Tomi Janhunen

Unfolding partiality and disjunctions in stable model semantics

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.

Modularity aspects of disjunctive stable models

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.

Some (in)translatability results for normal logic programs and propositional theories

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|| × log2 |Hb(P)|). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems.

Computing Stable Models via Reductions to Difference Logic

Propositional satisfiability (SAT) solvers provide a promising computational platform for logic programs under the stable model semantics. However, computing stable models of a logic program using a SAT solver presumes translating the program into a set of clauses which is the input form accepted by most SAT solvers. This leads to fairly complex super-linear translations. There are, however, interesting extensions to plain clausal propositional representations such as difference logic. A number of solvers have been developed for difference logic, in particular in the context of the satisfiability modulo theories (SMT) framework, and the goal of the paper is to study whether such engines could be harnessed to the computation of stable models for logic programs in an effective way. To this end, we provide succinct translations from logic programs to theories of difference logic and evaluate the potential of SMT solvers in the computation of stable models using these translations and a selection of benchmarks.

PLATYPUS: a platform for distributed answer set solving

We propose a model to manage the distributed computation of answer sets within a general framework. This design incorporates a variety of software and hardware architectures and allows its easy use with a diverse cadre of computational elements. Starting from a generic algorithmic scheme, we develop a platform for distributed answer set computation, describe its current state of implementation, and give some experimental results.

On the intertranslatability of non-monotonic logics

This paper concentrates on comparing the expressive powers of five non‐monotonic logics that have appeared in the literature. For this purpose, the concept of a polynomial, faithful and modular (PFM) translation function is adopted from earlier work by Gottlob, but a weaker notion of faithfulness is proposed. The existence of a PFM translation function from one non‐monotonic logic to another is interpreted to indicate that the latter logic is capable of expressing everything that the former logic does. Several translation functions are presented in the paper and shown to be PFM. Moreover, it is shown that PFM translation functions are impossible in certain cases, which indicates that the expressive powers of the logics involved differ strictly. The comparisons made in terms of PFM translation functions give rise to an exact classification of non‐monotonic logics, which is then named as the expressive power hierarchy (EPH) of non‐monotonic logics. Three syntactically restricted variants of default logic are also analyzed, and EPH is refined accordingly. Most importantly, the classes of EPH indicate some astonishing relationships in light of earlier results on the expressive power of non‐monotonic logics presented by Gottlob as well as Bonatti and Eiter: Moore’s autoepistemic logic and prerequisite‐free default logic are of equal expressive power and less expressive than Reiter’s default logic and Marek and Truszczyński’s strong autoepistemic logic.

Achieving compositionality of the stable model semantics for smodels programs1

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. Turners 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.

Compact translations of non-disjunctive answer set programs to propositional clauses

Propositional satisfiability (SAT) solvers provide a promising computational platform for logic programs under the stable model semantics. Computing stable models of a logic program using a SAT solver presumes translating the program into a set of clauses in the DIMACS format which is accepted by most SAT solvers as input. In this paper, we present succinct translations from programs with choice rules, cardinality rules, and weight rules--also known as SMODELS programs--to sets of clauses. These translations enable us to harness SAT solvers as black boxes to the task of computing stable models for logic programs generated by any SMODELS compatible grounder such as LPARSE or GRINGO. In the experimental part of this paper, we evaluate the potential of SAT solver technology in finding stable models using NP-complete benchmark problems employed in the Second Answer Set Programming Competition.

GnT: A solver for disjunctive logic programs

Disjunctive logic programming under the stable model semantics [3] is a form of answer set programming (ASP) which is understood nowadays as a new logic programming paradigm. The basic idea is that a given problem is solved by devising a logic program such that the stable models of the program correspond to the solutions of the problem, which are then found by computing stable models for the program. The success of ASP is much due to efficient solvers, such as dlv [5] and smodels [9], which have been developed in recent years. Consequently, many interesting applications of the paradigm have emerged: planning, model checking, reachability analysis, and product configuration, just to mention some.

A Module-Based Framework for Multi-language Constraint Modeling

We develop a module-based framework for constraint modeling where it is possible to combine different constraint modeling languages and exploit their strengths in a flexible way. In the framework a constraint model consists of modules with clear input/output interfaces. When combining modules, apart from the interface, a module is a black box whose internals are invisible to the outside world. Inside a module a chosen constraint language (approaches such as CP, ASP, SAT, and MIP) can be used. This leads to a clear modular semantics where the overall semantics of the whole constraint model is obtained from the semantics of individual modules. The framework supports multi-language modeling without the need to develop a complicated joint semantics and enables the use of alternative semantical underpinnings such as default negation and classical negation in the same model. Furthermore, computational aspects of the framework are considered and, in particular, possibilities of benefiting from the known module structure in solving constraint models are studied.