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What is Negation in a System 2020? Gabbay, Dov M. in IfCoLog Journal of Logics and Their Applications (2021), 8(7), 1977--2034 The notion of negation is basic to any formal or informal logical system. When any such system is presented to us, it is presented either as a system without negation or as a system with some form of ... [more ▼] The notion of negation is basic to any formal or informal logical system. When any such system is presented to us, it is presented either as a system without negation or as a system with some form of negation. In both cases we are supposed to know intuitively whether there is no negation in the system or whether the form of negation presented in the system is indeed as claimed. To be more specific, suppose Robinson Crusoe writes a logical system with Hilbert type axioms and rules, which includes a unary connective *A. He puts the document in a bottle and let it lose at sea. We find it and take a look. We ask: is the connective "*" a negation in the system? Yet the notion of what is negation in a formal system is not clear. When we see a unary connective *A, (A a wff) together with some other axioms for some additional connectives, how can we tell whether *A is indeed a form of negation of A? Are there some axioms which the connective "*" must satisfy in order to qualify * as a negation? [less ▲] Detailed reference viewed: 20 (0 UL)Explainable Reasoning in Face of Contradictions: From Humans to Machines ; Gabbay, Dov M. in Calvaresi, Davide; Najjar, Amro; Winikoff, Michael (Eds.) et al Explainable and Transparent AI and Multi-Agent Systems - Third International Workshop, EXTRAAMAS 2021, Virtual Event, May 3-7, 2021, Revised Selected Papers (2021) A well-studied trait of human reasoning and decision-making is the ability to not only make decisions in the presence of contradictions, but also to explain why a decision was made, in particular if a ... [more ▼] A well-studied trait of human reasoning and decision-making is the ability to not only make decisions in the presence of contradictions, but also to explain why a decision was made, in particular if a decision deviates from what is expected by an inquirer who requests the explanation. In this paper, we examine this phenomenon, which has been extensively explored by behavioral economics research, from the perspective of symbolic artificial intelligence. In particular, we introduce four levels of intelligent reasoning in face of contradictions, which we motivate from a microeconomics and behavioral economics perspective. We relate these principles to symbolic reasoning approaches, using abstract argumentation as an exemplary method. This allows us to ground the four levels in a body of related previous and ongoing research, which we use as a point of departure for outlining future research directions. [less ▲] Detailed reference viewed: 23 (0 UL)Preface - Journal of Applied Logics Gabbay, Dov M. ; ; et al in IfCoLog Journal of Logics and Their Applications (2021), 8(6), 1335-1338 Detailed reference viewed: 27 (0 UL)A Brief Introduction to the Shkop Approach to Conflict Resolution in Formal Argumentation Gabbay, Dov M. ; in Liao, Beishui; Jieting, Luo; van der Torre, Leon (Eds.) Logics for New-Generation AI 2021 (2021) In this paper, we formalise the Shkop approach to conflict resolution in formal argumentation, in which we start with an empty abstract argumentation framework AF and an initially empty set of inferred ... [more ▼] In this paper, we formalise the Shkop approach to conflict resolution in formal argumentation, in which we start with an empty abstract argumentation framework AF and an initially empty set of inferred arguments. Then, we expand AF one argument at a time, and evaluate after each expansion if i) arguments that have previously been inferred can be kept (or have to be discarded due to sufficient doubt) and ii) if the newly added argument can be added to the set of inferred arguments. Based on this idea, we introduce a novel approach for designing abstract argumentation semantics. As a particular semantics, we define grounded Shkop semantics – a naive set-based argumentation semantics that does not inhibit a well-known problem of CF2 semantics. [less ▲] Detailed reference viewed: 21 (0 UL)The Burden of Persuasion in Abstract Argumentation ; Gabbay, Dov M. ; in Baroni, Pietro; Benzmüller, Christoph; Wang, Yiqun (Eds.) Logic and Argumentation - 4th International Conference, CLAR 2021 Hangzhou, China, October 20-22, 2021, Proceedings (2021) In this paper, we provide a formal framework for modeling the burden of persuasion in legal reasoning. The framework is based on abstract argumentation, a frequently studied method of non-monotonic ... [more ▼] In this paper, we provide a formal framework for modeling the burden of persuasion in legal reasoning. The framework is based on abstract argumentation, a frequently studied method of non-monotonic reasoning, and can be applied to different argumentation semantics; it supports burdens of persuasion with arbitrary many levels, and allows for the placement of a burden of persuasion on any subset of an argumentation framework’s arguments. Our framework can be considered an extension of related works that raise questions on how burdens of persuasion should be handled in some conflict scenarios that can be modeled with abstract argumentation. An open source software implementation of the introduced formal notions is available as an extension of an argumentation reasoning library. [less ▲] Detailed reference viewed: 34 (2 UL)The Degrees of Monotony-Dilemma in Abstract Argumentation ; Gabbay, Dov M. in Vejnarová, Jirina; Wilson, Nic (Eds.) Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 16th European Conference, ECSQARU 2021, Prague, Czech Republic September 21-24, 2021, Proceedings (2021) In this paper, we introduce the notion of the degree of monotony to abstract argumentation, a well-established method for drawing inferences in face of conflicts in non-monotonic reasoning. Roughly ... [more ▼] In this paper, we introduce the notion of the degree of monotony to abstract argumentation, a well-established method for drawing inferences in face of conflicts in non-monotonic reasoning. Roughly speaking, the degree of monotony allows us, given an abstract argumentation semantics and an abstract argumentation framework to be as monotonic as possible, when iteratively drawing inferences and expanding the argumentation framework. However, we also show that when expanding an argumentation framework several times using so-called normal expansions, an agent may, at any given step, select a conclusion that has the highest degree of monotony w.r.t. the previous conclusion (considering the constraints of the semantics), but end up with a conclusion that has a suboptimal degree of monotony w.r.t. one or several conclusions that precede the previous conclusion. We formalize this observation as the degrees of monotony-dilemma. [less ▲] Detailed reference viewed: 26 (0 UL)Normality, non-contamination and logical depth in classical natural deduction ; Gabbay, Dov M. ; in Studia Logica (2020), 108(2), 291--357 In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard ... [more ▼] In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-Contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially to formal argumentation, (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. [less ▲] Detailed reference viewed: 46 (3 UL)A bimodal simulation of defeasibility in thenormative domain Libal, Tomer ; van der Torre, Leon ; Gabbay, Dov M. et al in CEUR Workshop Proceedings (2020) In the present work we illustrate how two sorts of defeasiblereasoning that are fundamental in the normative domain, that is, reasoning about exceptions and reasoning about violations, can be simulated ... [more ▼] In the present work we illustrate how two sorts of defeasiblereasoning that are fundamental in the normative domain, that is, reasoning about exceptions and reasoning about violations, can be simulated via monotonic propositional theories based on a bimodal language with primitive operators representing knowledge and obligation. The proposed theoretical framework paves the way to using native theorem provers for multimodal logic, such as MleanCoP, in order to automate normative reasoning. [less ▲] Detailed reference viewed: 37 (3 UL)Forgetting an Argument ; Gabbay, Dov M. ; in Proceedings of the AAAI Conference on Artificial Intelligence (2020) The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming ... [more ▼] The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axiomatic-driven and not limited to any specific semantics: we propose semantical and syntactical desiderata encoding different criteria for what forgetting an argument might mean; analyze how these criteria relate to each other; and check whether the criteria can be satisfied in general. The analysis is done for a number of widely used argumentation semantics. Our investigation shows that almost all desiderata are individually satisfiable. However, combinations of semantical and/or syntactical conditions reveal a much more interesting landscape. For instance, we found that the ad hoc approach to forgetting an argument, i.e., by the syntactical removal of the argument and all of its associated attacks, is too restrictive and only compatible with the two weakest semantical desiderata. Amongst the several interesting combinations identified, we showed that one satisfies a notion of minimal change and presented an algorithm that given an AF F and argument x, constructs a suitable AF G satisfying the conditions in the combination. [less ▲] Detailed reference viewed: 44 (2 UL)Talmudic Norms Approach to Mixtures with a Solution to the Paradox of the Heap: A Position Paper ; ; Gabbay, Dov M. et al in Beyond Faith and Rationality (2020) This paper offers a Talmudic norms solution to the paradox of the heap. The claim is that the paradox arises because philosophers use the wrong language to discuss it. We need a language about objects ... [more ▼] This paper offers a Talmudic norms solution to the paradox of the heap. The claim is that the paradox arises because philosophers use the wrong language to discuss it. We need a language about objects which is capable of expressing not only the declarative properties of the object (such as being a heap) but also how the object/heap was constructed. Such a view of objects comes from the Talmudic theory of mixtures. To this we add a first attempt at modelling the Talmudic normative theory of mixing (Talmudic calculus of Sorites). We seek a correlation between Talmudic positions on mixtures and philosophical positions on Sorites. The Talmud is very practical and cannot allow for any theoretically unresolved paradox to get in the way, and so it has a lot to offer to philosophy in general and to the heap paradox in particular. [less ▲] Detailed reference viewed: 59 (2 UL)Attack-Defence Frameworks: Argumentation-Based Semantics for Attack-Defence Trees. Gabbay, Dov M. ; Horne, Ross James ; Mauw, Sjouke et al in Graphical Models for Security - 7th International Workshop (2020) Detailed reference viewed: 49 (11 UL)Introducing Abstract Argumentation with Many Lives Gabbay, Dov M. in Journal of Applied Logic (2020), 2631(3), 295 Detailed reference viewed: 59 (8 UL)Argumentation as information input Gabbay, Dov M. ; in Argumentation-based Proofs of Endearment (2019) Given a network (S,R) , with R ⊆ S2, we view the nodes of S as containing information and view xRy as x transmitting information to y. We argue that such networks provide a more general account of attack ... [more ▼] Given a network (S,R) , with R ⊆ S2, we view the nodes of S as containing information and view xRy as x transmitting information to y. We argue that such networks provide a more general account of attack and defense and general arguments exchange on issues between participants in Facebook and Twitter, as well as being able to simulate the traditional Dung approach. We define a general semantics for such networks. [less ▲] Detailed reference viewed: 46 (3 UL)A geometrical view of I/O logic Gabbay, Dov M. ; Parent, Xavier ; van der Torre, Leon Report (2019) Detailed reference viewed: 66 (9 UL)Theories of Joint Ownership in Talmudic Logic (Hebrew) ; ; Gabbay, Dov M. Book published by Collge Publications (2019) We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components ... [more ▼] We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools. We investigate principles of Talmudic Logic and publish a series of books, one book or more for each principle. http://www.collegepublications.co.uk/stl/ The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning, such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat. These books also criticize modern Talmudic research methodology. Later books deal with additional topics like Deontic logic, and Temporal logic, Agency and processes in the Talmud and more. The aims of the project are two fold: 1. To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed. 2. To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic. [less ▲] Detailed reference viewed: 70 (1 UL)Machine Argumentation. Can We Replace Taxi Drivers by Robots? Gabbay, Dov M. ; ; Dauphin, Jérémie et al in Natural Argument, A tribute to John Woods (2019) We need ethical non-monotonic action logics to control machines which interact heavily with humans. Such logics face special problems and require features which we need to recognise and to address. We ... [more ▼] We need ethical non-monotonic action logics to control machines which interact heavily with humans. Such logics face special problems and require features which we need to recognise and to address. We believe that injecting argumentation methods into action pre-conditions is possibly the way to proceed to model what is needed. To get an idea of what is needed we must investigate a typical problem of replacing a human with a robot operating in a highly interactive environment. This paper focuses on replacing a human taxi driver by a robot. Robot driven cars are already under production and so there is an urgent need for modelling the kind of Artificial Intelligence/Logic/Norms/Ethics which is to be involved and installed in the mind of the Robot. This is research in progress. [less ▲] Detailed reference viewed: 199 (7 UL)The Talmudic Logic Project, Ongoing Since 2008 Gabbay, Dov M. ; ; in Logica Universalis (2019), 13(4), 425--442 We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components ... [more ▼] We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools. We investigate principles of Talmudic Logic and publish a series of books, one book or more for each principle. http://www.collegepublications.co.uk/stl/ The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning, such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat. These books also criticize modern Talmudic research methodology. Later books deal with additional topics like Deontic logic, and Temporal logic, Agency and processes in the Talmud and more. The aims of the project are two fold: 1. To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed. 2. To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic. [less ▲] Detailed reference viewed: 70 (2 UL)Argumentation as Exogenous Coordination van der Torre, Leon ; ; Gabbay, Dov M. in It's All About Coordination (2018) Formal argumentation is one of the most popular approaches in modern logic and reasoning. The theory of abstract argumentation introduced by Dung in 1995 has shifted the focus from the internal structure ... [more ▼] Formal argumentation is one of the most popular approaches in modern logic and reasoning. The theory of abstract argumentation introduced by Dung in 1995 has shifted the focus from the internal structure of arguments to relations among arguments, and temporal dynamics for abstract argumentation was proposed by Barringer, Gabbay and Woods in 2005. In this tradition, we see arguments as reasoning processes, and the interaction among them as a coordination process.We argue that abstract argumentation can adopt ideas and techniques from formal theories of coordination, and as an example we propose a model of sequential abstract argumentation loosely inspired by Reo’s model of exogenous coordination. We show how the argumentation model can represent the temporal dynamics of the liar paradox and predator-prey like behaviour. [less ▲] Detailed reference viewed: 108 (5 UL)Present and Future of Formal Argumentation (Dagstuhl Perspectives Workshop 15362) Gabbay, Dov M. ; ; Liao, Beishui et al in Dagstuhl Manifestos (2018), 7(1), 69--95 Formal Argumentation is emerging as a key reasoning paradigm building bridges among knowledge representation and reasoning in artificial intelligence, informal argumentation in philosophy and linguistics ... [more ▼] Formal Argumentation is emerging as a key reasoning paradigm building bridges among knowledge representation and reasoning in artificial intelligence, informal argumentation in philosophy and linguistics, legal and ethical argumentation, mathematical and logical reasoning, and graph-theoretic reasoning. It aims to capture diverse kinds of reasoning and dialogue activities in the presence of uncertainty and conflicting information in a formal and intuitive way, with potential applications ranging from argumentation mining, via LegalTech and machine ethics, to therapy in clinical psychology. The turning point for the modern stage of formal argumentation theory, much similar to the introduction of possible worlds semantics for the theory of modality, is the framework and language of Dung’s abstract argumentation theory introduced in 1995. This means that nothing could remain the same as before 1995 — it should be a focal point of reference for any study of argumentation, even if it is critical about it. Now, in modal logic, the introduction of the possible worlds semantics has led to a complete paradigm shift, both in tools and new subjects of studies. This is still not fully true for what is going on in argumentation theory. The Dagstuhl workshop led to the first volume of a handbook series in formal argumentation, reflecting the new stage of the development of argumentation theory. [less ▲] Detailed reference viewed: 154 (6 UL)Preface ; ; Gabbay, Dov M. et al in Journal of Logic and Computation (2017) Detailed reference viewed: 58 (7 UL) |
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