kamp, Peter
  • Computing repairs from active integrity constraints
    Cruz-Filipe, Luís; Gaspar, Graça; Engrácia, Patrícia; Nunes, Isabel
  • Approximation fixpoint theory and the semantics of logic and answers set programs
    Denecker, Marc; Bruynooghe, Maurice; Vennekens, Joost
  • Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
    Denecker, Marc; Marek, Victor; Truszczyński, Mirosław
  • Uniform semantic treatment of default and autoepistemic logics
    Denecker, Marc; Marek, Victor; Truszczyński, Mirosław
  • Ultimate approximation and its application in nonmonotonic knowledge representation systems
    Denecker, Marc; Marek, Victor; Truszczyński, Mirosław
  • Reiter’s default logic is a logic of autoepistemic reasoning and a good one, too
    Denecker, Marc; Marek, Victor; Truszczyński, Mirosław
  • Well-founded semantics and the algebraic theory of non-monotone inductive definitions
    Denecker, Marc; Vennekens, Joost
  • Disjunctive datalog
    Eiter, Thomas; Gottlob, Georg; Mannila, Heikki
  • A Kripke-Kleene semantics for logic programs
    Fitting, Melvin
  • Active integrity constraints
    Flesca, Sergio; Greco, Sergio; Zumpano, Ester
  • The stable model semantics for logic programming
    Gelfond, Michael; Lifschitz, Vladimir
  • Towards a theory of knowledge and ignorance: Preliminary report
    Halpern, Joseph Y.; Moses, Yoram
  • On notation for ordinal numbers
    Kleene, Stephen Cole
  • On the relation between default and autoepistemic logic
    Konolige, Kurt
  • Splitting a logic program
    Lifschitz, Vladimir; Turner, Hudson
  • Solimul Chowdhury, Jia-Huai You, and Zhiyong Feng
    Liu, Fangfang; Bi, Yi; Md,
  • Revision programming
    Marek, V. Wiktor; Truszczynski, Miroslaw
  • Understanding the global semantics of referential actions using logic rules
    May, Wolfgang; Ludäscher, Bertram
  • Semantical considerations on nonmonotonic logic
    Moore, Robert C.
  • Active database systems
    Paton, Norman W.; Díaz, Oscar
  • Well-founded and stable semantics of logic programs with aggregates
    Pelov, Nikolay; Denecker, Marc; Bruynooghe, Maurice
  • On the declarative semantics of deductive databases and logic programs
    Przymusinski, Teodor C.
  • Update by means of inference rules
    Przymusinski, Teodor C.; Turner, Hudson
  • A logic for default reasoning
    Reiter, Raymond
  • Approximating operators and semantics for abstract dialectical frameworks
    Strass, Hannes
  • Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory
    Strass, Hannes; Wallner, Johannes Peter
  • Updating knowledge bases while maintaining their consistency
    Teniente, Ernest; Olivé, Antoni
  • Strong and uniform equivalence of nonmonotonic theories—An algebraic approach
    Truszczyński, Mirosław
  • The semantics of predicate logic as a programming language
    van Emden, Maarten H.; Kowalski, Robert A.
  • The well-founded semantics for general logic programs
    Van Gelder, Allen; Ross, Kenneth A.; Schlipf, John S.
  • Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
    Vennekens, Joost; Gilis, David; Denecker, Marc
  • Active Database Systems: Triggers and Rules for Advanced Database Processing
    Widom, Jennifer; (Eds, Stefano Ceri
  • Updating Logical Databases
    Winslett, Marianne