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Standpoint Logic: a Logic for Handling Semantic Variability, with Applications to Forestry Information

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Standpoint Logic: a Logic for Handling Semantic Variability, with Applications to Forestry Information Standpoint Logic: A Logic for Handling Semantic Variability, with Applications to Forestry Information Luc´ıaG´omez Alvarez´ University of Leeds School of Computing Submitted in accordance with the requirements for the degree of Doctor of Philosophy November 2019 2 Intellectual Property Statement The candidate confirms that the work submitted is her own, except where work which has formed part of jointly authored publications has been in- cluded. The contribution of the candidate and the other authors to this work is explicitly indicated below. The candidate confirms that appropri- ate credit has been given within the thesis where reference has been made to the work of others. In particular, Chapter2 elaborates on work published in: • L. G´omez Alvarez.´ Ambiguity: What is it that needs representing and what needs resolving? (short paper) Ambiguity: Perspectives on Representation and Resolution. Sofia, Bulgaria, 2018. Chapter4 elaborates on work published in: • L. G´omez Alvarez´ and B. Bennett. Dealing with conceptual indetermin- acy: A framework based on supervaluation semantics. L. Bozzato, M. Ho- mola, T. Mossakowski and A. Zimmermann, editors, the Joint Proceedings of MedRACER’18 and WOMoCoE’18, pages 38-50, CEUR-WS, 2018. Chapter6 includes work published in: • L. G´omez Alvarez,´ B. Bennett and A. Richard-Bollans. Talking about Forests: an Example of Sharing Information Expressed with Vague Terms. S. Borgo, O. Kutz, F. Loebe and F. Neuhaus, editors, Proceedings of the Joint Ontology Workshops (JOWO’17), pages 3:1-3:13, CEUR-WS, 2017. • L. G´omez Alvarez´ and B. Bennett. Classification, Individuation and De- marcation of Forests: Formalising the Multi-Faceted Semantics of Geographic Terms. E. Clementini, M. Donnelly, M. Yuan, C. Kray, P. Fobliarone and A. Ballatore, editors, Proceedings of the 13th International Conference on Spatial Information Theory (COSIT’17), pages 8:1-8:-15, LIPIcs, 2017. i The candidate confirms that she is the first author of all the jointly-authored publications, that the work contained within these publications is directly attributable to her and that Bennett’s and Richard-Bollans’ contribution has been in terms of general advice and assistance. This copy has been supplied on the understanding that it is copyright mater- ial and that no quotation from the thesis may be published without proper acknowledgement. The right of Luc´ıaG´omez Alvarez´ to be identified as Author of this work has been asserted by her in accordance with the Copyright, Designs and Patents Act 1988. © 2020 The University of Leeds and Luc´ıaG´omez Alvarez.´ ii Acknowledgements In the first place, I would like to thank my supervisor, Brandon Bennett, for all the trust, support and freedom, as well as all the good times shared in these four years. Freedom, while sweet, can sometimes be uncomfortable. I really appreciate having always felt trust and encouragement when making decisions and producing my own work. Thanks to Adam Richard-Bollans. Having a friend with whom you can have interesting and constructive conversations about your research is a gem, and I hope we can keep working together in the future. Thanks to my homes in Leeds. I am lucky that since I arrived at Leeds five years ago, to a completely new city, I have felt at home. Thanks to ‘the Turnways’ and particularly to Gauthier, for a lot of inspiring and familial conversations during endless breakfasts. And thanks to Firelight, my cur- rent home, for being an amazing housing co-operative and family. Thanks to its members, Ryan, Ersilia and all the rest of you. It has been amazing to live and share a project with you. I take with me a lot of learning and good memories, and I couldn’t be happier that we have seen the main historic burden for Firelight’s survival go. Most importantly, thanks to Marta, who’s company has always inspired, soothed and brightened my life. Thanks for being my family and uncon- ditional friend, for supporting me through the hardest bits of writing my thesis and for sharing my joy during the best ones. Having had you living close to me these five years in Leeds is invaluable, and I want to believe that there will be a lot more to go. iii Abstract It is widely accepted that most natural language expressions do not have precise universally agreed definitions that fix their meanings. Except in the case of certain technical terminology, humans use terms in a variety of ways that are adapted to different contexts and perspectives. Hence, even when conversation participants share the same vocabulary and agree on fundamental taxonomic relationships (such as subsumption and mutual exclusivity), their view on the specific meaning of terms may differ signi- ficantly. Moreover, even individuals themselves may not hold permanent points of view, but rather adopt different semantics depending on the par- ticular features of the situation and what they wish to communicate. In this thesis, we analyse logical and representational aspects of the semantic variability of natural language terms. In particular, we aim to provide a formal language adequate for reasoning in settings where different agents may adopt particular standpoints or perspectives, thereby narrowing the semantic variability of the vague language predicates in different ways. For that purpose, we present standpoint logic, a framework for inter- preting languages in the presence of semantic variability. We build on supervaluationist accounts of vagueness, which explain linguistic indeterm- inacy in terms of a collection of possible interpretations of the terms of the language (precisifications). This is extended by adding the notion of stand- point, which intuitively corresponds to a particular point of view on how to interpret vague terminology, and may be taken by a person or institution in a relevant context. A standpoint is modelled by sets of precisifications com- patible with that point of view and does not need to be fully precise. In this way, standpoint logic allows one to articulate finely grained and structured stipulations of the varieties of interpretation that can be given to a vague concept or a set of related concepts and also provides means to express relationships between different systems of interpretation. After the specification of precisifications and standpoints and the con- sideration of the relevant notions of truth and validity, a multi-modal logic language for describing standpoints is presented. The language includes a modal operator s for each standpoint s, such that s φ means that a proposition φ is unequivocally true according to the standpoint s — i.e. φ iv is true at all precisifications compatible with s. We provide the logic with a Kripke semantics and examine the characteristics of its intended models, of the class MS0 . Furthermore, we prove the soundness, completeness and decidability of standpoint logic with an underlying propositional language, and show that the satisfiability problem is NP-complete. We subsequently illustrate how this language can be used to represent logical properties and connections between alternative partial models of a domain and different accounts of the semantics of terms. As proof of concept, we explore the application of our formal framework to the domain of forestry, and in particular, we focus on the semantic vari- ability of ‘forest’. In this scenario, the problematic arising of the assignation of different meanings has been repeatedly reported in the literature, and it is especially relevant in the context of the unprecedented scale of publicly available geographic data, where information and databases, even when os- tensibly linked to ontologies, may present substantial semantic variation, which obstructs interoperability and confounds knowledge exchange. v Contents 1 Introduction1 1.1 Background . .2 1.2 Overview of the problem . .4 1.2.1 Statement of the problem . .4 1.2.2 Semantic variability notions . .4 1.2.3 Motivation . .5 1.3 Application scenario in forestry . .6 1.4 Achievements and contributions . .8 1.5 The structure of this thesis . .9 2 Background and Literature Review 12 2.1 Introduction . 13 2.2 A brief historical introduction . 13 2.2.1 Early history and introduction to the sorites paradox . 14 2.2.2 Approaches within the analytic tradition . 15 2.2.3 Multidisciplinarity and shift of the focus towards applied work . 17 2.3 The Semantic Variability of Natural Language Terms (SVoNLT) . 18 2.3.1 Terminology . 18 2.3.2 Vagueness and the sorites paradox . 19 2.3.3 Beyond single-dimensional vagueness . 21 2.3.4 Polysemy . 22 2.3.5 Related (yet distinct) phenomena . 22 2.4 Theories of (and approaches to) the SVoNLT . 25 2.4.1 Supervaluationism . 25 vi CONTENTS 2.4.2 Other formal theories of vagueness . 27 2.4.3 Other multidisciplinary approaches . 32 2.5 Formal logic frameworks . 34 2.5.1 Preliminary work on a standpoint framework . 34 2.5.2 Modal frameworks . 36 2.5.3 Other logic frameworks for supervaluationism . 41 3 Introduction to Standpoint Logic 43 3.1 Introduction . 44 3.2 Motivation . 44 3.3 Overview of the framework . 45 3.4 Precisifications . 47 3.4.1 A note on admissible precisifications . 48 3.5 Standpoints . 49 3.5.1 Standpoints as a tool for representation . 50 3.5.2 Stanpoints in relation to Fine’s theory . 51 3.5.3 Modelling standpoints with modal operators . 53 3.5.4 Other modal operators in the supervaluationist literature . 54 3.6 Truth and Validity . 56 3.6.1 Super-truth or relative truth . 59 3.7 Higher-order vagueness . 60 4 A Formal Language for Standpoint Logic 62 4.1 Introduction to a logic of standpoints . 63 4.2 Propositional Standpoint Logic, S0 ..................... 64 4.2.1 The formal language LS0 ...................... 64 4.2.2 Semantics . 65 4.2.3 Proof theory . 73 4.2.4 Correspondence between model properties and axioms .
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