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93Modal and temporal argumentation networksArgument and Computation 3 (2-3). 2012.The traditional Dung networks depict arguments as atomic and study the relationships of attack between them. This can be generalised in two ways. One is to consider various forms of attack, support, feedback, etc. Another is to add content to nodes and put there not just atomic arguments but more structure, e.g. proofs in some logic or simply just formulas from a richer language. This paper offers to use temporal and modal language formulas to represent arguments in the nodes of a network. The s…Read more
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18Labelled Natural Deduction for Conditional Logics of NormalityLogic 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
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13Natural Arguments: A Tribute to John Woods (edited book)College Publications. 2019.The present collection of essays honours John Woods on the occasion of his eightieth birthday from contributors who wish to pay homage to this remarkable researcher whom they see not only as a scholar of prodigious energy and insight, but as a friend, colleague, collaborator, or former teacher. All of the essays touch upon topics Woods has taken a direct or indirect interest in, ranging from technical problems of mathematical logic and applications of formal methods through philosophical logic, …Read more
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7The use of logic and argumentation in therapy of sex offendersLogic 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
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3Sampling Labeled Deductive SystemsIn 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.
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9The paradoxes of permission an action based solutionJournal of Applied Logic 12 (2): 179-191. 2014.
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6Modal Provability Foundations for Argumentation NetworksStudia 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.
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31Probabilistic Argumentation: An Equational ApproachLogica 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
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16Equilibrium States in Numerical Argumentation NetworksLogica 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
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236A sequence of decidable finitely axiomatizable intermediate logics with the disjunction propertyJournal of Symbolic Logic 39 (1): 67-78. 1974.
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11Parsing natural language using LDS: a prototypeLogic 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
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74Grafting modalities onto substructural implication systemsStudia Logica 59 (1): 65-102. 1997.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
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28Cut-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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21Special 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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