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29Cut-Based AbductionLogic Journal of the IGPL 16 (6): 537-560. 2008.In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: given an unprovable sequent Γ ⊢ G, find a sentence H such that Γ, H ⊢ G is provable ; given a provable sequent Γ ⊢ G, find a sentence H such that Γ ⊢ H and the proof of Γ, H ⊢ G is simpler than the proof of Γ ⊢ G . We argue that the two tasks should not be distinguished, and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is pro…Read more
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13Interpolation in practical formal developmentLogic Journal of the IGPL 9 (2): 231-244. 2001.Interpolation has become one of the standard properties that logicians investigate when designing a logic. In this paper, we provide strong evidence that the presence of interpolants is not only cogent for scientific reasoning but has also important practical implications in computer science. We illustrate that interpolation in general, and uniform splitting interpolants, in particular, play an important role in applications where formality and modularity are invoked. In recognition of the fact …Read more
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16Special issue on Combining Probability and LogicJournal of Applied Logic 1 (3-4): 135-138. 2003.
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3Conditionals and modularity in general logicsSpringer. 2011.This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result…Read more
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6Handbook of Philosophical Logic: Volume 17 (edited book)Imprint: Springer. 2014.This second edition of the Handbook of Philosophical Logic reflects great changes in the landscape of philosophical logic since the first edition. It gives readers an idea of that landscape and its relation to computer science and formal language and artificial intelligence. It shows how the increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics accelerated the development of the subject directly and indirectly. This development i…Read more
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9A New Perspective on Nonmonotonic LogicsImprint: Springer. 2016.Logics are like shadows on a wall; to understand why they dance as they do, and how they can be made to move differently, one needs to look at the mathematical structures from which they can be projected. That is a methodology that has long proven its value for classical and other forms of deductive inference; this book manifests its pertinence to logics of uncertain qualitative reasoning. It draws together and refines work from the literature on preferential and other quite different semantics …Read more
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9What Is Negation in a System 2020?In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, Springer Verlag. pp. 193-221. 2021.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 include…Read more
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22Proof 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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30Neural-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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11What 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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33Handbook 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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113Handbook 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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21Symbolic knowledge extraction from trained neural networks: A sound approachArtificial Intelligence 125 (1-2): 155-207. 2001.
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13On 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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9Homogeneous 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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55The 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