Explaining program execution in deductive systems

Abstract

Programs in deductive database and programming systems have a natural meaning that is based upon their mathematical reading as logical rules. High-level ‘explanations’ of a program evaluation/execution can be constructed to provide added functionality: (1) To debug a program by following a chain of deductions leading to an unexpected (and possibly incorrect) conclusion; (2) To follow the derivation of certain correct conclusions to determine why and how they are reached; (3) To identify consequences of a (typically, incorrect or unexpected) fact. This functionality can be utilized either to perform post-mortem analysis of a session, or to interactively develop programs by running queries and viewing their deductions simultaneously.

‘Explanations’ of programs are especially important in the context of deductive databases for three reasons: (1) These programs could involve recursion, and hence, the chain of inferences is often not evident. (2) When the input data set is large, it is very difficult for a user to inspect the data and determine which facts lead to which answers, and exactly how. (3) Such programs do not guarantee a fixed evaluation strategy, and this makes it difficult for a user to comprehend unexpected behavior of a program.

With this motivation, we have designed and implemented an explanation facility for the CORAL deductive database system. The design is based on the representation of a program evaluation as a set of derivation trees, and the facility provides a high-level explanation of the inferences carried out during program execution. A notable feature of the implementation is the boot-strapped use of CORAL in the implementation of the explanation tool. We believe that an explanation system can provide a novel approach to interactively querying data, and is useful even for standard relational databases.

The work of the authors was supported by a David and Lucile Packard Foundation Fellowship in Science and Engineering, a Presidential Young Investigator Award with matching grants from DEC, Tandem and Xerox, and NSF grant IRI-9011563.