Stefan Woltran

Answer-set programming encodings for argumentation frameworks

Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity.

Simplifying Logic Programs Under Uniform and Strong Equivalence

We consider the simplification of logic programs under the stable-model semantics, with respect to the notions of strong and uniform equivalence between logic programs, respectively. Both notions have recently been considered for nonmonotonic logic programs (the latter dates back to the 1980s, though) and provide semantic foundations for optimizing programs with input. Extending previous work, we investigate syntactic and semantic rules for program transformation, based on proper notions of consequence. We furthermore provide encodings of these notions in answer-set programming, and give characterizations of programs which are semantically equivalent to positive and Horn programs, respectively. Finally, we investigate the complexity of program simplification and determining semantical equivalence, showing that the problems range between coNP and \(\Pi_2^p\) complexity, and we present some tractable cases.

Encodings for Equilibrium Logic and Logic Programs with Nested Expressions

Equilibrium logic is an approach to nonmonotonic reasoning that generalises the stable model and answer set semantics for logic programs. We present a method to implement equilibrium logic and, as a special case, stable models for logic programs with nested expressions, based on polynomial reductions to quantified Boolean formulas (QBFs). Since there now exist efficient QBF-solvers, this reduction technique yields a practically relevant approach to rapid prototyping. The reductions for logic programs with nested expressions generalise previous results presented for other types of logic programs. We use these reductions to derive complexity results for the systems in question. In particular, we showthat deciding whether a program with nested expressions has a stable model is +2p -complete.

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.

ASPARTIX: Implementing Argumentation Frameworks Using Answer-Set Programming

The system ASPARTIX is a tool for computing acceptable extensions for a broad range of formalizations of Dungs argumentation framework and generalizations thereof. ASPARTIX relies on a fixed disjunctive datalog program which takes an instance of an argumentation framework as input, and uses the answer-set solver DLV for computing the type of extension specified by the user.

Semantical characterizations and complexity of equivalences in answer set programming

In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P∪R and Q∪R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answer sets (which is the particular case for R=∅), and has its applications in program optimization, verification, and modular logic programming. In this article, we consider more liberal notions of strong equivalence, in which the actual form of R may be syntactically restricted. On the one hand, we consider uniform equivalence where R is a set of facts, rather than a set of rules. This notion, which is well-known in the area of deductive databases, is particularly useful for assessing whether programs P and Q are equivalent as components of a logic program which is modularly structured. On the other hand, we consider relativized notions of equivalence where R ranges over rules over a fixed alphabet, and thus generalize our results to relativized notions of strong and uniform equivalence. For all these notions, we consider disjunctive logic programs in the propositional (ground) case as well as some restricted classes, providing semantical characterizations and analyzing the computational complexity. Our results, which naturally extend to answer set semantics for programs with strong negation, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for input-based problem solving.

Complexity-sensitive decision procedures for abstract argumentation

Abstract argumentation frameworks (AFs) provide the basis for various reasoning problems in the areas of Knowledge Representation and Artificial Intelligence. Efficient evaluation of AFs has thus been identified as an important research challenge. So far, implemented systems for evaluating AFs have either followed a straight-forward reduction-based approach or been limited to certain tractable classes of AFs. In this work, we present a generic approach for reasoning over AFs, based on the novel concept of complexity-sensitivity. Establishing the theoretical foundations of this approach, we derive several new complexity results for preferred, semi-stable and stage semantics which complement the current complexity landscape for abstract argumentation, providing further understanding on the sources of intractability of AF reasoning problems. The introduced generic framework exploits decision procedures for problems of lower complexity whenever possible. This allows, in particular, instantiations of the generic framework via harnessing in an iterative way current sophisticated Boolean satisfiability (SAT) solver technology for solving the considered AF reasoning problems. First experimental results show that the SAT-based instantiation of our novel approach outperforms existing systems.

Methods for solving reasoning problems in abstract argumentation - A survey

Within the last decade, abstract argumentation has emerged as a central field in Artificial Intelligence. Besides providing a core formalism for many advanced argumentation systems, abstract argumentation has also served to capture several non-monotonic logics and other AI related principles. Although the idea of abstract argumentation is appealingly simple, several reasoning problems in this formalism exhibit high computational complexity. This calls for advanced techniques when it comes to implementation issues, a challenge which has been recently faced from different angles. In this survey, we give an overview on different methods for solving reasoning problems in abstract argumentation and compare their particular features. Moreover, we highlight available state-of-the-art systems for abstract argumentation, which put these methods to practice.

The Added Value of Argumentation

We discuss the value of argumentation in reaching agreements, based on its capability for dealing with conflicts and uncertainty. Logic-based models of argumentation have recently emerged as a key topic within Artificial Intelligence. Key reasons for the success of these models is that they are akin to human models of reasoning and debate, and their generalisation to frameworks for modelling dialogues. They therefore have the potential for bridging between human and machine reasoning in the presence of uncertainty and conflict. We provide an overview of a number of examples that bear witness to this potential, and that illustrate the added value of argumentation. These examples amount to methods and techniques for argumentation to aid machine reasoning (e.g. in the form of machine learning and belief functions) on the one hand and methods and techniques for argumentation to aid human reasoning (e.g. for various forms of decision making and deliberation and for the Web) on the other. We also identify a number of open challenges if this potential is to be realised, and in particular the need for benchmark libraries.

Characterizations for Relativized Notions of Equivalence in Answer Set Programming

Recent research in nonmonotonic logic programming focuses on alternative notions of equivalence. In particular, strong and uniform equivalence are both proposed as useful tools to optimize (parts of) a logic program. More specifically, given a set P of program rules and a possible optimization Q, strong (resp. uniform) equivalence requires that adding any set S of rules (resp. facts) to P and Q simultaneously results in equivalent programs, i.e., P∪ S and Q∪ S possess the same stable models. However, in practice it is often necessary to relax this condition in such a way, that dedicated internal atoms in P or Q are no longer allowed to occur in the possible extensions S. In this paper, we consider these relativized notions of both uniform and strong equivalence and provide semantical characterizations by generalizing the notions of UE- and SE-modelhood. These new characterizations capture all notions of equivalence including ordinary equivalence in a uniform way. Finally, we analyze the complexity of the introduced equivalence tests for the important classes of normal and disjunctive logic programs. As a by-product, we reduce the tests for relativized equivalences to ordinary equivalence between two programs. These reductions may serve as a basis for implementation.