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The paper proposes a representation of the subsumption re- lation and of count as conditional in the context of argument ontologies. Starting from the weaker notion of classification represented by the subsumption relation towards the stronger notion of count as, we show how to reason whether an argu- ment is accepted in ontologies involving these two notions. We adopt the methodology of meta-argumentation in order to model the design decisions. Argumentation, being able to handle contradictory information, is proposed as technique to reason about count as for ontology interoperability.

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration.

In belief revision, an agent is faced with the problem of choosing between several alternatives when trying to restore con- sistency to theory. Ideally, the choice process is conducted in a way that verifies a number of fairness principles. On the other hand, be- lief merging concerns with the problem of determining a group’s be- liefs from individual members’ beliefs that are not always compatible with each other. Similarly, in voting systems, a social welfare func- tion takes individual preferences into account in order to produce a collective preference. Here again certain fairness principles are desir- able. In this paper, we investigate the relationship between revision, merging and voting.