# Reasoning with Conditionals

Default rules like "*If A, then usually B*"
are powerful constructs for knowledge representation. Such rules can
be formalized as conditionals, denoted by (B|A),
and a conditional knowledge base consists of
a set of conditionals. Different semantical models have been
proposed for conditional knowledge bases, including
quantitative, semi-quantitative, and qualitative approaches.
E.g., an Ordinal Conditional Function (OCF), ordering possible worlds
according to their degree of surprise, accepts the conditional
(B|A) if it considers a world where A holds, but B does not hold,
to be strictly more surprising than a world where both A and B are true.

The most important reasoning problems for conditional knowledge bases are to determine whether a knowledge base is consistent and to determine what a knowledge base entails. Some of the approaches to specifying the entailments of a conditional knowledge base are system P, system Z, or c-inference relations base on c-representations.

In this project, we design and investigate reasoning methods for conditional knowledge bases that may be based on both propositional logic or on first-order logic. We also develop software systems implementing these reasoning methods, supporting their empirical evaluation and comparison.