114 research outputs found

    Complexity of Nested Circumscription and Nested Abnormality Theories

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    The need for a circumscriptive formalism that allows for simple yet elegant modular problem representation has led Lifschitz (AIJ, 1995) to introduce nested abnormality theories (NATs) as a tool for modular knowledge representation, tailored for applying circumscription to minimize exceptional circumstances. Abstracting from this particular objective, we propose L_{CIRC}, which is an extension of generic propositional circumscription by allowing propositional combinations and nesting of circumscriptive theories. As shown, NATs are naturally embedded into this language, and are in fact of equal expressive capability. We then analyze the complexity of L_{CIRC} and NATs, and in particular the effect of nesting. The latter is found to be a source of complexity, which climbs the Polynomial Hierarchy as the nesting depth increases and reaches PSPACE-completeness in the general case. We also identify meaningful syntactic fragments of NATs which have lower complexity. In particular, we show that the generalization of Horn circumscription in the NAT framework remains CONP-complete, and that Horn NATs without fixed letters can be efficiently transformed into an equivalent Horn CNF, which implies polynomial solvability of principal reasoning tasks. Finally, we also study extensions of NATs and briefly address the complexity in the first-order case. Our results give insight into the ``cost'' of using L_{CIRC} (resp. NATs) as a host language for expressing other formalisms such as action theories, narratives, or spatial theories.Comment: A preliminary abstract of this paper appeared in Proc. Seventeenth International Joint Conference on Artificial Intelligence (IJCAI-01), pages 169--174. Morgan Kaufmann, 200

    Redundancy in Logic I: CNF Propositional Formulae

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    A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study the problem of checking whether a CNF formula (a set of clauses) is redundant, that is, it contains clauses that can be derived from the other ones. Any CNF formula can be made irredundant by deleting some of its clauses: what results is an irredundant equivalent subset (I.E.S.) We study the complexity of some related problems: verification, checking existence of a I.E.S. with a given size, checking necessary and possible presence of clauses in I.E.S.'s, and uniqueness. We also consider the problem of redundancy with different definitions of equivalence.Comment: Extended and revised version of a paper that has been presented at ECAI 200

    Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP

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    We study the existence of optimal and p-optimal proof systems for classes in the Boolean hierarchy over NP\mathrm{NP}. Our main results concern DP\mathrm{DP}, i.e., the second level of this hierarchy: If all sets in DP\mathrm{DP} have p-optimal proof systems, then all sets in coDP\mathrm{coDP} have p-optimal proof systems. The analogous implication for optimal proof systems fails relative to an oracle. As a consequence, we clarify such implications for all classes C\mathcal{C} and D\mathcal{D} in the Boolean hierarchy over NP\mathrm{NP}: either we can prove the implication or show that it fails relative to an oracle. Furthermore, we show that the sets SAT\mathrm{SAT} and TAUT\mathrm{TAUT} have p-optimal proof systems, if and only if all sets in the Boolean hierarchy over NP\mathrm{NP} have p-optimal proof systems which is a new characterization of a conjecture studied by Pudl\'ak

    ErklĂ€ren von ErfĂŒllbarkeitsanfragen fĂŒr Softwareproduktlinien

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    Many analyses have been proposed to ensure the correctness of the various models used throughout software product line development. However, these analyses often merely serve to detect such circumstances without providing any means for dealing with them once encountered. To aid the software product line developer in understanding the cause of defects, a new algorithm capable of explaining satisfiability queries in a software product line context is presented in this thesis. This algorithm finds explanations by using SAT solvers to extract minimal unsatisfiable subsets from the propositional formulas that express the defects. The algorithm is applied to feature model defects such as dead features and redundant constraints, automatic truth value propagations in configurations, and preprocessor annotations that are superfluous or cause dead code blocks. Using feature models and configurations from real software product lines of varying sizes, this approach is evaluated against an existing explanation approach based on Boolean constraint propagation. The results show that Boolean constraint propagation occasionally fails to find any explanation at all but is magnitudes faster than using minimal unsatisfiable subset extractors. In response, both algorithms are combined into a single one that is as fast as Boolean constraint propagation for the cases where that finds an explanation, but also finds an explanation for all the other cases.Viele Analysen wurden vorgeschlagen, um die Korrektheit der verschiedenen in der Entwicklung von Softwareproduktlinien genutzten Modelle zu gewĂ€hrleisten. Allerdings dienen diese Analysen hĂ€ufig lediglich dem Erkennen solcher UmstĂ€nde, ohne Mittel zu liefern, sie zu lösen, sobald sie angetroffen wurden. Um dem Entwickler der Softwareproduktlinie das Verstehen der Ursache der Defekte zu erleichtern, wird in dieser Arbeit ein neuer Algorithmus zum ErklĂ€ren von ErfĂŒllbarkeitsanfragen im Kontext von Softwareproduktlinien vorgestellt. Dieser Algorithmus findet ErklĂ€rungen, indem mittels SAT-Solvern eine minimale unerfĂŒllbare Teilmenge aus der aussagenlogischen Formel, die den Defekt ausdrĂŒckt, extrahiert wird. Der Algorithmus wird angewandt auf Defekte in Feature-Modellen wie tote Features und redundante Constraints, automatische Resolution von Wahrheitswerten in Konfigurationen sowie PrĂ€prozessorannotationen, die ĂŒberflĂŒssig sind oder tote Code-Blocks verursachen. Dieser Ansatz wird anhand von Feature-Modellen und Konfigurationen aus echten Softwareproduktlinien verschiedener GrĂ¶ĂŸen gegen einen existierenden, auf Boolean-Constraint-Propagation basierenden Ansatz zum ErklĂ€ren evaluiert. Die Ergebnisse zeigen, dass Boolean-Constraint-Propagation gelegentlich gar keine ErklĂ€rung findet, aber um GrĂ¶ĂŸenordnungen schneller als mittels Extraktoren fĂŒr minimale unerfĂŒllbare Teilmengen ist. Daraufhin werden beide Algorithmen in einem einzigen verbunden, der so schnell wie Boolean-Constraint-Propagation ist, wenn dieser eine ErklĂ€rung findet, aber auch eine ErklĂ€rung in allen ĂŒbrigen FĂ€llen findet

    Logic-Based Specification Languages for Intelligent Software Agents

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    The research field of Agent-Oriented Software Engineering (AOSE) aims to find abstractions, languages, methodologies and toolkits for modeling, verifying, validating and prototyping complex applications conceptualized as Multiagent Systems (MASs). A very lively research sub-field studies how formal methods can be used for AOSE. This paper presents a detailed survey of six logic-based executable agent specification languages that have been chosen for their potential to be integrated in our ARPEGGIO project, an open framework for specifying and prototyping a MAS. The six languages are ConGoLog, Agent-0, the IMPACT agent programming language, DyLog, Concurrent METATEM and Ehhf. For each executable language, the logic foundations are described and an example of use is shown. A comparison of the six languages and a survey of similar approaches complete the paper, together with considerations of the advantages of using logic-based languages in MAS modeling and prototyping.Comment: 67 pages, 1 table, 1 figure. Accepted for publication by the Journal "Theory and Practice of Logic Programming", volume 4, Maurice Bruynooghe Editor-in-Chie
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