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

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 significantly. Moreover, even individuals themselves may not hold permanent points of view, but rather adopt different semantics depending on the particular 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 interpreting languages in the presence of semantic variability. We build on supervaluationist accounts of vagueness, which explain linguistic indeterminacy in terms of a collection of possible interpretations of the terms of the language (precisifications). This is extended by adding the notion of standpoint, 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 compatible 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 consideration of the relevant notions of truth and validity, a multi-modal logic language for describing standpoints is presented. The language includes a modal operator for each standpoint, such that \standb{s}\phi means that a proposition $\phi$ is unequivocally true according to the standpoint $s$ --- i.e.\ $\phi$ is true at all precisifications compatible with $s$. We provide the logic with a Kripke semantics and examine the characteristics of its intended models. 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 variability 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 ostensibly linked to ontologies, may present substantial semantic variation, which obstructs interoperability and confounds knowledge exchange