Unity and Unification in Intensional Semantics

自然语言预设了丰富的语义本体论：为了解释“每个男孩都钦佩玛丽”这句话，我们假设存在个体（例如玛丽）、命题（每个男孩都钦佩玛丽）、个体的属性（作为男孩）、个体之间的关系（钦佩）和其他类型的对象。自然语言语义的形式模型（特别是Montague 1970a； 1973）通过只假设少量的原始对象，并通过这些原始对象的构造获得所有其他对象，从而驯服了这个对象动物园。通过这种方式，蒙塔古（1970a）将英语基本片段的指称物简化为由三种类型的原语构成的结构：个体、可能世界和真值。然而，在过去的三十年里，试图修改和扩展蒙塔古的模型已经引入了大量的模型，这些模型假设了大不相同的原语集。结果，原始物体的动物园被模型的动物园所取代。该项目旨在统一自然语言语义的不同模型。特别是，它旨在识别这些模型在选择原语方面的共性，揭示不同原语之间的编码关系，并使用这些关系来识别模型之间的缩减。这些约简实现了不同语义模型的统一。我期望这些缩减将进一步深入了解对特定语言现象的最小模型的要求，并将有助于更好地理解语言类型系统。除了一些孤立的裁减外，从未作出这种努力。然而，只有这种努力才允许我们将一个模型的解释成功转移到其他模型。为了确保这个项目在提议的时间框架内的可行性，我将重点关注一类特定的模型（称为“内涵模型”），其成员解释（Montague 1973）中的标准英语片段。这个片段包含命题态度动词(例如：‘believe’)、语气名词（‘temperature‘）和不及物动词（’rise’）。这个片段的不同模型将个体、个体概念、世界、情境、命题和真值集合的某个子集作为它们的原语。为了统一这些模型，我将把形式语义学和类型理论的技术与比较本体分析的方法结合起来。为了显示内蕴模型约简对的可能性，我证明了约简模型中的原始对象可以被编码为约简模型中的对象。早期形式语义的结果和我自己的相关工作都支持为此目的使用编码。这些结果进一步表明，“统一”模型实际上是一类模型，其成员直到编码都是等效的。这些模型在选择原语方面的稳健性解释了大量内涵模型的出现。

Natural languages presuppose a rich semantic ontology: To interpret the sentence 'Every boy admires Mary', we assume the existence of individuals (e.g. Mary), propositions (Every boy admires Mary), properties of individuals (being a boy), relations between individuals (admire), and other types of objects. Formal models for natural language semantics (esp. Montague 1970a; 1973) tame this zoo of objects by assuming only a small number of primitive objects and obtaining all other objects via constructions out of these primitives. In this way, Montague (1970a) reduces the referents of a basic fragment of English to constructions out of three types of primitives: individuals, possible worlds, and truth-values. However, in the last thirty years, attempts at revising and extending Montague's model have introduced a plethora of models which assume greatly varying sets of primitives. As a result, the zoo of primitive objects has been traded for a zoo of models.This project seeks to unify the different models for natural language semantics. In particular, it aims to identify the commonalities of these models with respect to their choice of primitives, disclose coding relations between the different primitives, and use these relations to identify reductions between models. These reductions achieve a unification of the different semantic models. I expect that the reductions will further yield insights into the requirements on minimal models of a given linguistic phenomenon and that they will contribute to a better understanding of the linguistic type system. Apart from some isolated reductions, such an effort has never been undertaken. However, only this effort allows us to transfer the interpretive success of one model to other models.To ensure the feasibility of this project in the proposed time frame, I will focus on one particular class of models (called 'intensional models') whose members interpret the standard fragment of English from (Montague 1973). This fragment contains propositional attitude verbs (e.g. 'believe') and intensional nouns ('temperature') and intransitive verbs ('rise'). Different models of this fragment assume as their primitives some subset of the set of individuals, individual concepts, worlds, situations, propositions, and truth-values.To unify these models, I will combine techniques from formal semantics and type theory with methods for comparative ontology analysis. To show the possibility of reducing pairs of intensional models, I demonstrate that primitive objects in the reduced model can be coded as objects in the reducing model. The use of coding for this purpose is supported by earlier results in formal semantics and by my own related work. These results further suggest that 'the' unifying model is, in fact, a class of models whose members are equivalent up to coding. The robustness of these models with respect to their choice of primitives explains the emergence of the large number of intensional models.