An Extension-based Approach for Computing and Verifying Preferences in Abstract Argumentation

We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from an argumentation framework, there is a lack of justification behind their acceptability based on implicit argument preferences. Preference-based argumentation frameworks allow one to determine what arguments are justified given a set of preferences. Our research considers the inverse of the standard reasoning problem, i.e., given an abstract argumentation framework and a set of justified arguments, we compute what the possible preferences over arguments are. Furthermore, there is a need to verify (i.e., assess) that the computed preferences would lead to the acceptable sets of arguments. This paper presents a novel approach and algorithm for exhaustively computing and enumerating all possible sets of preferences (restricted to three identified cases) for a conflict-free set of arguments in an abstract argumentation framework. We prove the soundness, completeness and termination of the algorithm. The research establishes that preferences are determined using an extension-based approach after the evaluation phase (acceptability of arguments) rather than stated beforehand. In this work, we focus our research study on grounded, preferred and stable semantics. We show that the complexity of computing sets of preferences is exponential in the number of arguments, and thus, describe an approximate approach and algorithm to compute the preferences. Furthermore, we present novel algorithms for verifying (i.e., assessing) the computed preferences. We provide details of the implementation of the algorithms (source code has been made available), various experiments performed to evaluate the algorithms and the analysis of the results.

Abstract Weighted Based Gradual Semantics in Argumentation Theory

Weighted gradual semantics provide an acceptability degree to each argument representing the strength of the argument, computed based on factors including background evidence for the argument, and taking into account interactions between this argument and others. We introduce four important problems linking gradual semantics and acceptability degrees. First, we reexamine the inverse problem, seeking to identify the argument weights of the argumentation framework which lead to a specific final acceptability degree. Second, we ask whether the function mapping between argument weights and acceptability degrees is injective or a homeomorphism onto its image. Third, we ask whether argument weights can be found when preferences, rather than acceptability degrees for arguments are considered. Fourth, we consider the topology of the space of valid acceptability degrees, asking whether gaps exist in this space. While different gradual semantics have been proposed in the literature, in this paper, we identify a large family of weighted gradual semantics, called abstract weighted based gradual semantics. These generalise many of the existing semantics while maintaining desirable properties such as convergence to a unique fixed point. We also show that a sub-family of the weighted gradual semantics, called abstract weighted (Lp,lambda,mu,A)-based gradual semantics and which include well-known semantics, solve all four of the aforementioned problems.

Evaluation of Human-Understandability of Global Model Explanations using Decision Tree

In explainable artificial intelligence (XAI) research, the predominant focus has been on interpreting models for experts and practitioners. Model agnostic and local explanation approaches are deemed interpretable and sufficient in many applications. However, in domains like healthcare, where end users are patients without AI or domain expertise, there is an urgent need for model explanations that are more comprehensible and instil trust in the model's operations. We hypothesise that generating model explanations that are narrative, patient-specific and global(holistic of the model) would enable better understandability and enable decision-making. We test this using a decision tree model to generate both local and global explanations for patients identified as having a high risk of coronary heart disease. These explanations are presented to non-expert users. We find a strong individual preference for a specific type of explanation. The majority of participants prefer global explanations, while a smaller group prefers local explanations. A task based evaluation of mental models of these participants provide valuable feedback to enhance narrative global explanations. This, in turn, guides the design of health informatics systems that are both trustworthy and actionable.

Inferring Attack Relations for Gradual Semantics

A gradual semantics takes a weighted argumentation framework as input and outputs a final acceptability degree for each argument, with different semantics performing the computation in different manners. In this work, we consider the problem of attack inference. That is, given a gradual semantics, a set of arguments with associated initial weights, and the final desirable acceptability degrees associated with each argument, we seek to determine whether there is a set of attacks on those arguments such that we can obtain these acceptability degrees. The main contribution of our work is to demonstrate that the associated decision problem, i.e., whether a set of attacks can exist which allows the final acceptability degrees to occur for given initial weights, is NP-complete for the weighted h-categoriser and cardinality-based semantics, and is polynomial for the weighted max-based semantics, even for the complete version of the problem (where all initial weights and final acceptability degrees are known). We then briefly discuss how this decision problem can be modified to find the attacks themselves and conclude by examining the partial problem where not all initial weights or final acceptability degrees may be known.

Utility Functions for Human/Robot Interaction

In this paper, we place ourselves in the context of human robot interaction and address the problem of cognitive robot modelling. More precisely we are investigating properties of a utility-based model that will govern a robot's actions. The novelty of this approach lies in embedding the responsibility of the robot over the state of affairs into the utility model via a utility aggregation function. We describe desiderata for such a function and consider related properties.

Analytical Solutions for the Inverse Problem within Gradual Semantics

Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived. While some semantics operate over standard argumentation frameworks, many utilise a weighted framework, where a numeric initial weight is associated with each argument. Recent work has examined the inverse problem within gradual semantics. Rather than determining a preference ordering given an argumentation framework and a semantics, the inverse problem takes an argumentation framework, a gradual semantics, and a preference ordering as inputs, and identifies what weights are needed to over arguments in the framework to obtain the desired preference ordering. Existing work has attacked the inverse problem numerically, using a root finding algorithm (the bisection method) to identify appropriate initial weights. In this paper we demonstrate that for a class of gradual semantics, an analytical approach can be used to solve the inverse problem. Unlike the current state-of-the-art, such an analytic approach can rapidly find a solution, and is guaranteed to do so. In obtaining this result, we are able to prove several important properties which previous work had posed as conjectures.

The Inverse Problem for Argumentation Gradual Semantics

Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each following different principles and producing different argument rankings. A sub-class of such semantics, the so-called weighted semantics, takes, in addition to the graph structure, an initial set of weights over the arguments as input, with these weights affecting the resultant argument ranking. In this work, we consider the inverse problem over such weighted semantics. That is, given an argumentation framework and a desired argument ranking, we ask whether there exist initial weights such that a particular semantics produces the given ranking. The contribution of this paper are: (1) an algorithm to answer this problem, (2) a characterisation of the properties that a gradual semantics must satisfy for the algorithm to operate, and (3) an empirical evaluation of the proposed algorithm.

Norm Identification through Plan Recognition

Societal rules, as exemplified by norms, aim to provide a degree of behavioural stability to multi-agent societies. Norms regulate a society using the deontic concepts of permissions, obligations and prohibitions to specify what can, must and must not occur in a society. Many implementations of normative systems assume various combinations of the following assumptions: that the set of norms is static and defined at design time; that agents joining a society are instantly informed of the complete set of norms; that the set of agents within a society does not change; and that all agents are aware of the existing norms. When any one of these assumptions is dropped, agents need a mechanism to identify the set of norms currently present within a society, or risk unwittingly violating the norms. In this paper, we develop a norm identification mechanism that uses a combination of parsing-based plan recognition and Hierarchical Task Network (HTN) planning mechanisms, which operates by analysing the actions performed by other agents. While our basic mechanism cannot learn in situations where norm violations take place, we describe an extension which is able to operate in the presence of violations.

Representing Pure Nash Equilibria in Argumentation

In this paper we describe an argumentation-based representation of normal form games, and demonstrate how argumentation can be used to compute pure strategy Nash equilibria. Our approach builds on Modgil's Extended Argumentation Frameworks. We demonstrate its correctness, prove several theoretical properties it satisfies, and outline how it can be used to explain why certain strategies are Nash equilibria to a non-expert human user.

Preference Elicitation in Assumption-Based Argumentation

Various structured argumentation frameworks utilize preferences as part of their standard inference procedure to enable reasoning with preferences. In this paper, we consider an inverse of the standard reasoning problem, seeking to identify what preferences over assumptions could lead to a given set of conclusions being drawn. We ground our work in the Assumption-Based Argumentation (ABA) framework, and present an algorithm which computes and enumerates all possible sets of preferences over the assumptions in the system from which a desired conflict free set of conclusions can be obtained under a given semantic. After describing our algorithm, we establish its soundness, completeness and complexity.