Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
What does a conditional knowledge base entail?
Artificial Intelligence
Modal logic
A logical theory of nonmonotonic inference and belief change
A logical theory of nonmonotonic inference and belief change
A representation theorem for recovering contraction relations satisfying wci
Theoretical Computer Science
Normal conditions for inference relations and injective models
Theoretical Computer Science
Similarity between preferential models
Theoretical Computer Science
| Hi-index | 5.23 |
We continue the work in Zhu et al. [Normal conditions for inference relations and injective models, Theoret. Comput. Sci. 309 (2003) 287-311]. A class Ω of strict partial order structures (posets, for short) is said to be axiomatizable if the class of all injective preferential models from Ω may be characterized in terms of general rules. This paper aims to obtain some characteristics of axiomatizable classes. To do this, a monadic second-order frame language is presented. The relationship between χ0-axiomatizability and second-order definability is explored. Then a notion of an admissible set is introduced. Based on this notion, we show that any preferential model, which does not contain any four-node substructure, must be a reduct of some injective model. Furthermore, we furnish a necessary and sufficient condition for the axiomatizability of classes of injective preferential models using general rules. Finally, we show that, in some sense, the class of all posets without any four-node substructure is the largest among axiomatizable classes.