In predicate invention (PI), new predicates are introduced into a logical theory, usually by rewriting a group of closely-related rules to use a common invented predicate as a "subroutine". PI is difficult, since a poorly-chosen invented predicate may lead to error cascades. Here we suggest a "soft" version of predicate invention: instead of explicitly creating new predicates, we implicitly group closely-related rules by using structured sparsity to regularize their parameters together. We show that soft PI, unlike hard PI, consistently improves over previous strong baselines for structure-learning on two large-scale tasks.
Predicate logic in which predicates take only individuals as arguments and quantifiers only bind individual variables. Predicate logic in which predicates take other predicates as arguments and quantifiers bind predicate variables. For example, second-order predicates take first-order predicates as arguments. Order n predicates take order n-1 predicates as arguments (n 1). Predicate logic that does not exclude interpretations with empty domains.
Stochastic processes that involve the creation of objects and relations over time are widespread, but relatively poorly studied. For example, accurate fault diagnosis in factory assembly processes requires inferring the probabilities of erroneous assembly operations, but doing this efficiently and accurately is difficult. Modeled as dynamic Bayesian networks, these processes have discrete variables with very large domains and extremely high dimensionality. In this paper, we introduce relational dynamic Bayesian networks (RDBNs), which are an extension of dynamic Bayesian networks (DBNs) to first-order logic. RDBNs are a generalization of dynamic probabilistic relational models (DPRMs), which we had proposed in our previous work to model dynamic uncertain domains. We first extend the Rao-Blackwellised particle filtering described in our earlier work to RDBNs. Next, we lift the assumptions associated with Rao-Blackwellization in RDBNs and propose two new forms of particle filtering. The first one uses abstraction hierarchies over the predicates to smooth the particle filters estimates. The second employs kernel density estimation with a kernel function specifically designed for relational domains. Experiments show these two methods greatly outperform standard particle filtering on the task of assembly plan execution monitoring.
In a previous paper, Liu argued for the importance of establishing a precise theoretical foundation for program debugging from first principles. In this paper, we present a first step towards a theoretical exploration of program debugging algorithms. The starting point of our work is the recent debugging approach based on predicate switching. The idea is to switch the outcome of an instance of a predicate to bring the program execution to a successful completion and then identify the fault by examining the switched predicate. However, no theoretical analysis of the approach is available. In this paper, we generalize the above idea, and propose the bounded debugging via multiple predicate switching (BMPS) algorithm, which locates faults through switching the outcomes of instances of multiple predicates to get a successful execution where each loop is executed for a bounded number of times. Clearly, BMPS can be implemented by resorting to a SAT solver. We focus attention on RHS faults, that is, faults that occur in the control predicates and right-hand-sides of assignment statements. We prove that for conditional programs, BMPS is quasi-complete for RHS faults in the sense that some part of any true diagnosis will be returned by BMPS; and for iterative programs, when the bound is sufficiently large, BMPS is also quasi-complete for RHS faults. Initial experimentation with debugging small C programs showed that BMPS can quickly and effectively locate the faults.
In this paper, we propose a translation from normal first-order logic programs under the answer set semantics to first-order theories on finite structures. Specifically, we introduce ordered completions which are modifications of Clark's completions with some extra predicates added to keep track of the derivation order, and show that on finite structures, classical models of the ordered-completion of a normal logic program correspond exactly to the answer sets (stable models) of the logic program.