Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
An algorithm to compute circumscription
Artificial Intelligence
A circumscriptive theorem prover
Artificial Intelligence
Reasoning about truth (research note)
Artificial Intelligence
General theory of cumulative inference
Proceedings of the 2nd international workshop on Non-monotonic reasoning
RI: A logic for reasoning with inconsistency
Proceedings of the Fourth Annual Symposium on Logic in computer science
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
What does a conditional knowledge base entail?
Artificial Intelligence
A logic for reasoning with inconsistency
Journal of Automated Reasoning
General patterns in nonmonotonic reasoning
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Artificial Intelligence
Computing Circumscription Revisited: A Reduction Algorithm
Journal of Automated Reasoning
SCAN - Elimination of Predicate Quantifiers
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
The Logical Role of the Four-Valued Bilattice
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Computing circumscription revisited: preliminary report
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Computational methods for database repair by signed formulae*
Annals of Mathematics and Artificial Intelligence
Paraconsistent reasoning and preferential entailments by signed quantified Boolean formulae
ACM Transactions on Computational Logic (TOCL)
Inferring with inconsistent OWL DL ontology: a multi-valued logic approach
EDBT'06 Proceedings of the 2006 international conference on Current Trends in Database Technology
Four-Valued semantics for default logic
AI'06 Proceedings of the 19th international conference on Advances in Artificial Intelligence: Canadian Society for Computational Studies of Intelligence
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We introduce a general method for paraconsistent reasoning in knowledge systems by classical second-order formulae. A standard technique for paraconsistent reasoning on inconsistent classical theories is by shifting to multiple-valued logics. We show how these multiple-valued theories can be "shifted back" to two-valued classical theories (through a polynomial transformation), and how preferential reasoning based on multiple-valued logic can be represented by classical circumscription-like axioms. By applying this process we manage to overcome the shortcoming of classical logic in properly handling inconsistent data, and provide new ways of implementing multiple-valued paraconsistent reasoning in knowledge systems. Standard multiple-valued reasoning can thus be performed through theorem provers for classical logic, and multiple-valued preferential reasoning can be implemented using algorithms for processing circumscriptive theories (such as DLS and SCAN).