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Finite Satisfiability of Unary Negation Fragment with Transitivity

Authors Daniel Danielski, Emanuel Kieroński

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Author Details

Daniel Danielski
  • University of Wrocław, Poland
Emanuel Kieroński
  • University of Wrocław, Poland

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Daniel Danielski and Emanuel Kieroński. Finite Satisfiability of Unary Negation Fragment with Transitivity. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 17:1-17:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


We show that the finite satisfiability problem for the unary negation fragment with an arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require that some binary symbols are interpreted as arbitrary transitive relations, some as partial orders and some as equivalences. We also consider finite satisfiability of various extensions of our primary logic, in particular capturing the concepts of nominals and role hierarchies known from description logic. As the unary negation fragment can express unions of conjunctive queries, our results have interesting implications for the problem of finite query answering, both in the classical scenario and in the description logics setting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • unary negation fragment
  • transitivity
  • finite satisfiability
  • finite open-world query answering
  • description logics


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