Bottom-up Evaluation Of Logic Programs Research Articles

Detecting Decidable Classes of Finitely Ground Logic Programs with Function Symbols

In this article, we propose a new technique for checking whether the bottom-up evaluation of logic programs with function symbols terminates. The technique is based on the definition of mappings from arguments to strings of function symbols, representing possible values which could be taken by arguments during the bottom-up evaluation. Starting from mappings, we identify mapping-restricted arguments, a subset of limited arguments, namely arguments that take values from finite domains. Mapping-restricted programs, consisting of rules whose arguments are all mapping restricted, are terminating under the bottom-up computation, as all of its arguments take values from finite domains. We show that mappings can be computed by transforming the original program into a unary logic program: this allows us to establish decidability of checking if a program is mapping restricted. We study the complexity of the presented approach and compare it to other techniques known in the literature. We also introduce an extension of the proposed approach that is able to recognize a wider class of logic programs. The presented technique provides a significant improvement, as it can detect terminating programs not identified by other criteria proposed so far. Furthermore, it can be combined with other techniques to further enlarge the class of programs recognized as terminating under the bottom-up evaluation.

Checking termination of bottom-up evaluation of logic programs with function symbols

AbstractRecently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness of models and termination of the evaluation procedure, in the general case, are not guaranteed anymore. Since the program termination problem is undecidable in the general case, several decidable criteria (called program termination criteria) have been recently proposed. However, current conditions are not able to identify even simple programs, whose bottom-up execution always terminates. The paper introduces new decidable criteria for checking termination of logic programs with function symbols under bottom-up evaluation, by deeply analyzing the program structure. First, we analyze the propagation of complex terms among arguments by means of the extended version of the argument graph calledpropagation graph. The resulting criterion, calledacyclicity, generalizes most of the decidable criteria proposed so far. Next, we study how rules may activate each other and define a more powerful criterion, calledsafety. This criterion uses the so-calledsafety functionable to analyze how rules may activate each other and how the presence of some arguments in a rule limits its activation. We also study the application of the proposed criteria to bound queries and show that the safety criterion is well-suited to identify relevant classes of programs and bound queries. Finally, we propose a hierarchy of classes of terminating programs, calledk-safety, where thek-safe class strictly includes the (k-1)-safe class.

Linear tabling strategies and optimizations

AbstractRecently there has been a growing interest in research in tabling in the logic programming community because of its usefulness in a variety of application domains including program analysis, parsing, deductive databases, theorem proving, model checking, and logic-based probabilistic learning. The main idea of tabling is to memorize the answers to some subgoals and use the answers to resolve subsequent variant subgoals. Early resolution mechanisms proposed for tabling such as OLDT and SLG rely on suspension and resumption of subgoals to compute fixpoints. Recently, the iterative approach named linear tabling has received considerable attention because of its simplicity, ease of implementation, and good space efficiency. Linear tabling is a framework from which different methods can be derived on the basis of the strategies used in handling looping subgoals. One decision concerns when answers are consumed and returned. This article describes two strategies, namely,lazyandeagerstrategies, and compares them both qualitatively and quantitatively. The results indicate that, while the lazy strategy has good locality and is well suited for finding all solutions, the eager strategy is comparable in speed with the lazy strategy and is well suited for programs with cuts. Linear tabling relies on depth-first iterative deepening rather than suspension to compute fixpoints. Each cluster of interdependent subgoals as represented by a topmost looping subgoal is iteratively evaluated until no subgoal in it can produce any new answers. Naive re-evaluation of all looping subgoals, albeit simple, may be computationally unacceptable. In this article, we also introduce semi-naive optimization, an effective technique employed in bottom-up evaluation of logic programs to avoid redundant joins of answers, into linear tabling. We give the conditions for the technique to be safe (i.e., sound and complete) and propose an optimization technique calledearly answer promotionto enhance its effectiveness. Benchmarking in B-Prolog demonstrates that with this optimization linear tabling compares favorably well in speed with the state-of-the-art implementation of SLG.

Efficient goal directed bottom-up evaluation of logic programs

This paper introduces a new strategy for the efficient goal directed bottom-up evaluation of logic programs. Instead of combining a standard bottom-up evaluation strategy with a Magicset transformation, the evaluation strategy is specialized for the application to Magic-set programs which are characterized by clause bodies with a high degree of overlapping. The approach is similar to other techniques which avoid re-computation by maintaining and reusing partial solutions to clause bodies. However, the overhead is considerably reduced as these are maintained implicitly by the underlying Prolog implementation. The technique is presented as a simple meta-interpreter for goal directed bottom-up evaluation. No Magic-set transformation is involved as the dependencies between calls and answers are expressed directly within the interpreter. The proposed technique has been implemented and shown to provide substantial speed-ups in applications of semantic based program analysis based on bottom-up evaluation.

Magic sets with full sharing

In this paper, we study the relationship between tabulation and goal-oriented bottom-up evaluation of logic programs. Differences emerge when one tries to identify features of one evaluation method in the other. We show that to obtain the same effect as tabulation in top-down evaluation, one has to perform a careful adornment in programs to be evaluated bottom-up. Furthermore, we propose an efficient algorithm to perform forward subsumption checking over adorned magic facts.

Space optimization in deductive databases

In the bottom-up evaluation of logic programs and recursively defined views on databases, all generated facts are usually assumed to be stored until the end of the evaluation. Discarding facts during the evaluation, however, can considerably improve the efficiency of the evaluation: the space needed to evaluate the program, the I/O costs, the costs of maintaining and accessing indices, and the cost of eliminating duplicates may all be reduced. Given an evaluation method that is sound, complete, and does not repeat derivation steps, we consider how facts can be discarded during the evaluation without compromising these properties. We show that every such space optimization method has certain components, the first to ensure soundness and completeness, the second to avoid redundancy (i.e., repetition of derivations), and the third to reduce “fact lifetimes” (i.e., the time period for which each fact must be retained during evaluation). We present new techniques based on providing bounds on the number of derivations and uses of facts, and using monotonicity constraints for each of the first two components, and provide novel synchronization techniques for the third component of a space optimization method. We describe how techniques for each of the three components can be combined in practice to obtain a space optimization method for a program. Our results are also of importance in applications such as sequence querying, and in active databases where triggers are defined over multiple “events.”

Depth-bounded bottom-up evaluation of logic programs

We present here a depth-bounded bottom-up evaluation algorithm for logic programs. We show that it is sound, complete, and terminating for finite-answer queries if the programs are syntactically restricted to Datalog nS , a class of logic programs with limited function symbols. Datalog nS is an extension of Datalog capable of representing infinite phenomena. Predicates in Datalog nS can have arbitrary unary and limited n-ary function symbols in one distinguished argument. We precisely characterize the computational complexity of depth-bounded evaluation for Datalog nS and compare depth-bounded evaluation with other evaluation methods, top-down and Magic Sets among others. We also show that universal safety (finiteness of query answers for any database) is decidable for Datalog nS .

Space optimization in the bottom-up evaluation of logic programs

Space optimization in the bottom-up evaluation of logic programs