Domain-Lifted Sampling for Universal Two-Variable Logic and Extensions

Given a first-order sentence ? and domain size n, how can one sample model of on the {1, . , n} efficiently as n scales? We consider two variants this problem: uniform sampling regime, in which goal is to uniformly at random, symmetric weighted models are according number groundings each predicate appearing them. Solutions problem have applications scalable generation combinatorial structures, well several statistical-relational such Markov logic networks probabilistic programs. In paper, we identify certain classes sentences that domain-liftable under sampling, sense they admit algorithm runs time polynomial n. particular, prove every form ∀x∀y: ?(x, y) for some quantifier-free formula ?(x,y) sampling. then further show result continues hold presence or more cardinality constraints single tree axiom constraint.