Uwe Egly

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.

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.

Comparing different prenexing strategies for quantified Boolean formulas

The majority of the currently available solvers for quantified Boolean formulas (QBFs) process input formulas only in prenex conjunctive normal form. However, the natural representation of practicably relevant problems in terms of QBFs usually results in formulas which are not in a specific normal form. Hence, in order to evaluate such QBFs with available solvers, suitable normal-form translations are required. In this paper, we report experimental results comparing different prenexing strategies on a class of structured benchmark problems. The problems under consideration encode the evaluation of nested counterfactuals over a propositional knowledge base, and span the entire polynomial hierarchy. The results show that different prenexing strategies influence the evaluation time in different ways across different solvers. In particular, some solvers are robust to the chosen strategies while others are not.

Long-Distance Resolution: Proof Generation and Strategy Extraction in Search-Based QBF Solving

Strategies (and certificates) for quantified Boolean formulas (QBFs) are of high practical relevance as they facilitate the verification of results returned by QBF solvers and the generation of solutions to problems formulated as QBFs. State of the art approaches to obtain strategies require traversing a Q-resolution proof of a QBF, which for many real-life instances is too large to handle. In this work, we consider the long-distance Q-resolution (LDQ) calculus, which allows particular tautological resolvents. We show that for a family of QBFs using the LDQ-resolution allows for exponentially shorter proofs compared to Q-resolution. We further show that an approach to strategy extraction originally presented for Q-resolution proofs can also be applied to LDQ-resolution proofs. As a practical application, we consider search-based QBF solvers which are able to learn tautological clauses based on resolution and the conflict-driven clause learning method. We prove that the resolution proofs produced by these solvers correspond to proofs in the LDQ calculus and can therefore be used as input for strategy extraction algorithms. Experimental results illustrate the potential of the LDQ calculus in search-based QBF solving.

On different structure-preserving translations to normal form

Abstract In this paper, we compare different definitional transformations into normal form with respect to the Herbrand complexity of the resulting normal forms. Usually, such definitional transformations introduce labels defining subformulae. An obvious optimization is to use implications instead of equivalences, if the subformula occurs in one polarity only, in order to reduce the length of the resulting normal form. We identify a sequence of formulae H 1 , H 2 ,..., for which the difference of the Herbrand complexity of the different translations of H κ is bounded from below by a non-elementary function in κ. If the optimized translation is applied instead of the unoptimized one, the length of any resolution or cut-free LK-proof of H κ is non-elementary in κ instead of exponential in κ.

Enhancing Search-Based QBF Solving by Dynamic Blocked Clause Elimination

Among preprocessing techniques for quantified Boolean formula QBF solving, quantified blocked clause elimination QBCE has been found to be extremely effective. We investigate the power of dynamically applying QBCE in search-based QBF solving with clause and cube learning QCDCL. This dynamic application of QBCE is in sharp contrast to its typical use as a mere preprocessing technique. In our dynamic approach, QBCE is applied eagerly to the formula interpreted under the assignments that have been enumerated in QCDCL. The tight integration of QBCE in QCDCL results in a variant of cube learning which is exponentially stronger than the traditional method. We implemented our approach in the QBF solver DepQBF and ran experiments on instances from the QBF Gallery 2014. On application benchmarks, QCDCL with dynamic QBCE substantially outperforms traditional QCDCL. Moreover, our approach is compatible with incremental solving and can be combined with preprocessing techniques other than QBCE.

A solver for QBFs in negation normal form

Various problems in artificial intelligence can be solved by translating them into a quantified boolean formula (QBF) and evaluating the resulting encoding. In this approach, a QBF solver is used as a black box in a rapid implementation of a more general reasoning system. Most of the current solvers for QBFs require formulas in prenex conjunctive normal form as input, which makes a further translation necessary, since the encodings are usually not in a specific normal form. This additional step increases the number of variables in the formula or disrupts the formula’s structure. Moreover, the most important part of this transformation, prenexing, is not deterministic. In this paper, we focus on an alternative way to process QBFs without these drawbacks and describe a solver,

SAT-Based Methods for Circuit Synthesis

\ensuremath{\sf qpro}

On sequent systems and resolution for QBFs

, which is able to handle arbitrary formulas. To this end, we extend algorithms for QBFs to the non-normal form case and compare

Incremental QBF Solving

\ensuremath{\sf qpro}