Boole's logic and probability: a critical exposititon from the standpoint of contemporary algebra, logic, and probability theory
A quantitative approach to logical inference
Decision Support Systems
On the consistency of defeasible databases
Artificial Intelligence
Mixed integer programming methods for computing nonmonotonic deductive databases
Journal of the ACM (JACM)
Implementing deductive databases by mixed integer programming
ACM Transactions on Database Systems (TODS)
Default reasoning from conditional knowledge bases: complexity and tractable cases
Artificial Intelligence
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
ICAIL '05 Proceedings of the 10th international conference on Artificial intelligence and law
Contract clause negotiation by game theory
Proceedings of the 11th international conference on Artificial intelligence and law
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We introduce a mathematical model of legal reasoning using an underlying conditional logic semantics, to allow its tractability in some special cases. The main idea is to capture the entailment of legal consequences through a model of 0-1 programming. For such task, first we model legal reasoning with Lehmann's Lexicographic semantics and then we translate it to an instance of weighted MAXSAT problem, in order to compute the logical consequences of legal reasoning. Hence, combinatorial optimization algorithms can be used to yield the legal consequences of defeasible reasoning over legal conditional knowledge bases.