A logical formulation of rough set definability

Tuan Fang Fan*, Churn Jung Liau, Duen-Ren Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In data mining problems, data is usually provided in the form of data tables. To represent knowledge discovered from data tables, a decision logic (DL) is proposed in rough set theory. DL is an instance of propositional logic, but we can use other logical formalisms to describe data tables. In this paper, we propose two descriptions of data tables based on first-order data logic (FODL) and attribute value-sorted logic (AVSL) respectively. In the context of FODL, we show that explicit definability and implicit definability in classical logic implies the notion of definability in rough set theory. We also show that AVSL is particularly useful for the representation of properties of many-valued data tables.

Original languageEnglish
Pages (from-to)27-37
Number of pages11
JournalInternational Journal of Uncertainty, Fuzziness and Knowlege-Based Systems
Issue number1
StatePublished - 1 Feb 2011


  • Data table
  • decision logic
  • definability
  • first-order logic
  • rough set theory


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