DLEAC and the Rejection Paradox

In this paper we first develop a Dialetheic Logic with Exclusive Assumptions and Conclusions, DLEAC. We adopt the semantics of the logic of paradox (LP) extended with a notion of model suitable for DLEAC, and we modify its proof theory by refining the notions of assumption and conclusion, which are understood as speech acts. We introduce a new paradox – the rejectability paradox – first informally, then formally. We then provide its derivation in an extension of DLEAC contanining the rejectability predicate

A PWK-style Argumentation Framework and Expansion

In this article we consider argumentation as an epistemic process performed by an agent to extend and revise her beliefs and gain knowledge, according to the information provided by the environment. Such a process can also generate the suspension of the claim under evaluation. How can we account for such a suspension phenomenon in argumentation process? We propose: (1) to distinguish two kinds of suspensions – critical suspension and non-critical suspension – in epistemic change processes; (2) to introduce a Paraconsistent Weak Kleene logic (PWK) based belief revision theory which makes use of the notion of topic to distinguish the two kinds of suspensions previously mentioned, and (3) to develop a PWK-style argumentation framework and its expansion. By doing that, we can distinguish two kinds of suspensions in an epistemic process by virtue of the notion of topic

Canonical functions: a proof via topological dynamics

Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical functions in certain sets using topological dynamics, providing a shorter alternative to the original combinatorial argument. We moreover present equivalent algebraic characterisations of canonicity

A Formal Account of Disorders in Dialogues

International audienc

Le discours des schizophrènes par la formalisation langagière, interpréter les troubles de la pensée par les troubles du langages

National audienc

A discussion game for the grounded semantics of abstract dialectical frameworks

Abstract dialectical frameworks (ADFs) have been introduced as formalism for the modeling and evaluating argumentation. However, the role of discussion in evaluating of arguments in ADFs has not been clarified well so far. We focus on the grounded semantics of ADFs and provide the grounded discussion game. We show that an argument is acceptable (deniable) in the grounded interpretation of an ADF without any redundant links if and only if the proponent of a claim has a winning strategy in the grounded discussion game

Semi-Abstract Value-Based Argumentation Framework

In his seminal paper, Phan Minh Dung (1995) proposed abstract argumentation framework, which models argumentation using directed graphs where structureless arguments are the nodes and attacks among the arguments are the edges. In the following years, many extensions of this framework were introduced. These extensions typically add a certain form of structure to the arguments. This thesis showcases two such extensions -- value-based argumentation framework by Trevor Bench-Capon (2002) and semi-abstract argumentation framework by Esther Anna Corsi and Christian Ferm\"uller (2017). The former introduces a mapping function that links individual arguments to a set of ordered values, enabling a distinction between objectively and subjectively acceptable arguments. The latter links claims of individual arguments to propositional formulae and then applies newly-introduced attack principles in order to make implicit attacks explicit and to enable a definition of a consequence relation that relies on neither the truth values nor the interpretations in the usual sense. The contribution of this thesis is two-fold. Firstly, the new semi-abstract value-based argumentation framework is introduced. This framework maps propositional formulae associated with individual arguments to a set of ordered values. Secondly, a complex moral dilemma is formulated using the original and the value-based argumentation frameworks showcasing the expressivity of these formalisms.Comment: Submitted as a Bachelor Thesis at TU Wien on 2019-11-07. Advisor: Christian Ferm\"uller. 49 page

Greybox XAI: a Neural-Symbolic learning framework to produce interpretable predictions for image classification

Although Deep Neural Networks (DNNs) have great generalization and prediction capabilities, their functioning does not allow a detailed explanation of their behavior. Opaque deep learning models are increasingly used to make important predictions in critical environments, and the danger is that they make and use predictions that cannot be justified or legitimized. Several eXplainable Artificial Intelligence (XAI) methods that separate explanations from machine learning models have emerged, but have shortcomings in faithfulness to the model actual functioning and robustness. As a result, there is a widespread agreement on the importance of endowing Deep Learning models with explanatory capabilities so that they can themselves provide an answer to why a particular prediction was made. First, we address the problem of the lack of universal criteria for XAI by formalizing what an explanation is. We also introduced a set of axioms and definitions to clarify XAI from a mathematical perspective. Finally, we present the Greybox XAI, a framework that composes a DNN and a transparent model thanks to the use of a symbolic Knowledge Base (KB). We extract a KB from the dataset and use it to train a transparent model (i.e., a logistic regression). An encoder-decoder architecture is trained on RGB images to produce an output similar to the KB used by the transparent model. Once the two models are trained independently, they are used compositionally to form an explainable predictive model. We show how this new architecture is accurate and explainable in several datasets.French ANRT (AssociationNationale Recherche Technologie - ANRT)SEGULA TechnologiesJuan de la Cierva Incorporacion grant - MCIN/AEI by "ESF Investing in your future" I JC2019-039152-IGoogle Research Scholar ProgramDepartment of Education of the Basque Government (Consolidated Research Group MATHMODE) IT1456-2

Stable Normative Explanations: From Argumentation to Deontic Logic

This paper examines how a notion of stable explanation developed elsewhere in Defeasible Logic can be expressed in the context of formal argumentation. With this done, we discuss the deontic meaning of this reconstruction and show how to build from argumentation neighborhood structures for deontic logic where this notion of explanation can be characterised. Some direct complexity results are offered.Comment: 15 pages, extended version of the short paper accepted at JELIA 202

A General Semantics for Logics of Affirmation and Negation

A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and structured objects, unlike its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality