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MultiValued Symbolic ModelChecking
 ACM TRANSACTIONS ON SOFTWARE ENGINEERING AND METHODOLOGY
, 2003
"... This paper introduces the concept and the general theory of multivalued model checking, and describes a multivalued symbolic modelchecker \Chi Chek. Multivalued ..."
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Cited by 50 (16 self)
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This paper introduces the concept and the general theory of multivalued model checking, and describes a multivalued symbolic modelchecker \Chi Chek. Multivalued
Two views of the theory of rough sets in finite universes
 International Journal of Approximate Reasoning
, 1996
"... This paper presents and compares two views of the theory of rough sets. The operatororiented view interprets rough set theory as an extension of set theory with two additional unary operators. Under such a view, lower and upper approximations are related to the interior and closure operators in top ..."
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Cited by 46 (20 self)
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This paper presents and compares two views of the theory of rough sets. The operatororiented view interprets rough set theory as an extension of set theory with two additional unary operators. Under such a view, lower and upper approximations are related to the interior and closure operators in topological spaces, the necessity and possibility operators in modal logic, and lower and upper approximations in interval structures. The setoriented view focuses on the interpretation and characterization of members of rough sets. Iwinski type rough sets are formed by pairs of definable (composed) sets, which are related to the notion of interval sets. Pawlak type rough sets are defined based on equivalence classes of an equivalence relation on the power set. The relation is defined by the lower and upper approximations. In both cases, rough sets may be interpreted, or related to, families of subsets of the universe, i.e., elements of a rough set are subsets of the universe. Alternatively, rough sets may be interpreted using elements of the universe based on the notion of rough membership functions. Both operatororiented and setoriented views are useful in the understanding and application of the theory of rough sets.
Boolean Connection Algebras: A New Approach to the RegionConnection Calculus
 Artificial Intelligence
, 1999
"... The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and prove ..."
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Cited by 43 (7 self)
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The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and proves that these structures are equivalent to models of the RCC axioms. BCAs permit a wealth of results from the theory of lattices and boolean algebras to be applied to RCC. This is demonstrated by two theorems which provide constructions for BCAs from suitable distributive lattices. It is already well known that regular connected topological spaces yield models of RCC, but the theorems in this paper substantially generalize this result. Additionally, the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions. Keywords: RegionConnection Calculus, Qualitative Spatial Reasoning, Boolean Connection Algebra, Mer...
Generalization of Rough Sets using Modal Logics
 Intelligent Automation and Soft Computing, an International Journal
"... The theory of rough sets is an extension of set theory with two additional unary settheoretic operators defined based on a binary relation on the universe. These two operators are related to the modal operators in modal logics. By exploring the relationship between rough sets and modal logics, this ..."
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Cited by 43 (20 self)
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The theory of rough sets is an extension of set theory with two additional unary settheoretic operators defined based on a binary relation on the universe. These two operators are related to the modal operators in modal logics. By exploring the relationship between rough sets and modal logics, this paper proposes and examines a number of extended rough set models. By the properties satisfied by a binary relation, such as serial, reflexive, symmetric, transitive, and Euclidean, various classes of algebraic rough set models can be derived. They correspond to different modal logic systems. With respect to graded and probabilistic modal logics, graded and probabilistic rough set models are also discussed. Keywords Rough sets, modal logic, rough set operators, graded rough sets, probabilistic rough sets. 1 Introduction The theory of rough sets is an extension of set theory, in which a subset of a universe is described by a pair of ordinary sets called the lower and upper approximations [2...
Implementing a MultiValued Symbolic Model Checker
 In Proceedings of TACASâ€™01
, 2001
"... Multivalued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems where complete, agreed upon models of the system are not available. In this paper, we present ..."
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Cited by 25 (11 self)
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Multivalued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems where complete, agreed upon models of the system are not available. In this paper, we present an implementation of a symbolic model checker for multivalued temporal logics. The model checker works for any multivalued logic whose truth values form a quasiboolean lattice. Our models are generalized Kripke structures, where both atomic propositions and transitions between states may take any of the truth values of a given multivalued logic. Properties to be model checked are expressed in CTL, generalized with a multivalued semantics. The design of the model checker is based on the use of MDDs, a multivalued extension of Binary Decision Diagrams. We describe MDDs and their use in the model checker. We also give its theoretical time complexity and some preliminary empirical performance data.
Constructive and algebraic methods of the theory of rough sets
 Information Sciences
, 1998
"... This paper reviews and compares constructive and algebraic approaches in the study of rough sets. In the constructive approach, one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation. Different classes of rough set algebras are obtai ..."
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Cited by 21 (4 self)
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This paper reviews and compares constructive and algebraic approaches in the study of rough sets. In the constructive approach, one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation. Different classes of rough set algebras are obtained from different types of binary relations. In the algebraic approach, one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators. Various classes of rough set algebras are characterized by different sets of axioms. Axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators. 1
A comparative study of fuzzy sets and rough sets
 Information Sciences
, 1998
"... This paper reviews and compares theories of fuzzy sets and rough sets. Two approaches for the formulation of fuzzy sets are reviewed, one is based on manyvalued logic and the other is based on modal logic. Two views of rough sets are presented, setoriented view and operatororiented view. Rough se ..."
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Cited by 16 (2 self)
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This paper reviews and compares theories of fuzzy sets and rough sets. Two approaches for the formulation of fuzzy sets are reviewed, one is based on manyvalued logic and the other is based on modal logic. Two views of rough sets are presented, setoriented view and operatororiented view. Rough sets under setoriented view are closely related to fuzzy sets, which leads to nontruthfunctional fuzzy set operators. Both of them may be considered as deviations of classical set algebra. In contrast, rough sets under operatororiented view are different from fuzzy sets, and may be regarded as an extension of classical set algebra. Key words: approximation operators, fuzzy sets, interval fuzzy sets, modal logic, manyvalued logic, possibleworld semantics, product systems, rough sets. 1
On generalizing Pawlak approximation operators
 Proceedings of the First International Conference, RSCTCâ€™98, LNAI 1424
, 1998
"... Abstract. This paper reviews and discusses generalizations of Pawlak rough set approximation operators in mathematical systems, such as topological spaces, closure systems, lattices, and posets. The structures of generalized approximation spaces and the properties of approximation operators are anal ..."
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Cited by 13 (5 self)
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Abstract. This paper reviews and discusses generalizations of Pawlak rough set approximation operators in mathematical systems, such as topological spaces, closure systems, lattices, and posets. The structures of generalized approximation spaces and the properties of approximation operators are analyzed. 1
Model Checking with MultiValued Temporal Logics
 In Proceedings of the International Symposium on Multiple Valued Logics
, 2000
"... Multivalued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems even where complete, agreed upon models of the system are not available. In this paper, we pre ..."
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Cited by 10 (1 self)
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Multivalued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems even where complete, agreed upon models of the system are not available. In this paper, we present a symbolic model checker for multivalued temporal logics. The model checker works for any multivalued logic whose truth values form a quasiboolean lattice. Our models are generalized Kripke structures, where both atomic propositions and transitions between states may take any of the truth values of a given multivalued logic. Properties to be model checked are expressed in CTL, generalized with a multivalued semantics. The design of the model checker is based on the use of MDDs, a multivalued extension of Binary Decision Diagrams.