•  10
    Łukasiewicz Logic: From Proof Systems To Logic Programming
    with George Metcalfe and Nicola Olivetti
    Logic Journal of the IGPL 13 (5): 561-585. 2005.
    We present logic programming style “goal-directed” proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants
  •  53
    Handbook of Philosophical Logic (edited book)
    with Franz Guenthner
    Kluwer Academic Publishers. 1989.
    The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...
  •  7
    The Functional Interpretation of the Existential Quantifier
    with Ruy J. G. B. de Queiroz
    Logic Journal of the IGPL 3 (2-3): 243-290. 1995.
  •  4
    Products of modal logics. Part 2: relativised quantifiers in classical logic
    Logic Journal of the IGPL 8 (2): 165-210. 2000.
    In the first part of this paper we introduced products of modal logics and proved basic results on their axiomatisability and the f.m.p. In this continuation paper we prove a stronger result - the product f.m.p. holds for products of modal logics in which some of the modalities are reflexive or serial. This theorem is applied in classical first-order logic, we identify a new Square Fragment of the classical logic, where the basic predicates are binary and all quantifiers are relativised, and for…Read more
  •  3
    Alternatives to Standard first-order Semantics
    with Hugues Leblanc and F. Guenthner
    Journal of Symbolic Logic 54 (4): 1483-1484. 1989.
  •  50
    Belief revision in non-classical logics
    with Odinaldo Rodrigues and Alessandra Russo
    Review of Symbolic Logic 1 (3): 267-304. 2008.
    In this article, we propose a belief revision approach for families of (non-classical) logics whose semantics are first-order axiomatisable. Given any such (non-classical) logic , the approach enables the definition of belief revision operators for , in terms of a belief revision operation satisfying the postulates for revision theory proposed by Alchourrrdenfors and Makinson (AGM revision, Alchourrukasiewicz's many-valued logic. In addition, we present a general methodology to translate algebra…Read more
  •  9
    Speed with Quality
    with Ruy de Queiroz
    Logic Journal of the IGPL 2 (1): 1-2. 1994.
  • Frontiers of Combining Systems (edited book)
    with Maarten de Rijke
    Research Studies Press. 2000.
    The International workshop 'Frontiers of Combining Systems' is the only forum that is exclusively devoted to research efforts in this interdisciplinary area. This volume contains selected, edited papers from the second installment of the workshop. The contributions range from theorem proving, rewriting and logic to systems and constraints. While there is a clear emphasis on automated tools and logics, the contributions to this volume show that there exists a rapidly expanding body of solutions o…Read more
  •  16
    A neural cognitive model of argumentation with application to legal inference and decision making
    with Artur S. D'Avila Garcez and Luis C. Lamb
    Journal of Applied Logic 12 (2): 109-127. 2014.
    Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computati…Read more
  •  43
    Non-cooperation in dialogue logic
    with John Woods
    Synthese 127 (1-2). 2001.
  • Agenda Relevance: A Study in Formal Pragmatics
    with John Woods
    Studia Logica 77 (1): 133-139. 2004.
  • Selective filtration in modal logic
    Theoria 36 (3): 323. 1970.
  •  43
    Extending the Curry-Howard interpretation to linear, relevant and other resource logics
    with Ruy J. G. B. de Queiroz
    Journal of Symbolic Logic 57 (4): 1319-1365. 1992.
  •  11
    Labelled Natural Deduction for Conditional Logics of Normality
    with Krysia Broda, Luís Lamb, and Alessandra Russo
    Logic Journal of the IGPL 10 (2): 123-163. 2002.
    We propose a family of Labelled Deductive Conditional Logic systems by defining a Labelled Deductive formalisation for the propositional conditional logics of normality proposed by Boutilier and Lamarre. By making use of the Compilation approach to Labelled Deductive Systems we define natural deduction rules for conditional logics and prove that our formalisation is a generalisation of the conditional logics of normality
  •  58
    Many-Dimensional Modal Logics: Theory and Applications (edited book)
    Elsevier North Holland. 2003.
    Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a…Read more
  •  51
    What is a Logical System? (edited book)
    Oxford University Press. 1994.
    This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers--including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman--the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, W…Read more
  •  20
    A new version of Beth semantics for intuitionistic logic
    Journal of Symbolic Logic 42 (2): 306-308. 1977.
  •  9
    Forthcoming Papers
    with Y. Shramko, J. Barwise, and J. Van Benthem
    Logic Journal of the IGPL 1 (1): 119-119. 1993.
  •  4
    with Hans Ohlbach and Ruy de Queiroz
    Logic Journal of the Igpl 3 (1): 4-6. 1995.
  •  2
    Modelling evolvable component systems: Part I: A logical framework
    with Howard Barringer and David Rydeheard
    Logic Journal of the IGPL 17 (6): 631-696. 2009.
    We develop a logical modelling approach to describe evolvable computational systems. In this account, evolvable systems are built hierarchically from components where each component may have an associated supervisory process. The supervisor's purpose is to monitor and possibly change its associated component. Evolutionary change may be determined purely internally from observations made by the supervisor or may be in response to external change. Supervisory processes may be present at any level …Read more
  •  90
    Independence — Revision and Defaults
    with Karl Schlechta
    Studia Logica 92 (3): 381-394. 2009.
    We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.
  •  8
    The Logic System is the Way You Do Logic
    with Andrew Schumann
    Studia Humana 3 (4): 41-44. 2014.
  •  2
    Handbook of Logic in Computer Science (edited book)
    with S. Abramsky and T. Maibaurn
    Oxford University Press. 1992.
  •  1
    Handbook of Philosophical Logic, 2nd Edition, Volume 5
    with Franz Guenthner
    Tijdschrift Voor Filosofie 65 (1): 184-185. 2003.
  •  11
    The decidability of the Kreisel-Putnam system
    Journal of Symbolic Logic 35 (3): 431-437. 1970.
  •  8
    Equal Rights for the Cut: Computable Non-analytic Cuts in Cut-based Proofs
    with Marcelo Finger
    Logic Journal of the IGPL 15 (5-6): 553-575. 2007.
    This work studies the structure of proofs containing non-analytic cuts in the cut-based system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KE-tableau decision method. We study the structure of such proofs, proving the existence of a normal form for them in the form of a comb-tree proof. We then concentrate on the problem of efficiently computing non-analytic cuts. For that, we study …Read more