The effect of negative polarity items on inference verification

The scalar approach to negative polarity item (NPI) licensing assumes that NPIs are allowable in contexts in which the introduction of the NPI leads to proposition strengthening (e.g., Kadmon & Landman 1993, Krifka 1995, Lahiri 1997, Chierchia 2006). A straightforward processing prediction from such a theory is that NPI’s facilitate inference verification from sets to subsets. Three experiments are reported that test this proposal. In each experiment, participants evaluated whether inferences from sets to subsets were valid. Crucially, we manipulated whether the premises contained an NPI. In Experiment 1, participants completed a metalinguistic reasoning task, and Experiments 2 and 3 tested reading times using a self-paced reading task. Contrary to expectations, no facilitation was observed when the NPI was present in the premise compared to when it was absent. In fact, the NPI significantly slowed down reading times in the inference region. Our results therefore favor those scalar theories that predict that the NPI is costly to process (Chierchia 2006), or other, nonscalar theories (Giannakidou 1998, Ladusaw 1992, Postal 2005, Szabolcsi 2004) that likewise predict NPI processing cost but, unlike Chierchia (2006), expect the magnitude of the processing cost to vary with the actual pragmatics of the NPI

The acquisition of basque and spanish quantifiers: an empirical study.

300 p.Tesi honek zenbatzaileen jabekuntza eta garapena ikertzen du 4-9 urte bitarteko haur euskaldun eta gaztelaniadunekin, eta helduen interpretazioak ere ditu ikergai, kontrol moduan. Lan honek bi helburu nagusi ditu: (i) zenbatzaileekin eratorritako eskala inplikaturak aztertu, ikuspuntu semantiko-pragmatiko batetik; eta (ii) zenbatzaile unibertsal eta ezeztapenaren arteko interakzioa ikertu, analisi sintaktiko batean oinarrituz. Zenbatzaileen jabekuntza goiztiarraren literaturak (Katsos et al. 2016; a.o.) haurrek zenbatzaileen ezaugarri semantikoak era gradual batean jabetzen dituztela erakusten du. Gainera, 5 urteko haurrek egia-balioen ez-betetzea antzematen duten arren (semantikoki zuzenak eta okerrak diren esaldiak), zailtasunak dituzte azpi-informatiboak (pragmatikoki desegokiak) diren esaldiak errefusatu eta beharrezko eskala inplikatura eratortzeko (Grice 1985). Bestalde, zenbatzaile unibertsal eta ezeztapenaren arteko interakzioan oinarritutako lanek ikusi dute (Musolino 1998; Musolino et al. 2000; a.o.) 5-6 urte bitarteko haurrek esaldien estruktura sintaktikoa ardatz hartzen dutela irakurketa semantikoa eratortzeko (¿Observation of Isomorphism¿). Aurreko literatura eta Euskal Herriko egoera soziolinguistikoa kontuan hartuz, bi ikerketa esperimental burutu dira 384 partehartzaileekin: (i) lehen hizkuntzen jabekuntzari buruzkoa eta (ii) elebitasunari buruzkoa

Reasoning with Polarity in Categorial Type Logic

The research presented in this thesis follows the parsing as deduction approach to lin- guistics. We use the tools of Categorial Type Logic (CTL) to study the interface of natural language syntax and semantics. Our aim is to investigate the mathematical structure of CTL and explore the possibilities it offers for analyzing natural language structures and their interpretation. The thesis is divided into three parts. Each of them has an introductory chapter. In Chapter 1, we introduce the background assumptions of the categorial approach in linguistics, and we sketch the developments that have led to the introduction of CTL. We discuss the motivation for using logical methods in linguistic analysis. In Chapter 3, we propose our view on the use of unary modalities as `logical features'. In Chapter 5, we set up a general notion of grammatical composition taking into account the form and the meaning dimensions of linguistic expressions. We develop a logical theory of licensing and antilicensing relations that cross-cuts the form and meaning dimensions. Throughout the thesis we focus attention on polarity. This term refers both to the polarity of the logical operators of CTL and to the polarity items one finds in natural language, which, furthermore, are closely connected to natural reasoning. Therefore, the title of this thesis Reasoning with Polarity in Categorial Type Logic is intended to express three meanings. Firstly, we reason with the polarity of the logical operators of CTL and study their derivability patterns. In Chapter 2, we explore the algebraic principles that govern the behavior of the type-forming operations of the Lambek calculus. We extend the categorial vocabulary with downward entailing unary operations obtaining the full tool- kit that we use in the rest of the thesis. We employ unary operators to encode and compute monotonicity information (Chapter 4), to account for the different ways of scope taking of generalized quantifiers (Chapter 6), and to model licensing and antilicensing relations (Chapter 7). Secondly, in Chapter 4, we model natural reasoning inferences drawn from structures suitable for negative polarity item occurrences. In particular, we describe a system of inference based on CTL. By decorating functional types with unary operators we encode the semantic distinction between upward and downward monotone functions. Moreover, we study the advantages of this encoding by exploring the contribution of v monotone functions to the study of natural reasoning and to the analysis of the syntactic distribution of negative polarity items. Thirdly, in Chapter 7, we study the distribution of polarity-sensitive expressions. We show how our theory of licensing and antilicensing relations successfully differentiates between negative polarity items, which are `attracted' by their triggers, and positive polarity items, which are `repelled' by them. We investigate these compatibility and incompatibility relations from a cross-linguistic perspective, and show how we reduce distributional differences between polarity-sensitive items in Dutch, Greek and Italian to differences in the lexical type assignments of these languages

Modus Ponens and the Logic of Decision

If modus ponens is valid, then you should take up smoking

Stratified least fixpoint logic

Stratified least fixpoint logic, or SLFP, characterizes the expressibility of stratified logic programs and, in a different formulation, has been used as a logic of imperative programs. These two formulations of SLFP are proved to be equivalent. A complete sequent calculus with one infinitary rule is given for SLFP. It is argued that SLFP is the most appropriate assertion language for program verification. In particular, it is shown that traditional approaches using first-order logic as an assertion language only restrict to interpretations where first-order logic has the same expressibility as SLFP.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31383/1/0000296.pd