Default reasoning over domains and concept hierarchies
TL;DR: A default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning is obtained and it is shown that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis.
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Abstract: W.C. Rounds and G.-Q. Zhang have proposed to study a form of disjunctive logic programming generalized to algebraic domains [1]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with default negation, giving rise to a new nonmonotonic reasoning framework on hierarchical knowledge which encompasses answer set programming with extended disjunctive logic programs. We also show that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis. Together, we obtain a default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning.
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Citations
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A logic for default reasoning
TL;DR: This paper proposes a logic for default reasoning, develops a complete proof theory and shows how to interface it with a top down resolution theorem prover, and provides criteria under which the revision of derived beliefs must be effected.
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