Christian Straßer

We present a formal argumentation system for dealing with the detachment of prioritized conditional obligations and permissions. In the presence of facts and constraints, we answer the question whether an unconditional obligation or permission is detachable by considering arguments for and against its detachment. For the evaluation of arguments in favour of detachment, we use a Dung-style argumentation-theoretical semantics. We illustrate how violations and contrary-to-duty scenarios are dealt with in our framework and pay special attention to conflict-resolution via priorities.

In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are induced by the extended frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics, which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties.

In this article, we present an argumentative approach to normative reasoning. Special attention is paid to deontic conflicts, contrary-to-duty and specificity cases, which are modelled by means of argumentative attacks. For this, we adopt a recently proposed framework for logical argumentation in which arguments are generated by a sequent calculus of a given base logic of Argument & Computation ), and use standard deontic logic as our base logic. Argumentative attacks are realized by elimination rules that allow to discharge specific sequents. We demonstrate the usefulness of our approach by means of various well-known benchmark examples, and show that this approach is rich enough to capture a variety of paradigms for handling conflicting norms such as reasoning with maximally consistent sets, prioritized norms and deontic formalisms based on I/O logic.

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets.