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Default inheritance reasoning is a propositional approach to non monotonic reasoning designed to model reasoning with natural language generics. Inheritance reasoners model sets of natural language generics as directed acyclicgraphs,and inference corresponds to the specification of paths through those networks. A proliferation of inheritance proof theories exist in the literature along with extensive debate about the most reasonable way to construct inferences, based on intuitions about interpretations of particular inheritance networks. There has not been an accepted semantics for inheritance which unifies the set of possible proof theories, which would help identify truly ill motivated proof theories. This thesis attempts to clarify the inheritance literature in the three ways indicated in the title: psychological plausibility, proof theory and semantics.

Grammatical relations have always constituted a primary focus of attention in the study of language. Within the last three decades, the topicality of this trend has increasingly been determined by the quest for a universal characterization of the language faculty which has shaped the goals and directives of most current works in theoretical linguistics. Although the realization patterns and syntactic functionality of grammatical relations are subject to cross-linguistic variation, studies in comparative grammar have provided suggestive evidence that the range of variation found can often be contained within the limits fixed by a discrete set of parameters. The investigation of these parameters has broached the possibility of a universal specification of the nature of grammatical relations. This thesis proposes that such a specification should be achieved by establishing regularities in the syntax-semantics interface within a constraint-based approach to linguistic analysis that integrates a precise computational interpretation. In keeping with this objective, a unification-based categorial grammar framework is developed which incorporates the semantic insights of a Neo-Davidsonian approach to verb semantics and predicate-argument combination, where thematic roles are defined as clusters of entailments of verb meanings. This framework is extended with an integrated approach to argument selection and selection change. Properties of the resulting system are demonstrated with respect to a variety of natural language phenomena concerning grammatical function changing, unaccusativity and clitic dislocation.

Refactoring is an important Software Engineering technique for improving the structure of a program after it has been written. Refactorings improve the maintainability, readability, and design of a program without affecting its external behaviour. In analogy, this thesis introduces proof refactoring to make structured, semantics preserving changes to the proof documents constructed by interactive theorem provers as part of a formal proof development. In order to formally study proof refactoring, the first part of this thesis constructs a proof language framework, Hiscript. The Hiscript framework consists of a procedural tactic language, a declarative proof language, and a modular theory language. Each level of this framework is equipped with a formal semantics based on a hierarchical notion of proof trees. Furthermore, this framework is generic as it does not prescribe an underlying logical kernel. This part contributes an investigation of semantics for formal proof documents, which is proved to construct valid proofs. Moreover, in analogy with type-checking, static well-formedness checks of proof documents are separated from evaluation of the proof. Furthermore, a subset of the SSReflect language for Coq, called eSSence, is also encoded using hierarchical proofs. Both Hiscript and eSSence are shown to have language elements with a natural hierarchical representation. In the second part, proof refactoring is put on a formal footing with a definition using the Hiscript framework. Over thirty refactorings are formally specified and proved to preserve the semantics in a precise way for the Hiscript language, including traditional structural refactorings, such as rename item, and proof specific refactorings such as backwards proof to forwards proof and declarative to procedural. Finally, a concrete, generic refactoring framework, called Polar, is introduced. Polar is based on graph rewriting and has been implemented with over ten refactorings and for two proof languages, including Hiscript. Finally, the third part concludes with some wishes for the future.

The meanings of natural language sentences may be represented as compositional logical-forms. Each word or lexicalised multiword-element has an associated logicalform representing its meaning. Full sentential logical-forms are then composed from these word logical-forms via a syntactic parse of the sentence. This thesis develops two computational systems that learn both the word-meanings and parsing model required to map sentences onto logical-forms from an example corpus of (sentence, logical-form) pairs. One of these systems is designed to provide a general purpose method of inducing semantic parsers for multiple languages and logical meaning representations. Semantic parsers map sentences onto logical representations of their meanings and may form an important part of any computational task that needs to interpret the meanings of sentences. The other system is designed to model the way in which a child learns the semantics and syntax of their first language. Here, logical-forms are used to represent the potentially ambiguous context in which childdirected utterances are spoken and a psycholinguistically plausible training algorithm learns a probabilistic grammar that describes the target language. This computational modelling task is important as it can provide evidence for or against competing theories of how children learn their first language. Both of the systems presented here are based upon two working hypotheses. First, that the correct parse of any sentence in any language is contained in a set of possible parses defined in terms of the sentence itself, the sentence’s logical-form and a small set of combinatory rule schemata. The second working hypothesis is that, given a corpus of (sentence, logical-form) pairs that each support a large number of possible parses according to the schemata mentioned above, it is possible to learn a probabilistic parsing model that accurately describes the target language. The algorithm for semantic parser induction learns Combinatory Categorial Grammar (CCG) lexicons and discriminative probabilistic parsing models from corpora of (sentence, logical-form) pairs. This system is shown to achieve at or near state of the art performance across multiple languages, logical meaning representations and domains. As the approach is not tied to any single natural or logical language, this system represents an important step towards widely applicable black-box methods for semantic parser induction. This thesis also develops an efficient representation of the CCG lexicon that separately stores language specific syntactic regularities and domain specific semantic knowledge. This factorised lexical representation improves the performance of CCG based semantic parsers in sparse domains and also provides a potential basis for lexical expansion and domain adaptation for semantic parsers. The algorithm for modelling child language acquisition learns a generative probabilistic model of CCG parses from sentences paired with a context set of potential logical-forms containing one correct entry and a number of distractors. The online learning algorithm used is intended to be psycholinguistically plausible and to assume as little information specific to the task of language learning as is possible. It is shown that this algorithm learns an accurate parsing model despite making very few initial assumptions. It is also shown that the manner in which both word-meanings and syntactic rules are learnt is in accordance with observations of both of these learning tasks in children, supporting a theory of language acquisition that builds upon the two working hypotheses stated above.

This thesis by publication presents a study on English adpositions (e.g. to, in, at, from, in frontof, through). It attempts to offer a solution to the following three outstanding problems, whichare presented in each of the three parts making up the thesis, preceded by a general introduction(chapter 1) and followed by the general conclusions (chapter 7). The first part includes chapter2, and discusses the problem of What is the relation between adpositions and the non-linguistic,visual content they represent. The second part includes chapters 3 and 4, and discusses theproblem ofwhat is a proper compositional theory of the Syntax and Semantics of adpositions.The third part includes chapters 5 and 6, and discusses the problem of what is the psychologicalreality of this theory, regarding adults and children’s data.The following three solutions are suggested. First, the relation between adpositions and theircorresponding visual information is an isomorphism: adpositions capture how we “see” possiblespatio-temporal relations between objects, at a flexible level of fine-grainedness. Second, aproper compositional treatment of adpositions treats each syntactic unit (in front, of ) as offeringa distinct semantic contribution, hence spelling out a restricted instance of a spatio-temporalpart-of relation. Third, this compositional treatment of adpositions can also stand as a theory ofon-line interpretation in adults and a theory of their acquisition in children.These three answers are couched within a single theoretical approach, that of Discourse Representation Theory, and offer a unified solution to three apparently distinct problems regardingspatial adpositions and their linguistic properties.

In the field of robotics, there has recently been tremendous progress in the development of autonomous robots that offer various services to their users. Most of the systems developed so far, however, are restricted to indoor scenarios, non-urban outdoor environments, or road usage with cars. There is a serious lack of capabilities of mobile robots to navigate safely in highly populated outdoor environments. This ability, however, is a key competence for a series of robotic applications. We consider the task of developing a spatially motivated dialogue system that can operate on a robotic platform, where the purpose of such a robot is to aid pedestrians in urban environments to provide information about surrounding objects and services, and guide users to desired destinations. In this thesis, we make a number of contributions to the fields of spatial language interpretation/generation and discourse modelling. This includes the development of a dialogue framework called HURDLE which builds on the strengths of existing systems, accompanied by a specific implementation for spatially oriented dialogue including disambiguating amongst objects and locations in the environment, and a natural language parser which combines an extension of Synchronous Context Free Grammars with a Part-of-Speech tagger. Our research also presents a number of probabilistic models for spatial prepositions such as `in front of' and `between' that make significant advances in effectively utilising geometric environment data, encompassing visibility considerations and being reusable for both indoor and outdoor environments. We also present a number of algorithms in which these models can be utilised, most significantly a novel and highly effective algorithm that can generate natural language descriptions of objects that disambiguates on their location. All these components, while modular, operate in tandem and interact with a variety of external components (such as path planning) on the robot platform.

In this thesis, Semantics, Meta-Semantics, and Ontology, I provide a critique of the method of truth in metaphysics. Davidson has suggested that we can determine the metaphysical nature and structure of reality through semantic investigations. By contrast, I argue that it is not semantics, but meta-semantics, which reveals the metaphysically necessary and sufficient truth conditions of our claims. As a consequence I reject the Quinean (semantic) criterion of ontological commitment. In Part I, chapter 1, I argue that the metaphysically primary truth bearers are not propositions, but rather concrete representations, either beliefs or sentences. I show, in chapter 2, that we can give sense to a truth predicate applying to sentences, given a truth operator and quantification into sentence position. I argue that this strategy does not commit us to the existence of propositions serving as truth bearers. In Part II I argue that although we must assign semantic values to sentences and/or predicates, the meaningfulness of these expressions is not thereby explained. In chapter 3 I articulate Davidson’s problem of predication and his solution, but argue that he was wrong to attribute this solution to Tarski. In chapter 4 I examine the semantics of modal languages; I conclude that although they require semantic values for predicates and/or sentences we should be instrumentalists about these theories. In Part III I consider the relationship between truth and existence. In chapter 5, I defend Pluralism about truth: in some (though not all) domains of discourse, I claim, semantic reference plays a merely instrumental role in explaining truth. In chapter 6, I show that Hume’s Principle, which is committed by the Quinean criterion to the existence of numbers, can be true even though numbers do not exist. In doing so, I appeal to meta-semantic and diachronic considerations. In the conclusion I compare my views on ontology and commitment to Jody Azzouni’s; and in the appendix I suggest how one might pursue diachronic linguistics.

This thesis presents a computational text analysis tool called AFFECTiS (Affect Interpretation/Inference System) which focuses on the task of interpreting natural language text based on its subjective, non-factual, affective properties that go beyond the 'traditional' factual, objective dimensions of meaning that have so far been the main focus of Natural Language Processing and Computational Linguistics. The thesis presents a fully compositional uniform wide-coverage computational model of sentiment in text that builds on a number of fundamental compositional sentiment phenomena and processes discovered by detailed linguistic analysis of the behaviour of sentiment across key syntactic constructions in English. Driven by the Principle of Semantic Compositionality, the proposed model breaks sentiment interpretation down into strictly binary combinatory steps each of which explains the polarity of a given sentiment expression as a function of the properties of the sentiment carriers contained in it and the grammatical and semantic context(s) involved. An initial implementation of the proposed compositional sentiment model is de- scribed which attempts direct logical sentiment reasoning rather than basing compu- tational sentiment judgements on indirect data-driven evidence. Together with deep grammatical analysis and large hand-written sentiment lexica, the model is applied recursively to assign sentiment to all (sub )sentential structural constituents and to concurrently equip all individual entity mentions with gradient sentiment scores. The system was evaluated on an extensive multi-level and multi-task evaluation framework encompassing over 119,000 test cases from which detailed empirical ex- perimental evidence is drawn. The results across entity-, phrase-, sentence-, word-, and document-level data sets demonstrate that AFFECTiS is capable of human-like sentiment reasoning and can interpret sentiment in a way that is not only coherent syntactically but also defensible logically - even in the presence of the many am- biguous extralinguistic, paralogical, and mixed sentiment anomalies that so tellingly characterise the challenges involved in non-factual classification.

This thesis examines Romans 9:30-10:13 with a concentration on Paul's citations of the Old Testament. A critical review of the theory of intertextuality, including a critique of its application by Richard Hays, begins an adaptation of the theory for a methodology which is labelled herein as Intertextual Semantics. Intertextual Semantics describes the meaning of the text through its points of continuity between itself and its source, but also its discontinuity and the processes which have contributed to their lexical, syntactical, discursive, rhetorical, and cultural differences. Transformative factors may be evident from a synchronic perspective, but when considering Paul’s historical position in relation to Judaism and Israelite religion, a diachronic perspective is also valuable. The thesis devotes considerable space to the history of the texts which Paul quotes in Romans 9:30-10:13. It contributes new readings of Isaiah 28:16, Leviticus 18:5, and Deuteronomy 30:12-14 in their respective literary and historical contexts. From such 'original' contexts to other allusions or quotations in the Old Testament or in non-canonical Second Temple Jewish literature or in other New Testament writings, these intertexts are followed and described as part of this diachronic analysis. Disrupting or colliding with the continuity of meaning across changes of time, languages, and cultures are the exigencies facing each new generation. In the synchronic analysis, and in response to the relative neglect that Romans 10 suffers in relation to chs. 9 and 11, this study demonstrates that concerted attention to Romans 10 pays dividends for inquiries into the coherence, purpose, and function of chs.9-11 as well as for important topics such as Paul's conception of his own ministry, comparisons of Pauline religion with historical Israelite religion, and rhetoric in this letter.