The paper presents a spatio-temporal ontology guided by a particular methodology, in which the semantics is constructed within a spatio-temporal interpretation structure that is built up in three stages. The first, stage stipulates a standard classical model of time and space. This structure forms the grounding for the interpretation. The next stage is the specification of domains of entities, which are either elements of the grounding structure (time points and regions) or constructions from these elements (mappings from time to space associated with individuals existing within the spatio-temporal structure). The final stage is the definition of conceptual vocabulary in terms of the grounding structure and the specified domains. This definitional stage can be further subdivided into three types of specification: direct grounding of primitives onto the underlying structure, indirect grounding by defining additional vocabulary in terms of grounded primitives, partial grounding by specifying semantics types and axioms to constrain the meaning of vocabulary that is not explicitly defined. The main goal of the paper is to advocate a methodology rather than a specific ontology. We suggest that building up in this way, results in robust ontologies, whose assumptions can be clearly seen, since they are encapsulated within the grounding stage and domain specifications. Although the definitional stage may incorporate a diverse and expressive vocabulary, its terms are essentially just labels for properties and relations that were already implicit within the grounding structure.

Standard first-order logic interprets reference, predication and quantification in terms of fixed denotations with respect to a domain of precise objects. We explore ways to generalise this semantics to account for variability of meaning due to factors such as vagueness, context and diversity of definitions or opinions. We present Variable Reference Logic (VRL), an elaboration of Standpoint Logic, which is a multi-modal logic based on a variety of Supervaluation Semantics. VRL can accommodate several modes of variability in relation to both predicates and objects. Its principal novelty is that its semantics incorporates a domain of indefinite individuals, whose precise properties (such as spatial extension) are not fully determinate. Each indefinite individual is associated with a set of precise entities corresponding to possible precise versions of the individual.

The Winograd Schema Challenge is a general test for Artificial Intelligence, based on problems of pronoun reference resolution. I investigate the semantics and interpretation of Winograd Schemas, concentrating on the original and most famous example. This study suggests that a rich ontology, detailed commonsense knowledge as well as special purpose inference mechanisms are all required to resolve just this one example. The analysis supports the view that a key factor in the interpretation and disambiguation of natural language is the preference for coherence. This preference guides the resolution of co-reference in relation to both explicitly mentioned entities and also implicit entities that are required to form an interpretation of what is being described. I suggest that assumed identity of implicit entities arises from the expectation of coherence and provides a key mechanism that underpins natural language understanding. I also argue that conceptual ontologies can play a decisive role not only in directly determining pronoun references but also in identifying implicit entities and implied relationships that bind together components of a sentence.

The Winograd Schema Challenge (WSC) is a commonsense reasoning task that requires background knowledge. In this paper, we contribute to tackling WSC in four ways. Firstly, we suggest a keyword method to define a restricted domain where distinctive high-level semantic patterns can be found. A thanking domain was defined by keywords, and the data set in this domain is used in our experiments. Secondly, we develop a high-level knowledge-based reasoning method using semantic roles which is based on the method of Sharma [Sharma, 2019]. Thirdly, we propose an ensemble method to combine knowledge-based reasoning and machine learning which shows the best performance in our experiments. As a machine learning method, we used Bidirectional Encoder Representations from Transformers (BERT) [Jacob Devlin et al., 2018; Vid Kocijan et al., 2019]. Lastly, in terms of evaluation, we suggest a "robust" accuracy measurement by modifying that of Trichelair et al. [Trichelair et al., 2018]. As with their switching method, we evaluate a model by considering its performance on trivial variants of each sentence in the test set.

In cognitive accounts of concept learning and representation three modelling approaches provide methods for assessing typicality: rulebased, prototype and exemplar models.The prototype and exemplar models both rely on calculating a weighted semantic distance to some central instance or instances.However, it is not often discussed how the central instance(s) or weights should be determined in practice.In this paper we explore how to automatically generate prototypes and typicality measures of concepts from data, introducing a prototype model and discussing and testing against various cognitive models.Following a previous pilot study, we build on the data collection methodology and have conducted a new experiment which provides a case study of spatial language for the current proposal.After providing a brief overview of cognitive accounts and computational models of spatial language, we introduce our data collection environment and study.Following this, we then introduce various models of typicality as well as our prototype model, before comparing them using the collected data and discussing the results.We conclude that our model provides significant improvement over the other given models and also discuss the improvements given by a novel inclusion of functional features in our model.

Abstract In this paper, we present a formalism for handling polysemy in spatial expressions based on supervaluation semantics called standpoint semantics for polysemy (SSP). The goal of this formalism is, given a prepositional phrase, to define its possible spatial interpretations. For this, we propose to characterize spatial prepositions by means of a triplet $\langle $image schema, semantic feature, spatial axis$\rangle $. The core of SSP is predicate grounding theories, which are formulas of a first-order language that define a spatial preposition through the semantic features of its trajector and landmark. Precisifications are also established, which are a set of formulae of a qualitative spatial reasoning formalism that aims to provide the spatial characterization of the trajector with respect to the landmark. In addition to the theoretical model, we also present results of a computational implementation of SSP for the preposition ‘in’.

Many papers have considered the problem of how to define forest. However, as we shall illustrate, while most definitions capture some important aspects of what it means to be a forest, they almost invariably omit or are very vague regarding other aspects. In the current paper we address this issue, firstly by providing a definitional framework based on spatial and physical properties, within which one can make explicit the implicit variability of the natural language forest concept in terms of explicit parameters. Our framework explicitly differentiates between the functions of classification, individuation and demarcation that comprise the interpretation of predicative terms. Whereas ontologies have traditionally concentrated predominantly on classification, we argue that in many cases (especially in the case of geographic concepts) criteria for individuation (i.e. establishing how many distinct individual objects of a given type exist) and demarcation (establishing the boundary of an object) require separate attention, involve their own particular definitional issues and are affected by vagueness in different ways. We also describe a prototype Prolog system that illustrates how our framework can be implemented.

This paper aims to lay a foundation for a systematic study of mechanisms for construction of definitions within a formal theory, by investigating operators for incremental construction of definitions of new relations from an existing set of primitives and previously defined relations. To illustrate our method, we apply it to two of the best known relation sets studied in KRR: Allen's Interval Algebra and Region Connection Calculus. We also show that systematic exploration of definitional possibilities can yield interesting insights into relation sets that were originally defined in a more ad hoc way, and opens the possibility for discovering new vocabulary for extending or refining existing calculi or for developing completely new calculi.

The paper explores problems in ontology construction that arise due to the complex mapping between language and meaning. A new methodology is proposed, which combines a definitional approach using formal logic, with corpus-based statistical analysis of the use of terminology in natural language text. Underlying the approach is a semantic theory in which the notion of sense cluster plays a central role. Rather than having a single precise definition, the referent of a conceptual term is taken to be a sense cluster, modelled by a probability distribution over a set of precise definitions. This style of semantic specification pays heed to insights into the nature of language coming from philosophers such as Wittgenstein and his followers; but it also provides a framework supporting rigorous formal ontology development, which is often regarded as incompatible with the view of language suggested by Wittgenstein (in his later works).

The paper examines the semantics of the terms ‘environment’ and ‘habitat’ and presents a semi-formalised ontological framework in which these concepts are related to the spatial and material structure of the world. Since habitats are essentially associated with lives and behaviour of animals and plants the framework incorporates an abstract model of an organism. This enables the spatial extensions of habitats to be characterised in terms of the possible ‘life trajectories’ of organisms constrained by the physical properties of a geographic region and by the biological requirements for their survival.

Many geographic terms, such as “river” and “lake”, are vague, with no clear boundaries of application. In particular, the spatial extent of such features is often vaguely carved out of a continuously varying observable domain. We present a means of defining vague terms using standpoint semantics, a refinement of the philosophical idea of supervaluation semantics. Such definitions can be grounded in actual data by geometric analysis and segmentation of the data set. The issues raised by this process with regard to the nature of boundaries and domains of logical quantification are discussed. We describe a prototype implementation of a system capable of segmenting attributed polygon data into geographically significant regions and evaluating queries involving vague geographic feature terms.

The deployment of learning resources on the web by different experts has resulted in the accessibility of multiple viewpoints about the same topics. In this work we assume that learning resources are underpinned by ontologies. Different formalizations of domains may result from different contexts, different use of terminology, incomplete knowledge or conflicting knowledge. We define the notion of cognitive learning context which describes the cognitive context of an agent who refers to multiple and possibly inconsistent ontologies to determine the truth of a proposition. In particular we describe the cognitive states of ambiguity and inconsistency resulting from incomplete and conflicting ontologies respectively. Conflicts between ontologies can be identified through the derivation of conflicting arguments about a particular point of view. Arguments can be used to detect inconsistencies between ontologies. They can also be used in a dialogue between a human learner and a software tutor in order to enable the learner to justify her views and detect inconsistencies between her beliefs and the tutor's own. Two types of arguments are discussed, namely: arguments inferred directly from taxonomic relations between concepts, and arguments about the necessary and jointly sufficient features that define concepts.

I present a logical language for describing spatial, temporal and material properties of the physical world. The formalism is ontologically well-founded in the sense that it is interpreted with respect to model structures that have a specific physical interpretation in terms of the distribution of matter in space and time.

Representation theorems for systems of regions have been of interest for some time, and various contexts have been used for this purpose: Mormann [17] has demonstrated the fruitfulness of the methods of continuous lattices to obtain a topological representation theorem for his formalisation of Whiteheadian ontological theory of space; similar results have been obtained by Roeper [20]. In this note, we prove a topological representation theorem for a connection based class of systems, using methods and tools from the theory of proximity spaces. The key novelty is a new proximity semantics for connection relations.

We examine a variety of representations for storing and reasoning about spatial information and distinguish between quantitative representations grounded in numerical coordinate systems and qualitative representations, based on a high-level conceptual vocabulary for the description of spatial situations. We suggest that qualitative languages, can add powerful functionality to spatial information systems, which have traditionally processed only quantitative data. Trade-offs between expressive power, computational tractability and 'naturalness' are considered for several qualitative formalisms. We explain how a significant class of topological relations can be described by a 1st-order language and how these can be encoded into 0-order intuitionistic logic to yield an effective reasoning algorithm. We discuss ways of combining qualitative and quantitative information within a coherent architecture and describe an implementation of a hybrid spatial information system, incorporating three types of spatial information: quantitative data-structures are employed in a database of polygonal regions; a qualitative relational language is used to express high-level queries; and intuitionistic propositional logic is used to compute the inferences needed to answer these queries.