Tjitze Rienstra

Abduction and dialogical proof in argumentation and logic programming

We develop a model of abduction in abstract argumentation, where changes to an argumentation framework 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.

Multi-sorted argumentation

In the theory of abstract argumentation, the acceptance status of arguments is normally determined for the complete set of arguments at once, under a single semantics. However, this is not always desired. In this paper, we extend the notion of an argumentation framework to a multi-sorted argumentation framework, and we motivate this extension using an example which considers practical and epistemic arguments. In a multi-sorted argumentation framework, the arguments are partitioned into a number of cells, where each cell is associated with a semantics under which its arguments are evaluated. We prove the properties of the proposed framework, and we demonstrate our theory with a number of examples. Finally, we relate our theory to the theory of modal fibring of argumentation networks.

Conditional acceptance functions

Dung-style abstract argumentation theory centers on argumentation frameworks and acceptance functions. The latter take as input a framework and return sets of labelings. This methodology assumes full awareness of the arguments relevant to the evaluation. There are two reasons why this is not satisfactory. Firstly, full awareness is, in general, not a realistic assumption. Second, frameworks have explanatory power, which allows us to reason abductively or counterfactually, but this is lost under the usual semantics. To recover this aspect, we generalize conventional acceptance, and we present the concept of a conditional acceptance function.

Persistence and Monotony Properties of Argumentation Semantics

We study a number of properties concerning the behaviour of semantics for Dung style abstract argumentation when the argumentation framework changes. The properties are concerned with how the evaluation of an argumentation framework changes if an attack between two arguments is added or removed. The results provide insight into the behaviour of these semantics in a dynamic context.

Representing Argumentation Frameworks in Answer Set Programming

This paper studies representation of argumentation frameworks (AFs) in answer set programming (ASP). Four different transformations from AFs to logic programs are provided under the complete semantics, stable semantics, grounded semantics and preferred semantics. The proposed transformations encode labelling-based argumentation semantics at the object level, and different semantics of AFs are uniformly characterized by stable models of transformed programs. We show how transformed programs can be used for solving AF problems such as query-answering, enforcement of arguments, and agreement of different AFs. The results exploit new connection between AF and logic programming, and enables one to realize AF on top of existing answer set solvers.

Property-Based Preferences in Abstract Argumentation

Many works have studied preferences in Dung-style argumentation. Preferences over arguments may be derived, e.g., from their relative specificity, relative strength or from values promoted by the arguments. An underexposed aspect in these models is change of preferences. We present a dynamic model of preferences in argumentation, centering on what we call property-based AFs. It is based on Dietrich and Lists model of property-based preference and it provides an account of how and why preferences in argumentation may change. The idea is that preferences over arguments are derived from preferences over properties of arguments, and change as the result of moving to different motivational states. We also provide a dialogical proof theory that establishes whether there exists some motivational state in which an argument is accepted.

RankPL: A Qualitative Probabilistic Programming Language

In this paper we introduce RankPL, a modeling language that can be thought of as a qualitative variant of a probabilistic programming language with a semantics based on Spohn’s ranking theory. Broadly speaking, RankPL can be used to represent and reason about processes that exhibit uncertainty expressible by distinguishing “normal” from “surprising” events. RankPL allows (iterated) revision of rankings over alternative program states and supports various types of reasoning, including abduction and causal inference. We present the language, its denotational semantics, and a number of practical examples. We also discuss an implementation of RankPL that is available for download.