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20Proof Theory for Fuzzy LogicsSpringer. 2008.Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than te…Read more
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21Neural-Symbolic Cognitive ReasoningSpringer. 2009.This book explores why, regarding practical reasoning, humans are sometimes still faster than artificial intelligence systems. It is the first to offer a self-contained presentation of neural network models for many computer science logics.
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5Logical Tools for Handling Change in Agent-Based SystemsSpringer. 2009.Agents act on the basis of their beliefs and these beliefs change as they interact with other agents. In this book the authors propose and explain general logical tools for handling change. These tools include preferential reasoning, theory revision, and reasoning in inheritance systems, and the authors use these tools to examine nonmonotonic logic, deontic logic, counterfactuals, modal logic, intuitionistic logic, and temporal logic. This book will be of benefit to researchers engaged with arti…Read more
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10What is Negation? (edited book)Springer. 1999.The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relev…Read more
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11From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have inc…Read more
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4This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field. Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanfo…Read more
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29Handbook of Tableau Methods (edited book)Springer. 1999.Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labe…Read more
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109Handbook of Formal Argumentation (edited book)College Publications. 2018.The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation. The first volume of the Handbook is organised into five parts, containing nineteen chapters in all, each written by leading experts in the field. The first part provides a general and historical perspective on the field. The second part gives a comprehensive coverage of the argumentation …Read more
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19Symbolic knowledge extraction from trained neural networks: A sound approachArtificial Intelligence 125 (1-2): 155-207. 2001.
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12On 2nd order intuitionistic propositional calculus with full comprehensionArchive for Mathematical Logic 16 (3-4): 177-186. 1974.
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5The Formalization Of Pratical Reasoning: Problems And ProspectsIn Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic: Volume 18, Springer Verlag. 2018.Deontic logic, as traditionally conceived, provides only a deductive theory that constrains the states or possible worlds within which an agent should try to remain.
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8Homogeneous And Heterogeneous Logical Proportions: An IntroductionIn Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic: Volume 18, Springer Verlag. 2018.Commonsense reasoning often relies on the perception of similarity as well as dissimilarity between objects or situations.
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Dynamics of Practical Reasoning: A Position PaperIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 197-242. 1998.
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14Handbook of Philosophical Logic: Volume 18 (edited book)Springer Verlag. 2018.This eighteenth volume of the acclaimed Handbook of Philosophical Logic includes many contributors who are among the most famous leading figures of applied philosophical logic of our time. Coverage includes deontic logic, practical reasoning, homogeneous and heterogeneous logical proportion, and talmudic logic. Overall, it will appeal to students, practitioners, and researchers looking for an authoritative resource in these areas. The contributors first explore models in terms of dynamic logics …Read more
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46The Talmudic Logic Project, Ongoing Since 2008Logica Universalis 13 (4): 425-442. 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 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…Read more
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30Normality, Non-contamination and Logical Depth in Classical Natural DeductionStudia Logica 108 (2): 291-357. 2020.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 f…Read more
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Dynamics of Practical Reasoning: A Position PaperIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 197-242. 1998.
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16Embedding and Automating Conditional Logics in Classical Higher-Order LogicAnnals of Mathematics and Artificial Intelligence 66 (1-4): 257-271. 2012.
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24Meta-Argumentation Modelling I: Methodology and TechniquesStudia Logica 93 (2-3): 297-355. 2009.In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory o…Read more
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Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and LinguisticsSynthese 40 (2): 353-373. 1979.
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8Fibred Semantics and the Weaving of Logics Part 1: Modal and Intuitionistic LogicsJournal of Symbolic Logic 61 (3): 1057-1120. 1996.This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems $\mathbf{L}_i, i \in I$, to form a new system $\mathbf{L}_I$. The methodology `fibres' the semantics $\mathscr{K}_i$ of $\mathbf{L}_i$ into a semantics for $\mathbf{L}_I$, and `weaves' the proof theory of $\mathbf{L}_i$ into a proof system of $\mathbf{L}_I$. There are various ways of doing this, we distinguish by different names such as `fibring', `dov…Read more