There is a rich literature about the temporal conjunctions before/after, but at the time I gave the talk that underlies this paper I was not aware of any analysis of the temporal comparatives früher/später ‘earlier/later’, which may be used to express similar states of affairs, but are constructed differently.2 Recently I got acquainted with the del Prete’s thesis about It. prima/dopo, which analyses prima as a comparative and dopo as a preposition.3 This is the only paper known to me that (...) goes into the same direction as the following proposal. Del Prete’s analysis is very different from mine and I must leave the discussion of his theory to another occasion. The semantics of before/after is notoriously controversial and the semantics of the related adjectives is therefore interesting in itself. A study of the adjectives gains additional interest from the fact that they are entirely differently constructed: they are degree adjectives and have a comparative, an equative and a positive variant. I will study each of them. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

The grammatical constraints on anaphoric binding, known as binding principles, are observed to form a classical square of oppositions. These constraints are then analysed as the effect of phase quantifiers over reference markers in grammatical obliqueness hierarchies, and the resulting phase quantifiers are shown to be organised in a square of logical duality. The impact of this result on the distinction between quantificational and referential nominals as well as on the logical foundations of the semantics of nominals in general is (...) discussed. (shrink)

This paper provides a formal semantic analysis of past interpretation in Medumba, a graded tense language. Based on original fieldwork, the study explores the empirical behavior and meaning contribution of graded past morphemes in Medumba and relates these to the account of the phenomenon proposed in Cable for Gĩkũyũ. Investigation reveals that the behavior of Medumba gradedness markers differs from that of their Gĩkũyũ counterparts in meaningful ways and, more broadly, discourages an analysis as presuppositional eventuality or reference time modifiers. (...) Instead, the Medumba markers are most appropriately analyzed as quantificational tenses. It also turns out that Medumba, though belonging to the typological class of graded tense languages, shows intriguing similarities to genuinely tenseless languages in allowing for temporally unmarked sentences and exploiting aspectual and pragmatic cues for reference time resolution. The more general cross-linguistic implication of the study is that the set of languages often subsumed under the label “graded tense” does not in fact form a natural class and that more case-by-case research is needed to refine this category. (shrink)

Aspectual particles (the term is due to (König 1991)) appear to come in groups, related by negation, and therefore have attracted the attention of formal semanticists. The following examples list the particles of English, German and Hebrew; they show that the system is semantically transparent in various degrees.

This discussion explores the possibility of distinguishing a tighter notion of contrariety evident in the Square of Opposition, especially in its modal incarnations, than as that binary relation holding statements that cannot both be true, with or without the added rider ‘though can both be false’. More than one theorist has voiced the intuition that the paradigmatic contraries of the traditional Square are related in some such tighter way—involving the specific role played by negation in contrasting them—that distinguishes them from (...) other pairs of incompatible statements constructed from the same conceptual materials. Prominent among examples, these other nonstandard pairs are the ‘new contraries’ presented by Robert Blanché’s hexagon(s) of opposition. With special, though not exclusive, attention to these cases, we investigate whether contrariety in the distinguished sense can be captured by adding to the incompatibility condition the further demand that the pair of statements concerned can be represented as the results of applying some sentence operator to the content in its scope, for one of the pair, and, for the other, the application of that same operator to the negation of that content. For one of the two cases, a Blanché case, of nonstandard contrariety singled out for attention, the question of whether such a representation is available is settled at the end of Section 4, and then in a more satisfying way in Section 5, though for the other case, noticed by Peter Simons, the question remains open, after some tentative discussion in one subsection, 6.2, of an Appendix (Section 6). (shrink)