ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation functions between the classes. As a result, we obtain a strict ordering among the classes under consideration. Binary programs (n ≤2) are shown to be as expressive as unconstrained programs but strictly more expressive than unary programs (n ≤ 1) which, in turn, are strictly more expressive than atomic programs (n = 0). We also take propositional theories into consideration and prove them to be strictly less expressive than atomic programs. In spite of the gap in expressiveness, we develop a faithful but non-modular translation function from normal programs to propositional theories. We consider this as a breakthrough due to sub-quadratic time complexity (of the order of ||P || × log 2 |Hb(P )|). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems.

This article studies an implementation methodology for partial and disjunctive stable models where partiality and disjunctions are unfolded from a logic program so that an implementation of stable models for normal (disjunction-free) programs can be used as the core inference engine. The unfolding is done in two separate steps. First, it is shown that partial stable models can be captured by total stable models using a simple linear and modular program transformation. Hence, reasoning tasks concerning partial stable models can be solved using an implementation of total stable models. Disjunctive partial stable models have been lacking implementations which now become available as the translation handles also the disjunctive case. Second, it is shown how total stable models of disjunctive programs can be determined by computing stable models for normal programs. Thus an implementation of stable models of normal programs can be used as a core engine for implementing disjunctive programs. The feasibility of the approach is demonstrated by constructing a system for computing stable models of disjunctive programs using the SMODELS system as the core engine. The performance of the resulting system is compared to that of DLV, which is a state-of-the-art system for disjunctive programs.

Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stable-model semantics. We define the notion of a DLP-function, where a well-defined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stable-model semantics for DLP-functions. The module theorem extends the well-known splitting-set theorem and enables the decomposition of DLP-functions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLP-functions using a generalization of a translation-based verification method.

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In this paper, a Gaifman–Shapiro-style module architecture is tailored to the case of smodels programs under the stable model semantics. The composition of smodels program modules is suitably limited by module conditions which ensure the compatibility of the module system with stable models. Hence the semantics of an entire smodels program depends directly on stable models assigned to its modules. This result is formalized as a module theorem which truly strengthens V. Lifschitz and H. Turner's splitting-set theorem (June 1994, Splitting a logic program. In Logic Programming: Proceedings of the Eleventh International Conference on Logic Programming, Santa Margherita Ligure, Italy, P. V. Hentenryck, Ed. MIT Press, 23–37) for the class of smodels programs. To streamline generalizations in the future, the module theorem is first proved for normal programs and then extended to cover smodels programs using a translation from the latter class of programs to the former class. Moreover, the respective notion of module-level equivalence, namely modular equivalence, is shown to be a proper congruence relation: it is preserved under substitutions of modules that are modularly equivalent. Principles for program decomposition are also addressed. The strongly connected components of the respective dependency graph can be exploited in order to extract a module structure when there is no explicit a priori knowledge about the modules of a program. The paper includes a practical demonstration of tools that have been developed for automated (de)composition of smodels programs.

The recent series 5 of the Answer Set Programming (ASP) systemclingoprovides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using these constraints in a reactive context. More precisely, we introduce extensions toclingowith difference and linear constraints over integers and reals, respectively, and realize them in complementary ways. Finally, we empirically evaluate the resultingclingoderivativesclingo[dl] andclingo[lp] on common language fragments and contrast them to related ASP systems.

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