Correctness criteria of some algorithms for uncertain reasoning using incidence calculus
Journal of Automated Reasoning
Incidence calculus: A mechanism for probabilistic reasoning
Journal of Automated Reasoning
Comparison of rough-set and interval-set models for uncertain reasoning
Fundamenta Informaticae - Special issue: rough sets
Interpretations of belief functions in the theory of rough sets
Information Sciences: an International Journal - From rough sets to soft computing
On Generalizing Pawlak Approximation Operators
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
Constructive and algebraic methods of the theory of rough sets
Information Sciences: an International Journal
On generalizing rough set theory
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
Probabilistic inference on three-valued logic
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
Propositional, Probabilistic and Evidential Reasoning: Integrating Numerical and Symbolic Approaches
Propositional, Probabilistic and Evidential Reasoning: Integrating Numerical and Symbolic Approaches
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Incidence calculus is a probabilistic logic which possesses both numerical and symbolic approaches. However, Liu in [5] pointed out that the original incidence calculus had some drawbacks and she established a generalized incidence calculus theory (GICT) based on Łukasiewicz's three-valued logic to improve it. In a GICT, an incidence function is defined to relate each proposition φ in the axioms of the theory to a set of possible worlds in which φ has truth value true. But the incidence function only represents those absolute true states of propositions, so it can not deal with the uncertain states. In this paper, we use two incidence functions i$_*$ and i$^*$ to relate the axioms to the sets of possible worlds. For an axiom φ, i$_*$(φ) is to be thought of as the set of possible worlds in which φ has truth value true, while i$^*$(φ) is the set of possible worlds in which φ is true or undeterminable. Since i$^*$ can represent the undeterminable state, our newly defined theory is more efficient to handle vague information than GICT.