On the Complexity of Conditional Logics

N. Friedman and J.Y. Halpern

Principles of Knowledge Representation and Reasoning: Proc. Fourth International Conference (KR'94), 202-213., 1994.



Conditional logics, introduced by Stalnaker and Lewis, have been utilized in artificial intelligence to capture a broad range of phenomena. In this paper we examine the complexity of several variants discussed in the literature. We show that, in general, deciding satisfiability is PSPACE-complete for formulas with arbitrary conditional nesting and NP-complete for formulas with bounded nesting of conditionals. However, we provide several exceptions to this rule. Of particular note are results showing that (a) when assuming uniformity (i.e., that all worlds agree on what worlds are possible), the decision problem becomes EXPTIME-complete even for formulas with bounded nesting, and (b) when assuming absoluteness (i.e., that all worlds agree on all conditional statements), the decision problem is NP-complete for formulas with arbitrary nesting.