Aspect in Ancient Greek - Nijmegen Centre for Semantics

A.1 Introduction 179(202)u 1 . . .u nγ 1. . .γ m⊕u ′ 1 . . .u′ kδ 1. . .δ qM,f=u 1 . . .u n u ′ 1 . . .u′ kγ 1. . .γ mδ 1. . .if u ′ 1, ..., u ′ k do not occur in any of γ 1 , ..., γ m .δ qM,fIn what follows I will give a formal description of the language used in thisthesis, starting with a specification of its types (A.2). For my purposes, I addtwo more types to Muskens’ (1996) inventory: b for eventualities and a formoments of time. Then in section A.3 I specify the models of the language,in particular the structure of the domains of eventualities and times. This isfollowed by the syntax and semantics of the language in sections A.4 and A.5,respectively. We will see that although in the main text I have been speakingabout e, e ′ , e 1 ... as variables over eventualities, they are actually names ofvariable registers for eventualities. In the same way are t, t ′ , t 1 ... names ofvariable registers for times rather than variables over times. Our familiar P’sand Q’s which I have treated as variables over predicates over eventualities andtimes, respectively, will be shown to also have a more complicated type. Anoverview of my conventions is given in Table A.1 on page 183. Section A.6 givesthe axioms that ensure that states and variable registers behave as assignmentsand variables, and those that guarantee that constant registers have a fixedinhabitant. Section A.7 specifies how DRSs can be viewed as abbreviationsof type-logical expressions. Section A.8 gives the truth preserving syntacticoperations of lambda conversion and renaming of bound variables. In sectionA.9 I work out one example.In this appendix I deviate from the main text of this thesis by taking τ tobe a two-place predicate rather than a function. I do this to avoid unnecessarycomplications with function constants. Because I require functionality for thispredicate (AX5), τ nevertheless still behaves like a function.A few preliminary remarks concerning the typography: as before, I use atypewriter font for expressions in the formal object language, Greek letters asmeta-variables over object-language expressions, 2 calligraphic and italic symbolsto denote set-theoretic entities and boldface symbols to denote types.2 Sometimes, however, I sloppily use the typewritter font for expressions in the metalanguage.Compare, for example, u and δ in (202).