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39Resource-origins of NonmonotonicityStudia Logica 88 (1): 85-112. 2008.Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin w…Read more
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35Normative Models of Rational Agency: The Theoretical Disutility of Certain ApproachesLogic Journal of the IGPL 11 (6): 597-613. 2003.Much of cognitive science seeks to provide principled descriptions of various kinds and aspects of rational behaviour, especially in beings like us or AI simulacra of beings like us. For the most part, these investigators presuppose an unarticulated common sense appreciation of the rationality that such behaviour consists in. On those occasions when they undertake to bring the relevant norms to the surface and to give an account of that to which they owe their legitimacy, these investigators ten…Read more
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10More on non-cooperation in dialogue logicLogic Journal of the IGPL 9 (2): 305-324. 2001.Stone-walling dialogues are exercises in structured non-cooperation. It is true that dialogue participants need to cooperate with one another and in ways sufficient to make possible the very dialogue they are now having. Beyond that there is room for non-cooperation on a scale that gives great offence to what we call the Goody Two-Shoes Model of argument. In this paper, we argue that non-cooperation dialogues have perfectly legitimate objectives and that in relation to those objectives they need…Read more
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27Filtration structures and the cut down problem in abductionIn Kent A. Peacock & Andrew D. Irvine (eds.), Mistakes of reason: essays in honour of John Woods, University of Toronto Press. pp. 398-417. 2005.
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35Context-dependent Abduction and RelevanceJournal of Philosophical Logic 35 (1): 65-81. 2006.Based on the premise that what is relevant, consistent, or true may change from context to context, a formal framework of relevance and context is proposed in which • contexts are mathematical entities • each context has its own language with relevant implication • the languages of distinct contexts are connected by embeddings • inter-context deduction is supported by bridge rules • databases are sets of formulae tagged with deductive histories and the contexts they belong to • abduction and rev…Read more
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14Belief Contraction, Anti-formulae and Resource Overdraft: Part I Deletion in Resource Bounded LogicsLogic Journal of the IGPL 10 (6): 601-652. 2002.There are several areas in applied logic where deletion from databases is involved in one way or another:Belief contraction Triggers of the form ‘If condition then remove A’, which are extensively used in database management systemsResource considerations as in relevance and linear logics, where addition or removal of resource can affect provabilityFree logic and the like, where existence and non-existence of individuals affects quantification.All of these areas have certain logical difficulties…Read more
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139Advice on Abductive LogicLogic Journal of the IGPL 14 (2): 189-219. 2006.One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological expression of this diffidence. A s…Read more
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19Linguistic and cognitive prominence in anaphor resolution: topic, contrastive focus and pronounsTopoi 26 (1): 3-18. 2007.This paper examines the role that linguistic and cognitive prominence play in the resolution of anaphor–antecedent relationships. In two experiments, we found that pronouns are immediately sensitive to the cognitive prominence of potential antecedents when other antecedent selection cues are uninformative. In experiment 1, results suggest that despite their theoretical dissimilarities, topic and contrastive focus both serve to enhance cognitive prominence. Results from experiment 2 suggest that …Read more
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44Temporal, numerical and meta-level dynamics in argumentation networksArgument and Computation 3 (2-3). 2012.This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks …Read more
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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, Wiley-blackwell. 2002.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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10The 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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76Grafting 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