Aspect in Ancient Greek - Nijmegen Centre for Semantics

Appendix AThe language of CompositionalDRTA.1 IntroductionIn this appendix I explicate the model, syntax, and semantics of the languagethat underlies the analyses in this thesis. The language combines the lambdasof Montague Semantics with the DRSs of DRT. Several such systems have beenproposed in the literature, for example the λ-DRT of Pinkal and Bos (Lateckiand Pinkal 1990, Bos et al. 1994, Blackburn and Bos 2006), Asher’s (1993)bottom-up DRT and Muskens’ (1996) Compositional DRT (CDRT). I followMuskens’ system which provides a semantics for its language, is mathematicallyclean, easy to use in practice, and accessible.The formalism used in CDRT is that of classical type logic. Muskens (1996)shows that, if we adopt certain first-order axioms, DRSs are already presentin this logic in the sense that they can be viewed as abbreviations of certainfirst-order terms. Thus, we can have lambdas and DRSs in one and the samelogic. Moreover, the merge operator of DRT is definable in type logic as well,which means type logic provides everything needed to mimic DRT.To show that DRSs are part of type logic Muskens starts from the idea thatthe meaning of a DRS can be viewed as a binary relation between input andoutput assignments (or, in DRT terminology, embeddings). 1 Assignments arefunctions from the set of variables (or, in DRT terminology, discourse markers)to the domain. A DRS K is a pair of a set of variables x 1 , . . .,x n (the universeof K) and a set of conditions γ 1 , . . .,γ 2 . The meaning of a DRS K is theset of pairs of assignments 〈f, f ′ 〉 such that f ′ differs from f at most in thevariables in the universe of K (we write this as f⌊x 1 , . . ., x n ⌋f ′ ) and f ′ makes1 Muskens (1996) follows the Groenendijk and Stokhof semantics of DRT. Van Leusen enMuskens (2003) show that the same can be done starting from the Zeevat (1989) semanticsof DRT which remains closer to the original formulation of DRT. Here I follow the former.