Discussion Graph Semantics of First-Order Logic with Equality for Reasoning about Discussion and Argumentation

We formulate discussion graph semantics of first-order logic with equality for reasoning about discussion and argumentation as naturally as we would reason about sentences. While there are a few existing proposals to use a formal logic for reasoning about argumentation, they are constructed bottom-up and specialised to the argumentation model by Dung. There is indeed a conspicuous lack of a formal reasoning framework for handling general discussion and argumentation models. We achieve the generality through a top-down formulation of the semantics of first-order logic (with equality) formulas, addressing the current shortage.

Theme Aspect Argumentation Model for Handling Fallacies

In this paper, we present a novel approach to identify fallacies through formal constraints, as a viable alternative to more traditional fallacy classifications by informal criteria. To achieve this objective, we introduce a novel argumentation model, the theme aspect argumentation model, which can do both: modelling of a given argumentation as it is expressed (rhetoric modelling); and deeper semantic analysis of the rhetoric argumentation model. By the help of formal constraints on the theme aspect argumentation model, it is for example possible to see if 'attack's which are claimed to be attacks at the rhetoric level are really attacks. We present core formal constraints that a reasonable argumentation should observe, and then more formal constraints that improve fallacy identification capability. We show and prove consequences of these formal constraints. We then define the concept of normal forms and that of logico-rhetorical conclusion, which we use to demonstrate detection of specific fallacies, informal and logical.

Relational Argumentation Semantics

In this paper, we propose a fresh perspective on argumentation semantics, to view them as a relational database. It offers encapsulation of the underlying argumentation graph, and allows us to understand argumentation semantics under a single, relational perspective, leading to the concept of relational argumentation semantics. This is a direction to understand argumentation semantics through a common formal language. We show that many existing semantics such as explanation semantics, multi-agent semantics, and more typical semantics, that have been proposed for specific purposes, are understood in the relational perspective.

Abstract Interpretation in Formal Argumentation: with a Galois Connection for Abstract Dialectical Frameworks and May-Must Argumentation (First Report)

Labelling-based formal argumentation relies on labelling functions that typically assign one of 3 labels to indicate either acceptance, rejection, or else undecided-to-be-either, to each argument. While a classical labelling-based approach applies globally uniform conditions as to how an argument is to be labelled, they can be determined more locally per argument. Abstract dialectical frameworks (ADF) is a well-known argumentation formalism that belongs to this category, offering a greater labelling flexibility. As the size of an argumentation increases in the numbers of arguments and argument-to-argument relations, however, it becomes increasingly more costly to check whether a labelling function satisfies those local conditions or even whether the conditions are as per the intention of those who had specified them. Some compromise is thus required for reasoning about a larger argumentation. In this context, there is a more recently proposed formalism of may-must argumentation (MMA) that enforces still local but more abstract labelling conditions. We identify how they link to each other in this work. We prove that there is a Galois connection between them, in which ADF is a concretisation of MMA and MMA is an abstraction of ADF. We explore the consequence of abstract interpretation at play in formal argumentation, demonstrating a sound reasoning about the judgement of acceptability/rejectability in ADF from within MMA. As far as we are aware, there is seldom any work that incorporates abstract interpretation into formal argumentation in the literature, and, in the stated context, this work is the first to demonstrate its use and relevance.

Broadening Label-based Argumentation Semantics with May-Must Scales

The semantics as to which set of arguments in a given argumentation graph may be acceptable (acceptability semantics) can be characterised in a few different ways. Among them, labelling-based approach allows for concise and flexible determination of acceptability statuses of arguments through assignment of a label indicating acceptance, rejection, or undecided to each argument. In this work, we contemplate a way of broadening it by accommodating may- and must- conditions for an argument to be accepted or rejected, as determined by the number(s) of rejected and accepted attacking arguments. We show that the broadened label-based semantics can be used to express more mild indeterminacy than inconsistency for acceptability judgement when, for example, it may be the case that an argument is accepted and when it may also be the case that it is rejected. We identify that finding which conditions a labelling satisfies for every argument can be an undecidable problem, which has an unfavourable implication to semantics. We propose to address this problem by enforcing a labelling to maximally respect the conditions, while keeping the rest that would necessarily cause non-termination labelled undecided.

Numerical Abstract Persuasion Argumentation for Expressing Concurrent Multi-Agent Negotiations

A negotiation process by 2 agents e1 and e2 can be interleaved by another negotiation process between, say, e1 and e3. The interleaving may alter the resource allocation assumed at the inception of the first negotiation process. Existing proposals for argumentation-based negotiations have focused primarily on two-agent bilateral negotiations, but scarcely on the concurrency of multi-agent negotiations. To fill the gap, we present a novel argumentation theory, basing its development on abstract persuasion argumentation (which is an abstract argumentation formalism with a dynamic relation). Incorporating into it numerical information and a mechanism of handshakes among members of the dynamic relation, we show that the extended theory adapts well to concurrent multi-agent negotiations over scarce resources.

Formulating Manipulable Argumentation with Intra-/Inter-Agent Preferences

From marketing to politics, exploitation of incomplete information through selective communication of arguments is ubiquitous. In this work, we focus on development of an argumentation-theoretic model for manipulable multi-agent argumentation, where each agent may transmit deceptive information to others for tactical motives. In particular, we study characterisation of epistemic states, and their roles in deception/honesty detection and (mis)trust-building. To this end, we propose the use of intra-agent preferences to handle deception/honesty detection and inter-agent preferences to determine which agent(s) to believe in more. We show how deception/honesty in an argumentation of an agent, if detected, would alter the agent's perceived trustworthiness, and how that may affect their judgement as to which arguments should be acceptable.

Turing-Completeness of Dynamics in Abstract Persuasion Argumentation

Abstract Persuasion Argumentation (APA) is a dynamic argumentation formalism that extends Dung argumentation with persuasion relations. In this work, we show through two-counter Minsky machine encoding that APA dynamics is Turing-complete.

Block Argumentation

We contemplate a higher-level bipolar abstract argumentation for non-elementary arguments such as: X argues against Ys sincerity with the fact that Y has presented his argument to draw a conclusion C, by omitting other facts which would not have validated C. Argumentation involving such arguments requires us to potentially consider an argument as a coherent block of argumentation, i.e. an argument may itself be an argumentation. In this work, we formulate block argumentation as a specific instance of Dung-style bipolar abstract argumentation with the dual nature of arguments. We consider internal consistency of an argument(ation) under a set of constraints, of graphical (syntactic) and of semantic nature, and formulate acceptability semantics in relation to them. We discover that classical acceptability semantics do not in general hold good with the constraints. In particular, acceptability of unattacked arguments is not always warranted. Further, there may not be a unique minimal member in complete semantics, thus sceptic (grounded) semantics may not be its subset. To retain set-theoretically minimal semantics as a subset of complete semantics, we define semi-grounded semantics. Through comparisons, we show how the concept of block argumentation may further generalise structured argumentation.

Abstractly Interpreting Argumentation Frameworks for Sharpening Extensions

Cycles of attacking arguments pose non-trivial issues in Dung style argumentation theory, apparent behavioural difference between odd and even length cycles being a notable one. While a few methods were proposed for treating them, to - in particular - enable selection of acceptable arguments in an odd-length cycle when Dung semantics could select none, so far the issues have been observed from a purely argument-graph-theoretic perspective. Per contra, we consider argument graphs together with a certain lattice like semantic structure over arguments e.g. ontology. As we show, the semantic-argumentgraphic hybrid theory allows us to apply abstract interpretation, a widely known methodology in static program analysis, to formal argumentation. With this, even where no arguments in a cycle could be selected sensibly, we could say more about arguments acceptability of an argument framework that contains it. In a certain sense, we can verify Dung extensions with respect to a semantic structure in this hybrid theory, to consolidate our confidence in their suitability. By defining the theory, and by making comparisons to existing approaches, we ultimately discover that whether Dung semantics, or an alternative semantics such as cf2, is adequate or problematic depends not just on an argument graph but also on the semantic relation among the arguments in the graph.