Systems and Implementations for Solving Reasoning Problems in Conditional Logics

Default rules like "If A, then normally B" or probabilistic rules like "If A, then B with probability x" are powerful constructs for knowledge representation. Such rules can be formalized as conditionals, denoted by (B vertical bar A) or (B vertical bar A)[x], and a conditional knowledge base consists of a set of conditionals. Different semantical models have been proposed for conditional knowledge bases, and the most important reasoning problems are to determine whether a knowledge base is consistent and to determine what a knowledge base entails. We present an overview on systems and implementations our group has been working on for solving reasoning problems in various semantics that have been developed for conditional knowledge bases. These semantics include quantitative, semi-quantitative, and qualitative conditional logics, based on both propositional logic and on first-order logic.