Synthesizing Datalog Programs using Numerical Relaxation

Abstract

The problem of learning logical rules from examples arises in diverse fields, including program synthesis, logic programming, and machine learning. Existing approaches either involve solving computationally difficult combinatorial problems, or performing parameter estimation in complex statistical models. In this paper, we present DIFFLOG, a technique to extend the logic programming language Datalog to the continuous setting. By attaching real-valued weights to individual rules of a Datalog program, we naturally associate numerical values with individual conclusions of the program. Analogous to the strategy of numerical relaxation in optimization problems, we can now first determine the rule weights which cause the best agreement between the training labels and the induced values of output tuples, and subsequently recover the classical discrete-valued target program from the continuous optimum. We evaluate DIFFLOG on a suite of 34 benchmark problems from recent literature in knowledge discovery, formal verification, and database query-byexample, and demonstrate significant improvements in learning complex programs with recursive rules, invented predicates, and relations of arbitrary arity.

Provenance-guided synthesis of Datalog programs

“…However, this under-constrained nature of the problem specification also greatly increases the difficulty of program synthesis, as it is now not possible to consider an individual rule and determine whether it is the cause of undesirable behavior in the candidate program. The proof of Theorem 3.2 in [Si et al 2019] crucially exploits this observation.…”

“…In contrast, a version-space search based system, ALPS [Si et al 2018], takes 56 seconds and invokes the Datalog solver 47,527 times, reflecting modest ability to generalize from failures. Likewise, a numerical relaxation based system D [Si et al 2019] takes 47 minutes and invokes the Datalog solver 4,008 times-each invocation of the solver is significantly more expensive because the same set of 166 rules is run in each iteration with different rule weights.…”

“…In this context, syntax guidance may be viewed as a form of inductive bias [Kitzelmann 2010], both to enable efficient convergence to the target program, and to prevent overfitting. In this paper, we follow [Si et al 2019] in uniformly capturing all these forms of syntactic bias in the form of rule selection: we assume that the user provides a large soup of candidate rules, P all , and the goal of the synthesizer is to find a concrete Datalog program P ⊆ P all with the desired input-output behavior.…”

“…A variety of different techniques have been proposed for synthesizing Datalog programs, including meta-interpretive learning , reverse entailment [Muggleton 1995], version-space search [Si et al 2018], SMT constraint solving [Albarghouthi et al 2017], and numerical relaxation [Si et al 2019]. Despite significant strides, however, all of these approaches are hindered by poor scalability, high variance in running times, or limited ability to handle expressive features such as recursion and invented predicates.…”

“…to two state-of-the-art approaches: ALPS [Si et al 2018], which uses a version-space search approach, and D [Si et al 2019], which uses an approach based on numerical relaxation. On a suite of 40 synthesis tasks from three different domains-knowledge discovery, program analysis, and relational queries-P S is able to synthesize the desired program in 10 seconds on average per task, taking only under a second each for 28 of them.…”