• Principles Of Talmudic Logic
    with Franz Guenthner, U. Schild, and M. Abraham
    In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Kluwer Academic Publishers. 1983.
  •  1
    Handbook of the History of Logic
    with John Woods
    Bulletin of Symbolic Logic 10 (4): 579-583. 2004.
  • Agenda Relevance: A Study in Formal Pragmatics
    with John Woods
    Studia Logica 77 (1): 133-139. 2004.
  • Dag Westerstahl
    with Elisabeth Engdahl, U. Cambridge, Johan van Benthem, Jon Barwise, Robin Cooper, Jon Doyle, Brian Skyrms, and U. Irvine
    Journal of Logic, Language, and Information 5 107-112. 1996.
  • Cooperate with your logic ancestors
    with John Woods
    Journal of Logic, Language and Information 8 3-5. 1999.
  •  26
    Benton, RA, 527 Blackburn, P., 281 Braüner, T., 359 Brink, C., 543
    with S. Chopra, B. J. Copeland, E. Corazza, S. Donaho, F. Ferreira, H. Field, L. Goldstein, J. Heidema, and M. J. Hill
    Journal of Philosophical Logic 31 (615). 2002.
  •  5
    Alternative Set Theories
    with Thierry Libert, T. Forster, R. Holmes, John Woods, and Akihiro Kanamori
    In Dov Gabbay (ed.), The Handbook of the History of Logic, Elsevier. 2009.
  •  2
    Belief contraction, anti-formulae and resource overdraft: Part II deletion in resource unbounded logics
    with Odinaldo Rodrigues and John Woods
    In S. Rahman (ed.), Logic, Epistemology, and the Unity of Science, Kluwer Academic Publishers. pp. 291--326. 2004.
  • Sets and extensions in the twentieth century
    with Akihiro Kanamori and John Woods
    In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the history of logic, Elsevier. 2004.
  •  14
    Fallacies as cognitive virtues
    with John Woods
    In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy, Springer Verlag. pp. 57--98. 2009.
  •  13
    Logical Analysis of the Talmudic Rules of General and Specific (Klalim-u-Pratim)
    with Michael Abraham, Gabriel Hazut, Yosef E. Maruvka, and Uri Schild
    History and Philosophy of Logic 32 (1): 47-62. 2011.
    This article deals with a set-theoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP)
  •  24
    Obligations and prohibitions in Talmudic deontic logic
    with M. Abraham and U. Schild
    Artificial Intelligence and Law 19 (2-3): 117-148. 2011.
    This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives: O T A Talmudic obligation F T A Talmudic prohibition F D A Standard deontic prohibition O D A Standard deontic obligation. In classical logic one would have expected that deontic obligation O D is definable by $O_DA \equiv F_D\neg A$ and that O T and F T are connected by $O_TA \equiv F_T\neg A$ This is not the case in the Talmud f…Read more
  •  21
    Contrary to time conditionals in Talmudic logic
    with M. Abraham and U. Schild
    Artificial Intelligence and Law 20 (2): 145-179. 2012.
    We consider conditionals of the form A ⇒ B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals.Three main aspects will be investigated: Inverse causality from future to past, where a future condition can influence a legal event in the past (this is a man made causality).Comparison with similar features in modern law.New types of temporal logics arising from mod…Read more
  •  12
    We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix $${\mathbb {A}}$$ with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i,j =?. The method allows us to decide whether to declare a i,j = 0 or a i,j = 1 or a i,j =? undecided. This algorithmic method is then applied to modelling several legal and practi…Read more
  •  9
    A bimodal simulation of defeasibility in the normative domain
    with Tomer Libal, Matteo Pascucci, and Leendert van der Torre
    In Tomer Libal, Matteo Pascucci, Leendert van der Torre & Dov Gabbay (eds.), Proceedings of FCR-2020, Ceur Workshop Proceedings. pp. 41-54. 2020.
    In the present work we illustrate how two sorts of defeasible reasoning 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.
  • Proceedings of FCR-2020 (edited book)
    with Tomer Libal, Matteo Pascucci, and Leendert van der Torre
    CEUR Workshop Proceedings. 2020.
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    Handbook of the History of Logic. Volume 10: Inductive Logic (edited book)
    with Stephan Hartmann and John Woods
    Elsevier. 2011.
    Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific…Read more
  •  11
    Philosophy of economics (edited book)
    with Uskali Mäki, Paul Thagard, and John Woods
    North Holland. 2012.
    This volume serves as a detailed introduction for those new to the field as well as a rich source of new insights and potential research agendas for those already engaged with the philosophy of economics.
  •  16
    Handbook of the history of logic (edited book)
    with John Woods and Akihiro Kanamori
    Elsevier. 2004.
    Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, includ…Read more
  •  15
    Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific…Read more
  •  1
    22. Filtration Structures and the Cut Down Problem for Abduction
    with John Woods
    In Kent A. Peacock & Andrew D. Irvine (eds.), Mistakes of reason: essays in honour of John Woods, University of Toronto Press. pp. 398-417. 2005.
  •  10
    Abductive reasoning in neural-symbolic systems
    with A. Garcez, O. Ray, and J. Woods
    Topoi 26 (1): 37-49. 2007.
    Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abdu…Read more
  •  18
    Abductive reasoning in neural-symbolic systems
    with Artur S. D’Avila Garcez, Oliver Ray, and John Woods
    Topoi 26 (1): 37-49. 2007.
    Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abdu…Read more
  •  8
    The new logic
    with J. Woods
    Logic Journal of the IGPL 9 (2): 141-174. 2001.
    The purpose of this paper is to communicate some developments in what we call the new logic. In a nutshell the new logic is a model of the behaviour of a logical agent. By these lights, logical theory has two principal tasks. The first is an account of what a logical agent is. The second is a description of how this behaviour is to be modelled. Before getting on with these tasks we offer a disclaimer and a warning. The disclaimer is that although the new logic is significantly different from it,…Read more