The theory of the Theta System (Reinhart 2000 (Reinhart , 2002 gives a compositional account of verbal argument structure and argument structure alternations. Although it makes concrete predictions with respect to argument projection and syntax, Reinhart has not provided a definition of the semantics, and semantic operations, associated with the system's primitive elements and operators. In this paper I provide a semantic implementation of the system's components, based on a straightforward

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... dding of the Theta System in the "event semantics" of Davidson (1967 ), Parsons (1990 . While it has not been my intent to extend or "explain" the theta system, the design proposed in these pages turns out to have empirical consequences; these are explored in section 5. The Theta System does not consider the order of thematic arguments to be specified in the lexical entry; it is determined after the operation of lexical marking and argument-structure operations, according to the CS merging instructions. But syntactic constituency as well as lambda formulas involve argument positions that must be saturated in a particular order. In order to end up with the usual kind of semantic object, a function expressible as a formula of lambda calculus, there must be a change in representation at some point between the lexical entry and the interpretation of the sentence at the LF interface. Before the change-over, which I will refer to as translation, argument structure information is represented as a complex structure which we are at liberty to define as it suits us; afterwards, we must deal exclusively with the entities standardly employed by current theories of grammar: formulas of intensional logic for the semantics, and syntactic features for the syntax. I will show that translation takes place after the application of lexical-component arity operations, but before syntactic operations; it is simplest to locate it just before insertion of lexical items in the numeration. This architecture, adopted as a natural solution to the practical problem of designing a semantics of the theta system, turns out to have desirable empirical consequences: It accounts, in a natural way, for certain well-known distributional asymmetries of arity operations. In particular, the theta system recognizes two domains of application for arity operations: the lexicon and the (morpho)syntax. While some arity operations, such as reflexivization, take place in the lexicon in some languages and in the syntax in others, other arity operations are cross-linguistically restricted to the lexicon. A number of known differences between the lexicon and the syntax can be brought to bear on the question of why some operations can apply in either domain while others cannot, but until now there has been no comprehensive explanation. In formalizing both types of arity operations within the semantic framework I will propose below, it turns out that the arity operations that can apply in the syntax are exactly those that can be expressed as basic operations on logical formulas: Namely, an operator on formulas can existentially close off a role or identify two roles; but it cannot simply delete the first (or n-th) theta role (which would be tantamount to deleting one of the conjuncts of a logical formula), nor replace it with another. On the other hand, any of This work was inspired by Tanya Reinhart's seminars on the Theta System in 2001 and 2002. I am grateful to Tanya Reinhart, Marijana Marelj, Tali Siloni, Maribel Romero, and Danny Fox for discussion, suggestions, questions, and answers that have contributed to the direction and substance of this work. This paper is a revision of a draft circulated in 2002. Earlier versions have been presented at the 26th GLOW Colloquium in Lund, Sweden, at the Brown University Workshop on Direct Compositionality (2003), and to audiences at the Utrecht institute of Linguistics. 1 these manipulations can be carried out in a suitably-structured system of our own design. Indeed, we find that operations that require existential closure of an argument position or identification of two argument positions (Saturation, Arbitrarization, Reflexivization) can occur in the syntax, while operations that require outright deletion of a theta role, or substitution of one thematic role for another (Reduction, Causativization) only occur in the lexicon. I will argue that this correlation explains the distribution of arity operations: an operation can take place in the syntax only if its effect can be stated as a general rule that manipulates the semantic encoding available during syntactic derivation. In the lexicon a different, more articulated encoding is used, which allows all of the arity operations to take place. While it could be argued in response that we are dealing simply with accidental consequences of an arbitrary system, the encoding I have assumed for the syntactic component is simply the usual view of meanings as functions in some intensional calculus, expressible as lambda terms. Although any system can be elaborated in such a way that it allows arbitrary transformations on its objects, the natural (and standard) way to encode the semantics of verbs simply does not provide enough structure to allow certain manipulations. Since these manipulations are exactly the ones that are unattested in the syntactic component, their distribution confirms the view that the expressive power of the standard semantic framework is approximately right for a semantics of natural language. The paper is organized as follows: In the next section, I provide an overview of the theory of the theta system and some of its more relevant properties. Section 3 discusses the embedding of event semantics in the framework of the theta system, and defends the conclusion that there is a change in representation between the lexicon and eventual semantic interpretation. Section 4 presents an explicit derivational model for the operations of the theta system. Finally, section 5 takes up the issue of the lexicon-syntax division, and the expression of the various arity operations in each component.