Unity and Unification in Intensional Semantics

自然语言以丰富的语义本体论为前提：为了解释“每个男孩都崇拜玛丽”这句话，我们假设了个体(例如玛丽)、命题(每个男孩都崇拜玛丽)、个体的属性(作为一个男孩)、个体之间的关系(崇拜)和其他类型的物体的存在。自然语言语义的形式化模型(特别是蒙塔古1970a；1973年)驯服了这个对象动物园，只假设了一小部分原始对象，并通过这些原始对象的构造获得了所有其他对象。通过这种方式，蒙塔古(1970a)将英语的一个基本片段的指称简化为由三种原语组成的结构：个人、可能世界和真值。然而，在过去的三十年里，修改和扩展蒙太古模型的尝试引入了过多的模型，这些模型假设了非常不同的基元集合。因此，原始对象的动物园已经被交易成了模型的动物园。这个项目试图统一自然语言语义的不同模型。特别是，它的目的是识别这些模型关于其基元选择的共性，揭示不同基元之间的编码关系，并使用这些关系来识别模型之间的约简。这些简化实现了不同语义模型的统一。我预计，这些削减将进一步深入了解对特定语言现象的最小模式的要求，并将有助于更好地理解语言类型系统。除了一些个别的削减外，从来没有进行过这样的努力。然而，只有这样的努力才能使我们将一个模型的解释成功转移到其他模型上。为了确保这个项目在建议的时间框架内的可行性，我将专注于一类特定的模型(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(如‘Believe’)、内涵名词(‘温度’)和不及物动词(‘Rise’)。这个片段的不同模型假设个体、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，我将形式语义学和类型理论的技术与比较本体论的方法相结合。为了说明减少内涵模型对的可能性，我演示了简化模型中的原始对象可以被编码为简化模型中的对象。形式语义学的早期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成员相当于编码的模型。这些模型相对于其原语选择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.