Theoretical Computer Science
Introduction to knowledge base systems
Introduction to knowledge base systems
Neighborhood systems and relational databases
CSC '88 Proceedings of the 1988 ACM sixteenth annual conference on Computer science
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Approximate Operators: Axiomatic Rough Set Theory
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
Rough Set Semantics for Non-classical Logics
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
On a Logic of Information for Reasoning About Knowledge
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
Generalized Rough Logics with Rough Algebraic Semantics
International Journal of Cognitive Informatics and Natural Intelligence
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Earlier the authors have shown that rough sets can be characterized by six topological properties. In this paper, a new formal logic system based on such axioms is proposed. It will be called First-Order Logic for Rough Approximation or simply Rough Logic. The axiom schemas of rough logic turn out to be the same as those of the modal logic S 5. In other words, topological and modal logic considerations led to the same conclusion. So rough logic must have captured the intrinsic meaning of approximate reasoning However, their interpretations are different. To reflect the differences in semantics, possible worlds are renamed as observable worlds. Each observable world represents a different rough observation of the actual world. Rough logic also provides a frame work for approximation. It integrates imperfect observations (observable worlds) into an approximation of actual world. Any good approximation theory should have a convergence theorem-its details are deferred to next paper. A sample theorem is as follows: If there is a convergent sequence of rough observations (namely, equivalence relations), then the corresponding rough models converge to the Tarskian model of first-order classical logic.