Equivalence of Semantics in Argumentation

A large number of evaluation methods, called semantics, have been proposed in the literature for assessing strength of arguments. This paper investigates their equivalence. It argues that for being equivalent, two semantics should have compatible evaluations of both individual arguments and pairs of arguments. The first requirement ensures that the two semantics judge an argument in the same way, while the second states that they provide the same ranking of arguments. We show that the two requirements are completely independent. The paper introduces three novel relations between semantics based on their rankings of arguments: weak equivalence, strong equivalence and refinement. They state respectively that two semantics do not disagree on their strict rankings; the rankings of the semantics coincide; one semantics agrees with the strict comparisons of the second and it may break some of its ties. We investigate the properties of the three relations and their links with existing principles of semantics, and study the nature of relations between most of the existing semantics. The results show that the main extensions semantics are pairwise weakly equivalent. The gradual semantics we considered are pairwise incompatible, however some pairs are strongly equivalent in case of flat graphs including Max-based (Mbs) and Euler-based (Ebs), for which we provide full characterizations in terms respectively of Fibonacci numbers and the numbers of an exponential series. Furthermore, we show that both semantics (Mbs, EMbs) refine the grounded semantics, and are weakly equivalent with the other extension semantics. We show also that in case of flat graphs, the two gradual semantics Trust-based and Iterative Schema characterize the grounded semantics, making thus bridges between gradual semantics and extension semantics. Finally, the other gradual semantics are incompatible with extension semantics.

Comparing logic programming and formal argumentation; the case of ideal and eager semantics

The connection between logic programming and formal argumentation has been studied starting from the landmark 1995 paper of Dung. Subsequent work has identified a standard translation from logic programs to (instantiated) argumentation frameworks, under which pairwise correspondences hold between various logic programming semantics and various formal argumentation semantics. This includes the correspondence between 3-valued stable and complete semantics, between well-founded and grounded semantics and between 2-valued stable (LP) and stable (argumentation) semantics. In the current paper, we show that the existing translation is able to yield the additional correspondence between ideal semantics for logic programming and ideal semantics for formal argumentation. We also show that correspondence does not hold between eager semantics for logic programming and eager semantics for formal argumentation, at least when translating from logic programming to formal argumentation. Overall, the current work should be seen as completing the analysis of correspondences between mainstream admissibility-based argumentation semantics and their logic programming counterparts.

CONTRASTING ENGLISH AND SERBIAN THROUGH THE LENSES OF MULTILEVEL-GROUNDED SEMANTICS

The paper illustrates how the author’s emerging theory of “multi-level grounding” may be applied to some contrastive phenomena in English and Serbian. The theory argues that classic semantic approaches based on cross-space interaction may profit enormously from a more thorough consideration of contextual constraints on meaning generation. For example, to understand even a fairly simple comparison such as “Achilles is a lion”, one needs to know a lot more than just how to, depending on the paradigm of choice, “cross-domain map”, “blend”, or “analogize” appropriate formal elements of the two concepts understood as mere mental representations. Rather, to be meaningful in more than just an academic sense, the interpretation needs to call layers of context, from the very general knowledge of who Achilles is and what lions are to specific cultural and even personal connotations appropriate to the two agents and their interaction. In relation to the earlier work of Searle and Langacker, cognitive linguists Coulson and Oakley propose to allocate such knowledge to the construct of the “grounding box” (containing implicit information on the agents, forum, and circumstances surrounding the utterance). The author’s theory makes this concept more refined, suggesting a series of at least six hierarchical and partly recursive grounding boxes constraining meaning generation – from the perceptual attributes of objects cognized to such percepts’ cross-modal interaction with the interlocutors’ embodied experience, to their affective, conceptual, and discourse-driven (re) interpretations. The analysis in this paper aims to show how this approach may be instrumental in disentangling the (seemingly) shared and different semantic strategies in the way English and Serbian treat a simple stock expression (“You are right” / “U pravu si”), grammatical construction (“tolerant of” / “tolerantan prema”), and widely used idiom (“a finger in every pie” / “u svakoj čorbi mirođija”).

Characterizing strongly admissible sets

The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility (in contrast to grounded semantics) ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of arguments. We are interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable.

An experimental analysis on the similarity of argumentation semantics

In this paper we ask whether approximation for abstract argumentation is useful in practice, and in particular whether reasoning with grounded semantics – which has polynomial runtime – is already an approximation approach sufficient for several practical purposes. While it is clear from theoretical results that reasoning with grounded semantics is different from, for example, skeptical reasoning with preferred semantics, we investigate how significant this difference is in actual argumentation frameworks. As it turns out, in many graphs models, reasoning with grounded semantics actually approximates reasoning with other semantics almost perfectly. An algorithm for grounded reasoning is thus a conceptually simple approximation algorithm that not only does not need a learning phase – like recent approaches – but also approximates well – in practice – several decision problems associated to other semantics.

No false grounds and topology of argumentation

We integrate Dung’s argumentation framework with a topological space to formalize Clark’s no false lemmas theory for solving the Gettier problem and study its logic. Our formalization shows that one of the two notions of knowledge proposed by Clark, justified belief with true grounds, satisfies Stalnaker’s axiom system of belief and knowledge except for the axiom of closure under conjunction. We propose a new notion of knowledge, justified belief with a well-founded chain of true grounds, which further improves on Clark’s two notions of knowledge. We pinpoint a seemingly reasonable condition which makes these three notions of knowledge collapse into the same one and explain why this result looks counter-intuitive. From a technical point of view, our formal analysis driven by the philosophical issues reveals the logical structure of the grounded semantics in Dung’s argumentation theory.

Modelling the Polysemy of Spatial Prepositions in Referring Expressions

In previous work exploring how to automatically generate typicality measures for spatial prepositions in grounded settings, we considered a semantic model based on Prototype Theory and introduced a method for learning its parameters from data. However, though there is much to suggest that spatial prepositions exhibit polysemy, each term was treated as exhibiting a single sense. The ability for terms to represent distinct but related meanings is unexplored in the work on grounded semantics and referring expressions, where even homonymy is rarely considered. In this paper we address this problem by analysing the issue of reference using spatial language and examining how the polysemy exhibited by spatial prepositions can be incorporated into semantic models for situated dialogue. We support our approach on theoretical developments of Prototype Theory, which suggest that polysemy may be analysed in terms of radial categories, characterised by having several prototypicality centres. After providing a brief overview of polysemy in spatial language and a review of the related work, we define the Baseline Model and discuss how polysemy may be incorporated to improve it. We introduce a method of identifying polysemes based on `ideal meanings' and a modification of the `principled polysemy' framework. In order to compare polysemes and aid typicality judgements we then introduce a notion of `polyseme hierarchy'. Subsequently, we test the performance of the extended Polysemy Model by comparing it to the Baseline Model as well as a data-driven model of polysemy which we derive with a clustering algorithm. We conclude that our method for incorporating polysemy into the Baseline Model provides significant improvement. Finally, we analyse the properties and behaviour of the generated Polysemy Model, providing some insight into the improvement in performance, as well as justification for the given methods.

Do You Feel Me?

In working towards accomplishing a human-level acquisition and understanding of language, a robot must meet two requirements: the ability to learn words from interactions with its physical environment, and the ability to learn language from people in settings for language use, such as spoken dialogue. The second requirement poses a problem: If a robot is capable of asking a human teacher well-formed questions, it will lead the teacher to provide responses that are too advanced for a robot, which requires simple inputs and feedback to build word-level comprehension. In a live interactive study, we tested the hypothesis that emotional displays are a viable solution to this problem of how to communicate without relying on language the robot doesn't--indeed, cannot--actually know. Emotional displays can relate the robot's state of understanding to its human teacher, and are developmentally appropriate for the most common language acquisition setting: an adult interacting with a child. For our study, we programmed a robot to independently explore the world and elicit relevant word references and feedback from the participants who are confronted with two robot settings: a setting in which the robot displays emotions, and a second setting where the robot focuses on the task without displaying emotions, which also tests if emotional displays lead a participant to make incorrect assumptions regarding the robot's understanding. Analyzing the results from the surveys and the Grounded Semantics classifiers, we discovered that the use of emotional displays increases the number of inputs provided to the robot, an effect that's modulated by the ratio of positive to negative emotions that were displayed.

Revisiting the Foundations of Abstract Argumentation – Semantics Based on Weak Admissibility and Weak Defense

In his seminal 1995 paper, Dung paved the way for abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack loop, unless the loop is broken up by some argument attacking the loop from outside. Motivated by the fact that such arguments represent self-contradictory or paradoxical arguments, he asked for reasonable semantics which overcome the problem that such arguments may indeed invalidate any argument they attack. This paper tackles this problem from scratch. More precisely, instead of continuing to use previous concepts defined by Dung we provide new foundations for abstract argumentation, so-called weak admissibility and weak defense. After showing that these key concepts are compatible as in the classical case we introduce new versions of the classical Dung-style semantics including complete, preferred and grounded semantics. We provide a rigorous study of these new concepts including interrelationships as well as the relations to their Dung-style counterparts. The newly introduced semantics overcome the issue with self-defeating arguments, and they are semantically insensitive to syntactic deletions of self-attacking arguments, a special case of self-defeat.

A Case Representation and Similarity Measurement Model with Experience-Grounded Semantics

Case-based reasoning heavily depends on the structure and content of the cases, and semantics is essential to effectively represent cases. In the field of structured case representation, most of the works regarding case representation and measurement of semantic similarity between cases are based on model-theoretic semantics and their extensions. The purpose of this study is to explore the potential of experienced-grounded semantics in case representation and semantic similarity measurement. The main contents in this study are as follows: (i) a case representation model based on experience-grounded semantic is proposed, (ii) a novel semantic similarity measurement method with multi-strategy reasoning is introduced, and (iii) a case-based reasoning software for urban firefighting field based on the proposed model is designed and implemented. Theoretically, compared with traditional structured case representation methods, the proposed model not only represents case in a fully formalized way, but also provides a novel metric for computing the strength of the semantic relationship between cases. The proposed model has been applied in an intelligent decision-support software for urban firefighting.