Daniel Lehmann's Research on Default Reasoning

Title: Daniel Lehmann's Research on Default Reasoning

Abstract: Daniel Lehmann proposed a logic of normal defaults that is rich enough not to require the consideration of non-normal defaults. His lexicographic closure method provides a rational extension of a given set of normal defaults, which is different from Reiter's logic of defaults. The lexicographic closure is essentially a rational exten sion of D and its rational closure, defined in a previous paper. It provides a logic of normal defaults that is different from Reiter's logic and is rich enough not to require the consideration of non-normal defaults. A large number of examples are provided to show that the lexicographic closure corresponds to the basic intuitions behind Reiter's logic of defaults.

Research Question: How can we develop a logic of normal defaults that is rich enough not to require the consideration of non-normal defaults, while still providing a rational extension of a given set of normal defaults?

Methodology: Lehmann's research uses a set of normal defaults D and a fact a. The lexicographic closure of D is defined, which is essentially a rational exten sion of D and its rational closure. The lexicographic closure provides a logic of normal defaults that is different from Reiter's logic and is rich enough not to require the consideration of non-normal defaults.

Results: The lexicographic closure method provides a rational extension of a given set of normal defaults. It is essentially a rational exten sion of D and its rational closure, which is different from Reiter's logic of defaults. A large number of examples are provided to show that the lexicographic closure corresponds to the basic intuitions behind Reiter's logic of defaults.

Implications: Lehmann's research provides a logic of normal defaults that is rich enough not to require the consideration of non-normal defaults. This logic is different from Reiter's logic and provides a rational extension of a given set of normal defaults. The lexicographic closure method is essentially a rational exten sion of D and its rational closure, which is different from Reiter's logic of defaults. A large number of examples are provided to show that the lexicographic closure corresponds to the basic intuitions behind Reiter's logic of defaults.

Link to Article: https://arxiv.org/abs/0203002v1 Authors: arXiv ID: 0203002v1