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10:45 | Interactive Debugging of ASP Programs SPEAKER: Kostyantyn Shchekotykhin ABSTRACT. Broad application of answer set programming (ASP) for declarative problem solving requires the development of tools supporting the coding process. Program debugging is one of the crucial activities within this process. Recently suggested ASP debugging approaches allow efficient computation of possible explanations of a fault. However, even for a small program a debugger might return a large number of possible explanations and selection of the correct one must be done manually. In this paper we present an interactive query-based ASP debugging method which extends previous approaches and finds a preferred explanation by means of observations. The system queries a programmer whether a set of ground atoms must be true in all (cautiously) or some (bravely) answer sets of the program. Since some queries can be more informative than the others, we discuss query selection strategies which, given user's preferences for an explanation, can find the best query. That is, the query an answer of which reduces the overall number of queries required for the identification of a preferred explanation. |

11:15 | Semantics and Compilation of Answer Set Programming with Generalized Atoms SPEAKER: unknown ABSTRACT. Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper we refer to these constructs collectively as generalized atoms. The idea common to all of these constructs is that their satisfaction depends on the truth values of a set of (non-generalized) atoms, rather than the truth value of a single (non-generalized) atom. Motivated by several examples, we argue that for some of the more intricate generalized atoms, the previously suggested semantics provide unintuitive results and provide an alternative semantics, which we call supportedly stable or SFLP answer sets. We show that it is equivalent to the major previously proposed semantics for programs with convex generalized atoms, and that it in general admits more intended models than other semantics in the presence of non-convex generalized atoms. We show that the complexity of supportedly stable models is on the second level of the polynomial hierarchy, similar to previous proposals and to stable models of disjunctive logic programs. Given these complexity results, we provide a compilation method that compactly transforms programs with generalized atoms in disjunctive normal form to programs without generalized atoms. Variants are given for the new supportedly stable and the existing FLP semantics, for which a similar compilation technique has not been known so far. |

11:45 | A Family of Descriptive Approaches To Preferred Answer Sets SPEAKER: Alexander Šimko ABSTRACT. In logic programming under the answer set semantics, preferences on rules are used to choose which of the conflicting rules are applied. Many interesting semantics have been proposed. Brewka and Eiter's Principle I expresses the basic intuition behind the preferences. All the approaches that satisfy Principle I introduce a rather imperative feature into otherwise declarative language. They understand preferences as the order, in which the rules of a program have to be applied. In this paper we present two purely declarative approaches for preference handling that satisfy Principle I, and work for indirectly conflicting rules. The first approach is based on the idea that a rule cannot be defeated by a less preferred conflicting rule. This approach is able to ignore preferences between non-conflicting, and ,e.g., is equivalent with the answer set semantics for the subclass of stratified programs. It is suitable for the scenarios, when developers do not have full control over preferences. The second approach relaxes the requirement for ignoring conflicting rules, which ensures that it stays in the NP complexity class. It is based on the idea that a rule cannot be defeated by a rule that is less preferred or depends on a less preferred rule. The second approach can be also characterized by a transformation to logic programs without preferences. It turns out that the approaches form a hierarchy independent of the hierarchy of the approaches by Delgrande et. al., Wang et. al., and Brewka and Eiter. The approaches of the paper are equivalent with our earlier approach for direct conflicts, when the preferences are only between directly conflicting rules. Finally, we show an application for which the existing approaches are not usable, and the approaches of this paper produce expected results. |

14:30 | Revisiting Postulates for Inconsistency Measures SPEAKER: Philippe Besnard ABSTRACT. We discuss postulates for inconsistency measures as proposed in the literature. We examine them both individually and as a collection. |

16:30 | Compact Argumentation Frameworks SPEAKER: Thomas Linsbichler ABSTRACT. Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics. |

17:00 | Extension--based Semantics of Abstract Dialectical Frameworks SPEAKER: Sylwia Polberg ABSTRACT. One of the most common tools in abstract argumentation are the argumentation frameworks and their associated semantics. While the framework is used to represent a given problem, the semantics define methods of solving it, i.e. they describe requirements for accepting and rejecting arguments. The basic available structure is the Dung framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so--called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing problems inherited from other frameworks. One of the most controversial issues, recognized not only in argumentation, concerns the support cycles. In this paper we introduce a new method to ensure acyclicity of the chosen arguments and present a family of extension--based semantics built on it. We also continue our research on the semantics that permit cycles and fill in the gaps from the previous works. Moreover, we provide ADF versions of the properties known from the Dung setting. Finally, we also introduce a classification of the developed sub--semantics and relate them to the existing labeling--based approaches. |

17:30 | Credulous and Skeptical Argument Games for Complete Semantics in Conflict Resolution based Argumentation SPEAKER: Jozef Frtús ABSTRACT. Argumentation is one of the most popular approaches of defining a non-monotonic formalism and several argumentation based semantics were proposed for defeasible logic programs. Recently, a new approach based on notions of conflict resolutions was proposed, however with declarative semantics only. This paper gives a more procedural counterpart by developing skeptical and credulous argument games for complete semantics and soundness and completeness theorems for both games are provided. After that, distribution of defeasible logic program into several contexts is investigated and both argument games are adapted for multi-context system. |

18:00 | On the Relative Expressiveness of Argumentation Frameworks, Normal Logic Programs and Abstract Dialectical Frameworks SPEAKER: Hannes Strass ABSTRACT. We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional signature using only atoms from that signature. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness. |