ABSTRACT. Amsterdam-style logicians view modal logic as a fragment of classical logic, and description logicians view their own formalisms in much the same way. Moreover, first-order logic itself can be viewed as a modest fragment of the higher-order logics of Frege and Russell, a fragment with useful model-theoretic properties. All in all, the fine structure of logic is a key topic in contemporary research, as the intensive study of (say) the 2-variable and various guarded fragments attest.

In this talk I want to consider the role of logical fragments in applications. I will focus on applications in natural language, as this is an area rich in non-monotonic and defeasible inference. Moreover, as my perspective is that of computational (rather than theoretical) linguistics, I am interested in efficient solutions to computational tasks - that is, in fragments of computation. Drawing on a running example involving applications of description logic and classical planning to a dialogue system, I will discuss the role of computation to provide 'pragmatic glue' that lets us work with small well-explored logical fragments, while simultaneously providing the dynamics required to model various forms of non-monotonicity.

ABSTRACT. In the last 20 years many proposals have been made to incorporate non-monotonic reasoning into description logics, ranging from approaches based on default logic and circumscription to those based on preferential semantics. In particular, the non-monotonic description logic ALC+Tmin uses a combination of the preferential semantics with minimization of a certain kind of concepts, which represent atypical instances of a class of elements. One of its drawbacks is that it suffers from the problem known as the property blocking inheritance, which can be seen as a weakness from an inferential point of view. In this paper we propose an extension of ALC+Tmin, namely ALC+T+min, with the purpose to solve the mentioned problem. In addition, we show the close connection that exists between ALC+T+min and concept-circumscribed knowledge bases. Finally, we study the complexity of deciding the classical reasoning tasks in ALC+T+min.

ABSTRACT. Nonmonotonic Description Logic (DL-) programs couple nonmonotonic logic programs with DL-ontologies through queries in a loose way which may lead to inconsistency, i.e., lack of an answer set. Recently defined repair answer sets remedy this but a straightforward computation method lacks practicality. We present a novel evaluation algorithm for deletion repair answer sets based on support sets, which reduces evaluation of DL-Lite_A ontology queries to constraint matching. This leads to significant performance gains towards inconsistency management in practice.

ABSTRACT. The semantic web is an open and distributed environment in which it is hard to guarantee consistency of knowledge and information. Under the standard two-valued semantics everything is entailed if knowledge and information is inconsistent. The semantics of the paraconsistent logic LP offers a solution. However, if the available knowledge and information is consistent, the set of conclusions entailed under the three-valued semantics of the paraconsistent logic LP is smaller than the set of conclusions entailed under the two-valued semantics. Preferring conflict-minimal three-valued interpretations eliminates this difference.

Preferring conflict-minimal interpretations introduces non-monotonicity. To handle the non-monotonicity, this paper proposes an assumption-based argumentation system. Assumptions needed to close branches of a semantic tableaux form the arguments. Stable extensions of the set of derived arguments correspond to conflict minimal interpretations and conclusions entailed by all conflict-minimal interpretations are supported by arguments in all stable extensions.

ABSTRACT. Recently several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. Most of these semantics rely on the notion of a repair, defined as an inclusion-maximal subset of the facts (ABox) which is consistent with the ontology (TBox). In this paper, we study variants of two popular inconsistency-tolerant semantics obtained by replacing classical repairs by various types of preferred repair. We analyze the complexity of query answering under the resulting semantics, focusing on the lightweight logic DL-Lite_R. Unsurprisingly, query answering is intractable in all cases, but we nonetheless identify one notion of preferred repair, based upon priority levels, whose data complexity is "only" coNP-complete. This leads us to propose an approach combining incomplete tractable methods with calls to a SAT solver. An experimental evaluation of the approach shows good scalability on realistic cases.

ABSTRACT. The NMR community would like to build a repository of benchmarks to push forward the design of systems implementing NMR as it has been the case for many other area in AI. There are a number of lessons which can be learned from the experience of other communi- ties. Here are a few thoughts about the requirements and choices to make before building such a repository.

ABSTRACT. The connections among natural language processing and argumentation theory are becoming stronger in the latest years, with a growing amount of works going in this direction, in different scenarios and applying heterogeneous techniques. In this paper, we present two datasets we built to cope with the combination of the Textual Entailment framework and bipolar abstract argumentation. In our approach, such datasets are used to automatically identify through a Textual Entailment system the relations among the arguments (i.e., attack, support), and then the resulting bipolar argumentation graphs are analyzed to compute the accepted arguments.

ABSTRACT. Dialogical argumentation is an important cognitive activity by which agents exchange arguments and counterarguments as part of some process such as discussion, debate, persuasion and negotiation. Whilst numerous formal systems have been proposed, there is a lack of frameworks for implementing and evaluating these proposals. First-order executable logic has been proposed as a general framework for specifying and analysing dialogical argumentation. In this paper, we investigate how we can implement systems for dialogical argumentation using propositional executable logic. Our approach is to present and evaluate an algorithm that generates a finite state machine that reflects a propositional executable logic specification for a dialogical argumentation together with an initial state. We also consider how the finite state machines can be analysed, with the minimax strategy being used as an illustration of the kinds of empirical analysis that can be undertaken.

ABSTRACT. We develop a model of abduction in abstract argumentation, where changes to an argumentation frame- work act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e., finding hypotheses that explain skeptical/credulous support) and we show that our model can be instantiated on the basis of abductive logic programs.

ABSTRACT. This paper develops a Reasoning about Actions and Change framework integrated with Default Reasoning, suitable as a Knowledge Representation and Reasoning framework for Story Comprehension. The proposed framework, which is guided strongly by existing knowhow from the Psychology of Reading and Comprehension, is based on the theory of argumentation from AI. It uses argumentation to capture appropriate solutions to the frame, ramification and qualification problems and generalizations of these problems required for text comprehension. In this first part of the study the work concentrates on the central problem of integration (or elaboration) of the explicit information from the narrative in the text with the implicit (in the reader’s mind) common sense world knowledge pertaining to the topic(s) of the story given in the text. We also report on our empirical efforts to gather background common sense world knowledge used by humans when reading a story and to evaluate, through a prototype system, the ability of our approach to capture both the majority and the variability of understanding of a story by the human readers in the experiments.