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logic programming with function symbols: Checking termination of bottom-up evaluation through program adornments

THEORY AND PRACTICE OF logic programming 2013年第4-5期13卷 737-752页

作者： Greco, Sergio Molinaro, Cristian Trubitsyna, Irina Univ Calabria DIMES I-87030 Commenda Di Rende Italy

Recent years have witnessed an increasing interest in enhancing answer set solvers by allowing function symbols. Since the introduction of function symbols makes common inference tasks undecidable, research has focused on identifying classes of programs allowing only a restricted use of function symbols while ensuring decidability of common inference tasks. Finitely-ground programs, introduced in Calimeri et al. (2008), are guaranteed to admit a finite number of stable models with each of them of finite size. Stable models of such programs can be computed and thus common inference tasks become decidable. Unfortunately, checking whether a program is finitely-ground is semi-decidable. This has led to several decidable criteria, called termination criteria, providing sufficient conditions for a program to be finitely-ground. This paper presents a new technique that, used in conjunction with current termination criteria, allows us to detect more programs as finitely-ground. Specifically, the proposed technique takes a logic program P and transforms it into an adorned program P-mu with the aim of applying termination criteria to P-mu rather than P. The transformation is sound in that if the adorned program satisfies a certain termination criterion, then the original program is finitely-ground. Importantly, applying termination criteria to adorned programs rather than the original ones strictly enlarges the class of programs recognized as finitely-ground.

关键词： logic programming with function symbols bottom-up evaluation program evaluation termination stable models

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

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THEORY AND PRACTICE OF logic programming 2015年第6期15卷 854-889页

作者： Calautti, Marco Greco, Sergio Spezzano, Francesca Trubitsyna, Irina Univ Calabria DIMES I-87036 Arcavacata Di Rende CS Italy

Recently, 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 called propagation graph. The resulting criterion, called G-acyclicity, generalizes most of the decidable criteria proposed so far. Next, we study how rules may activate each other and define a more powerful criterion, called safety. This criterion uses the so-called safety function able 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, called k-safety, where the k-safe class strictly includes the (k-1)-safe class.

关键词： logic programming with function symbols bottom-up execution program termination stable models

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