Model counting and weighted model counting are key problems in artificial intelligence. Marginal inference can be reduced to model counting in many statistical-relational systems, such as Markov Logic. One common approach used by model counters is splitting a theory into disjoint subtheories, performing model counting on the subtheories, and then caching the result. If an identical subtheory is encountered again in the search, the cached result is used, greatly reducing runtime. In this work we introduce a way to cache symmetric subtheories compactly, which could potentially decrease required cache size, increase cache hits, and decrease runtime of solving.

Inconsistencies between different information sources may arise because of statements that are inaccurate, albeit not completely false. In such scenarios, the most natural way to restore consistency is often to interpret assertions in a more flexible way, i.e. to enlarge (or relax) their meaning. As this process inherently requires extra-logical information about the meaning of atoms, extensions of classical merging operators are needed. In this paper, we introduce syntactic merging operators, based on possibilistic logic, which employ background knowledge about the similarity of atomic propositions to appropriately relax propositional statements.