Adjectival and Adverbial Modification: The View from Modern Type Theories

In this paper we present a study of adjectival/adverbial modification using modern type theories (MTTs), i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented (e.g. in proof-assistants) given their proof-theoretic nature. In MTT-semantics, common nouns are interpreted as types rather than predicates. Therefore, in order to capture the semantics of adjectives adequately, one needs to meet the challenge of modeling CNs modified by adjectives as types. To explicate that this can be done successfully, we first look at the mainstream classification of adjectives, i.e. intersective, subsective and non-subsective adjectives. There, we show that the rich type structure available in MTTs, along with a suitable subtyping framework, offers an adequate mechanism to model these cases. In particular, this modelling naturally takes care of the characterising inferences associated with each class of adjectives. Then, more advanced issues on adjectival modification are discussed: (a) degree adjectives, (b) comparatives and (c) multidimensional adjectives. There, it is shown that the use of indexed types can be usefully applied in order to deal with these cases. In the same vein, the issue of adverbial modification is discussed. We study two general typings for sentence and VP adverbs respectively. It is shown that the rich type structure in MTTs further provides useful organisational mechanisms in giving formal semantics for adverbs. In particular, we discuss the use of \(\varSigma \)-types to capture the veridicality/non-veridicality distinction and further discuss cases of intensional adverbs using the type theoretic notion of context (i.e. without resorting to intensional typing). We also look at manner, subject and speech act adverbials and propose solutions using MTTs. Finally, we show that the current proof technology can help mechanically check the associated inferences. A number of our proposals concerning adjectival and adverbial modification have been formalised in the proof assistant Coq and many of the associated inference patterns are checked to be correctly captured.     

Underspecification,Parsing Mismatches and Routinisation: The Historical Development of the Clitic Systems of Greek Dialects

In this paper, the historical development of the clitic systems of Standard Modern, Cypriot and Pontic Greek is discussed. These three varieties not only present the whole range of variation one can find across clitic systems in Greek but, furthermore, derive from a common linguistic ancestor, i.e. Koine Greek. This paper argues that the transition from Koine Greek to the Medieval varieties and from the Medieval varieties to the respective modern ones can be explained by making the assumption that routinisation (in the sense of Pickering and Garrod in Behav Brain Sci 27:169–226, 2004) and parsing/hearer assymetries are two important factors behind syntactic change. The claim is that the transition from Koine to the Medieval Greek varieties involves the emergence of a clitic system with encoded syntactic constraints out of a freer one, where clitic positioning was regulated by pragmatic preferences rather than syntactic constraints. Then, the transition to the modern varieties from the respective medieval ones is explained, at least partly, on the assumption that production/parsing mismatches are capable of triggering syntactic change. This last assumption combined with: (a) the tendency to obtain more generalised parsing triggers for parsing the individual clitics and (b) the fact that the Medieval varieties in question differ in minimal but crucial ways, provides us an explanation for the transition to the modern varieties.

     

Natural Language Inference in Coq

In this paper we propose a way to deal with natural language inference (NLI) by implementing Modern Type Theoretical Semantics in the proof assistant Coq. The paper is a first attempt to deal with NLI and natural language reasoning in general by using the proof assistant technology. Valid NLIs are treated as theorems and as such the adequacy of our account is tested by trying to prove them. We use Luo’s Modern Type Theory (MTT) with coercive subtyping as the formal language into which we translate natural language semantics, and we further implement these semantics in the Coq proof assistant. It is shown that the use of a MTT with an adequate subtyping mechanism can give us a number of promising results as regards NLI. Specifically, it is shown that a number of inference cases, i.e. quantifiers, adjectives, conjoined noun phrases and temporal reference among other things can be successfully dealt with. It is then shown, that even though Coq is an interactive and not an automated theorem prover, automation of all of the test examples is possible by introducing user-defined automated tactics. Lastly, the paper offers a number of innovative approaches to NL phenomena like adjectives, collective predication, comparatives and factive verbs among other things, contributing in this respect to the theoretical study of formal semantics using MTTs.