Moral Uncertainty and the Problem of Fanaticism

While there is universal agreement that agents ought to act ethically, there is no agreement as to what constitutes ethical behaviour. To address this problem, recent philosophical approaches to `moral uncertainty' propose aggregation of multiple ethical theories to guide agent behaviour. However, one of the foundational proposals for aggregation - Maximising Expected Choiceworthiness (MEC) - has been criticised as being vulnerable to fanaticism; the problem of an ethical theory dominating agent behaviour despite low credence (confidence) in said theory. Fanaticism thus undermines the `democratic' motivation for accommodating multiple ethical perspectives. The problem of fanaticism has not yet been mathematically defined. Representing moral uncertainty as an instance of social welfare aggregation, this paper contributes to the field of moral uncertainty by 1) formalising the problem of fanaticism as a property of social welfare functionals and 2) providing non-fanatical alternatives to MEC, i.e. Highest k-trimmed Mean and Highest Median.

On the Graded Acceptability of Arguments in Abstract and Instantiated Argumentation

The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they meet. The paper investigates the fixpoint theory of these semantics, establishing existence results for them. Second, the paper shows how graded semantics readily provide an approach to argument rankings, offering a novel contribution to the recently growing research programme on ranking-based semantics. Third, this novel approach to argument ranking is applied and studied in the context of instantiated argumentation frameworks, and in so doing is shown to account for a simple form of accrual of arguments within the Dung paradigm. Finally, the theory is compared in detail with existing approaches.

A General Account of Argumentation with Preferences

This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC+'s modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung's framework and its extensions to accommodate preferences.

Prioritised Default Logic as Argumentation with Partial Order Default Priorities

We express Brewka's prioritised default logic (PDL) as argumentation using ASPIC+. By representing PDL as argumentation and designing an argument preference relation that takes the argument structure into account, we prove that the conclusions of the justified arguments correspond to the PDL extensions. We will first assume that the default priority is total, and then generalise to the case where it is a partial order. This provides a characterisation of non-monotonic inference in PDL as an exchange of argument and counter-argument, providing a basis for distributed non-monotonic reasoning in the form of dialogue.

Argumentation Semantics for Prioritised Default Logic

We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions. Argumentation semantics for PDL will allow for the application of argument game proof theories to the process of inference in PDL, making the reasons for accepting a conclusion transparent and the inference process more intuitive. This also opens up the possibility for argumentation-based distributed reasoning and communication amongst agents with PDL representations of mental attitudes.