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Sofia Almpani, Elena Lisanyuk, Andrew Schumann, Antonis Kakas, Dimitra Serakioti, Petros Stefaneas, Vladimir A. Stepanov, Panayiotis V. Frangos, Marcin Trepczyński, Ted Peters, Konrad Szocik, Vojko Strahovnik,


Trends in Argumentation Logic

In this paper, we introduce the subject of the special issue Trends in Argumentation Logic. Here we mainly describe two approaches to argumentation logic with explicating monotonic and non-monotonic, or defeasible, reasoning and explain the role of artificial intelligence in applying argumentation logic. Then we give a short overview of the papers contributed to the special issue.

Argumentation: Reasoning Universalis

The Author: Antonis Kakas,
Can argumentation form the basis for any form of reasoning, informal or formal logical reasoning? We examine this question from the particular perspective of the recent developments in logic-based Artificial Intelligence (AI). We propose that argumentation provides the wider framework encompassing uniformly all reasoning, with strict or formal logical reasoning being a special boundary case. We also attempt to link this unifying role of argumentation with Aristotle’s original investigation of methods and formalisms for the systematic study of human reasoning.

Ambiguity in Argumentation: The Impact of Contextual Factors on Semantic Interpretation

This article is concerned with the concept of ambiguity in argumentation. Ambiguity in linguistics lies on the coexistence of two possibly interpretations of an utterance, while the role of contextual factors and background/encyclopedic knowledge within a specific society seems to be crucial. From a systemic point of view, Halliday has proposed three main language functions (meta-functions): a) ideational function, b) interpersonal function, c) textual function. Language could reflect speaker’s experience of his external and internal world, interpersonal relationships and organization of text, respectively. Lexico-grammatical choices under a micro-level perspective and context (the environment of language) may lead to inconsistent interpretations through semantic or syntactic ambiguities. In philosophy and argumentation logic, strategies of ambiguity have been investigated by Aristotle, since the first sophistic movement. In his Topics, Metaphysics and Rhetoric, has pointed out the notion of “τὸ διττῶς / διχῶς λεγόμενον”, meaning that a term can have different senses and double interpretation. In this paper we discuss how we reconstruct the meaning of an utterance in dialogue through the mechanism of interpretation and how we analyze and construe ambiguities, combining the insights of argumentation theory and text linguistics. Research results show that in case of misunderstanding, the “best interpretation” is the less defeasible one according to contextual presumptions.

Dynamic Approximation of Self-Referential Sentences

Non-classical logic via approximation of self-referential sentences by dynamical systems are consistently presented. The new 6-valued truth values (here A=Liar, V=TruthTeller) are presented as a function of the classical truth values x_i∈{0,1}, which resulted in a philosophical standpoint known as Suszko’s Thesis. Three-valued truth tables were created corresponding to Priest’s tables of the same name. In the process of constructing 4-valued truth tables, two more new truth values (va, av) were revealed that do not coincide with the four original ones. Therefore, the closed tables turned out to be 6-valued. Prof Dunn’s 4-valued truth tables are compared with our 4-valued truth tables. De Morgan’s laws are confirmed by six-valued truth tables. Constructed 3-, 4- and 6-valued lattices obeying De Morgan’s laws.

Determining Argumentative Dispute Resolution Reveals Deep Disagreement Over Harassment Issue (A Case-Study of a Discussion in the Russian Parliament)

The Author: Elena Lisanyuk,
In 2018, three journalists accused one of the Members of the Russian Parliament of harassment at workplace. Many influential persons of the Russian elite engaged themselves in the public discussion of the conflict. We studied that high-profiled discussion using a hybrid method merging human- and logic-oriented approaches in argumentation studies. The method develops ideas of the new dialectics, the argumentation logic and the logical-cognitive approach to argumentation, on which is based the algorithm for determining of dispute resolution by aggregating formal and informal tools of analysis. We have reconstructed the discussion as two disputes about questions A and B. A: Did the MP violate the code of conduct by making statements or actions against the journalists? B: Are actions like the behavior of the MP harassment? The opinions of the discussion participants were grouped into the four points of view: A1 – the MP did not violate the code of conduct, A2 – the MP violated the code of conduct, B3 – the actions are not harassment, B4 – the actions are harassment. We mapped arguments in support or against each of them using OVA software, evaluated the arguments with the help of the critical questions, a tool proposed in the new dialectics, and determined the ultimate A + B resolution by applying of the algorithm that combines elements of gradual and labelling semantics from the argumentation logic and the classification of disputes from the dialectical approaches. The resolution was a subset of four arguments that ensured the victory of A1+B4. However, the substantial incompatibility of those arguments highlighted a deep disagreement, an unresolvable difference of opinion, between the parties about the permissibility of courtship. The deep disagreement, a bonus result yielded by the application of the hybrid method, excluded the interpretation of the determined resolution as convincing for the parties, but pointed out a way to smooth the difference of opinions by elaborating of legal, social and moral aspects of the problem of harassment at workplace.

Argumentation-Based Logic for Ethical Decision Making

As automation in artificial intelligence is increasing, we will need to automate a growing amount of ethical decision making. However, ethical decision-making raises novel challenges for engineers, ethicists and policymakers, who will have to explore new ways to realize this task. The presented work focuses on the development and formalization of models that aim at ensuring a correct ethical behaviour of artificial intelligent agents, in a provable way, extending and implementing a logic-based proving calculus that is based on argumentation reasoning with support and attack arguments. This leads to a formal theoretical framework of ethical competence that could be implemented in artificial intelligent systems in order to best formalize certain parameters of ethical decision-making to ensure safety and justified trust.

Non-Monotonic Reasoning in Medieval Theology: Problems and Assumptions

Some interesting cases of non-monotonic reasoning have already been identified in medieval theological texts. Jacob Archambault proved in 2015 that the argumentation presented by St Anselm of Canterbury in his Proslogion has non-monotonic “embeddings”. My own contribution from 2011 indicated that we can argue that a non-monotonic logic underlies some discussions provided by St Thomas Aquinas in his Summa theologiae, and showed that Boethius of Dacia used non-monotonic reasoning in his De aeternitate mundi. In this article, I would like to briefly present these examples and verify whether we can speak about similar cases in medieval Biblical exegesis. My aim is to outline particular problems connected with the identification of non-monotonicity which are specific to theology, as well as assumptions that should be adopted to successfully discuss this issue.

Public Theology Facing a Planet in Turmoil

Ted Peters pursues Public Theology at the intersection of science, religion, ethics, and public policy. Peters is an emeritus professor at the Graduate Theological Union, where he co-edits the journal, Theology and Science, on behalf of the Center for Theology and the Natural Sciences, in Berkeley, California, USA. His book, God in Cosmic History, traces the rise of the Axial religions 2500 years ago. He previously authored Playing God? Genetic Determinism and Human Freedom? (Routledge, 2nd ed., 2002) as well as Science, Theology, and Ethics (Ashgate 2003). He is editor of AI and IA: Utopia or Extinction? (ATF 2019). Along with Arvin Gouw and Brian Patrick Green, he co-edited the new book, Religious Transhumanism and Its Critics hot off the press (Roman and Littlefield/Lexington, 2022). Soon he will publish The Voice of Christian Public Theology (ATF 2022). See his websites: and

Intellectual and Ethical Virtues in the Situation of War

Vojko Strahovnik, Department Chair and Associate Professor at the Department of Philosophy and Research Fellow in Philosophy at the Faculty of Theology, University of Ljubljana. The impact of his work ranges from insights into the nature of normativity (the role of moral principles in the formation of moral judgments, the authority of the normative domain, epistemic agency, and epistemic virtuousness) to considerations related to practical dimensions of our lives (e.g., the role of guilt and moral shame in reconciliation processes, the importance of intellectual and ethical virtues in dialogue and education, global justice, animal ethics). His recent outreach activities include being a visiting lecturer (2017) and a Templeton and Fulbright research scholar (2016; 2022) at the University of Arizona, Department of Philosophy. The central question that incites him most is the structure and phenomenology of normativity. Webpage: