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12Handbook of the History of Logic. Volume 10: Inductive Logic (edited book)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
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The Handbook of the History of Logic. Volume 6: Logic and Modalities in the Twentieth Century (edited book)Elsevier. 2006.
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1The Handbook of the History of Logic, vol. 7: Logic and the Modalities in the Twentieth Century (edited book)Elsevier Press. 2006.
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57Philosophy of economics (edited book)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.
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154Handbook of the history of logic (edited book)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
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60Handbook of the History and Philosophy of Logic Vol. 10: Inductive Logic (edited book)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
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1022. Filtration Structures and the Cut Down Problem for 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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77Abductive reasoning in neural-symbolic systemsTopoi 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
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447Abductive reasoning in neural-symbolic systemsTopoi 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
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30The new logicLogic 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
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59Resource-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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32Normative 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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9More 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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25Filtration 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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73Context-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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11Belief 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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166Advice 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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11Linguistic 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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39Temporal, 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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43Modal 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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12Labelled 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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9Natural 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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76Obligations and prohibitions in Talmudic deontic logicArtificial 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
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26Future determination of entities in Talmudic public announcement logicJournal of Applied Logic 11 (1): 63-90. 2013.
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56Contrary to time conditionals in Talmudic logicArtificial 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