•  390
    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
  •  7
    The use of logic and argumentation in therapy of sex offenders
    with Gadi Rozenberg and Lydia Rivlin
    Logic Journal of the IGPL. forthcoming.
    This paper is intended first for the formal argumentation community (see https://comma.csc.liv.ac.uk/). This community develops logics and systems modelling argumentation and dialogues. The community is in search of major applications areas for their models. One such application area e.g. is Law. The message of this paper is that there is another major application area for formal argumentation. There is an international community of sex offender therapist that is well established and well funded…Read more
  • Sampling Labeled Deductive Systems
    In Dale Jacquette (ed.), A Companion to Philosophical Logic, Blackwell. 2006.
    This chapter contains sections titled: Labeled Deductive Systems in Context Examples from Monotonic Logics Examples from Non‐monotonic Logics Conclusion and Further Reading.
  •  6
    The paradoxes of permission an action based solution
    with Loïc Gammaitoni and Xin Sun
    Journal of Applied Logic 12 (2): 179-191. 2014.
  •  10
    The Logic System is the Way You Do Logic
    Studia Humana 3 (4): 41-44. 2014.
  •  3
    Modal Provability Foundations for Argumentation Networks
    with A. Szalas
    Studia Logica 93 (2-3): 147-180. 2009.
    Given an argumentation network we associate with it a modal formula representing the ‘logical content’ of the network. We show a one-to-one correspondence between all possible complete Caminada labellings of the network and all possible models of the formula.
  •  14
    Probabilistic Argumentation: An Equational Approach
    Logica Universalis 9 (3): 345-382. 2015.
    There is a generic way to add any new feature to a system. It involves identifying the basic units which build up the system and introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: the nature of the arguments involved; the membership relation in the set S of arguments; the attack relation; and the choice of extensions. Generically to add a new aspect to an argumentatio…Read more
  •  48
    Language and proof theory
    Journal of Logic, Language and Information 5 (3-4): 247-251. 1996.
  •  8
    Equilibrium States in Numerical Argumentation Networks
    Logica Universalis 9 (4): 411-473. 2015.
    Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula that takes the initial values and the attack relation and iterates a sequence of intermediate values that eventually converges leading to an extension. The properties surrounding the application of the iteration formula and its connection with other numerical …Read more
  •  13
    Decidability results in non-classical logics
    Annals of Mathematical Logic 8 (3): 237-295. 1975.
  •  10
    Parsing natural language using LDS: a prototype
    with M. Finger, R. Kibble, and R. Kempson
    Logic Journal of the IGPL 5 (5): 647-671. 1997.
    This paper describes a prototype implementation of a Labelled Deduction System for natural language interpretation, where interpretation is taken to be the process of understanding a natural language utterance. The implementation models the process of understanding wh-gap dependencies in questions and relative clauses for a fragment of English. The paper is divided in three main sections. In Section 1, we introduce the basic architecture of the system. Section 2 outlines a prototype implementati…Read more
  •  35
    Elementary Predicate Logic
    with Wilfrid Hodges and F. Guenthner
    Journal of Symbolic Logic 54 (3): 1089-1090. 1989.
  •  68
    We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implicat…Read more
  •  16
    Cut-Based Abduction
    with Marcello D'agostino and Marcelo Finger
    Logic 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
  •  4
    Editorial
    with J. Cunningham
    Logic Journal of the IGPL 9 (2): 139-140. 2001.
  •  12
    Interpolation in practical formal development
    with J. Bicarregui, T. Dimitrakos, and T. Maibaum
    Logic 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
  •  10
    Editorial
    with M. Baaz, A. Ciabattoni, and P. Hájek
    Logic Journal of the IGPL 13 (4): 363-363. 2005.
  • Editorial
    with M. Baaz, A. Ciabattoni, and P. Hájek
    Logic Journal of the IGPL 13 (5): 491-492. 2005.
  •  7
    Pragmatic Studies in Judaism (edited book)
    with Andrew Schumann, Aviram Ravitsky, Lenn E. Goodman, Furio Biagini, Alan Mittleman, Uri J. Schild, Michael Abraham, Peter Ochs, Yuval Jobani, and Tzvee Zahavy
    Gorgias Press. 2013.
  •  2
    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
  •  4
    International audience.
  •  1
    Handbook of Philosophical Logic: Volume 17 (edited book)
    with Franz Guenthner
    Imprint: Springer. 2013.
    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
  •  3
    A New Perspective on Nonmonotonic Logics
    Imprint: 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
  •  10
    Forthcoming Papers
    with Y. Shramko, J. Barwise, and J. van Benthem
    Logic Journal of the IGPL 3 (5): 815-816. 1995.
  •  7
    What 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
  •  12
    ‎Proof Theory for Fuzzy Logics
    with George Metcalfe and Nicola Olivetti
    Springer. 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
  •  14
    Neural-Symbolic Cognitive Reasoning
    with Artur S. D'Avila Garcez and Luís C. Lamb
    Springer. 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.