The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce (...) two new logical geometries, and develop a formal, well-motivated account of their informativity. This enables us to show that the square is strictly more informative than many of the more complex diagrams. (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)

According to Löbner (1989), Germanschon ‘already’ andnoch ‘still’ are related vianoch nicht ‘not yet’ as follows: ‘Noch p att’ presupposes ‘p beforet.’Noch nicht p is equivalent tonoch (~p). Therefore ‘noch nicht p att’ presupposes ‘~p beforet.’Schon p is the negation ofnoch nicht p. Therefore ‘schon p att’ also presupposes ‘~p beforet.’ This paper gives evidence to show thatnoch nicht p andschon p do not have the postulated presuppositions, and argues thatnoch nicht is not compositional. Like Löbner (1989), the present paper (...) claims that its conclusions apply crosslinguistically. (shrink)

The paper takes up the objections raised in van der Auwera (1993) against the joint analysis of the German particles schon, noch and erst published in Löbner (1989). Central to my analysis is the claim that the particles are organized in duality groups of four to which essentially the same type of analysis applies. Van der Auwera (1993) claims that already/schon, in its basic use, is different from the other three particles in having a more complex meaning which results in (...) an opposition of the particle to finally/endlich. As to the narrow-focus temporal uses he argues that the duality approach is inadequate in including improper members on the one hand, and excluding relevant particles on the other.The criticism will be refuted. After a recollection of the duality analysis in Section 2, van der Auwera's arguments against the general design of my analysis are dealt with in Section 3. It will be argued that his own analysis of already/schon and its group, as far as it is supported by the data, does not really differ from my approach. In Section 4, I will deal with the claim that finally/endlich contradicts already/schon, which if correct would provide an indirect argument against the duality analysis of schon and noch. I will argue that endlich is set apart from the particles of the schon group by the presence of a non-descriptive, expressive, meaning component. For its descriptive meaning, endlich logically entails schon and belongs to a parallel duality group of its own together with noch immer. The apparent incompatibility of finally/endlich and already/schon can be explained as a conflict between what is foregrounded by each particle, respectively. In Section 5, I will argue that, contrary to van der Auwera's claims, the narrow focus uses of schon and its kin do form proper duality groups. The existence of such uses of noch, not treated in Löbner (1989), does not invalidate the duality analysis of schon and erst. Rather, noch in its relevant narrow-focus use belongs to yet another duality group together with its dual nur noch. (shrink)

In this paper, I argue that the aspectual, marginality, and concessive uses of the grading particles still and already can be reduced to the fol lowing three classes of focus sensitive-grading particles: additive particles like too, scalar particles like even, and exclusive particles like only. The meaning differences among the occurrences of still (and already) are mostly reduced to the differences among these three classes of grading particles. In turn, these differences are shown to correlate with what type of object (...) is denoted by the phrase in the scope of the particle. The proposal has repercussions also for the focus-sensitive particle again. I investigate the latter too, and I propose a parallel between the temporal and nominal domains where the contrast between still and again is analyzed along the lines of the contrast between definite and indefinite noun phrases. (shrink)

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)

The paper develops a uniform compositional analysis of the various readings of the scalar particle still and its German counterpart noch. Noch/still is a presuppositional scalar particle that gives rise to implicatures. Interpretive possibilities arise through different choices for the scale that the particle associates with, different attachment sites in the syntax, and interaction with focus. These interpretive parameters allow for a wide range of possible sentence interpretations, which overlap, but do not coincide for still and noch. The contrastive perspective (...) allows us to examine the role of scales in the grammar. The implicatures triggered by the scalar item open an interesting perspective for the generation of implicatures in general. (shrink)

The wide range of interpretations of aoristic and imperfective aspect in Ancient Greek cannot be attributed to unambiguous aspectual operators but suggest an analysis in terms of coercion in the spirit of de Swart (Nat Lang Linguist Theory 16:347–385, 1998). But since such an analysis cannot explain the Ancient Greek data, we combine Klein’s (Time in language, 1994) theory of tense and aspect with Egg’s (Flexible semantics for reinterpretation phenomena, 2005) aspectual coercion approach. Following Klein. (grammatical) aspect relates the runtime (...) of an eventuality and the current time of reference (topic time). We claim that these relations can trigger aspectual selection restrictions (and subsequent aspectual coercions) just like e.g. aspectually relevant temporal adverbials, and are furthermore susceptible to the Duration Principle of Egg (Flexible semantics for reinterpretation phenomena, 2005): Properties of eventualities must be compatible with respect to the duration they specify for an eventuality. The Duration Principle guides the selection between different feasible coercion operators in cases of aspectual coercion but can also trigger coercions of its own. We analyse the interpretations of aorist and imperfective as cases of coercion that avoid impending violations of aspectual selection restrictions or of the Duration Principle, which covers cases that are problematic for de Swart’s (Nat Lang Linguist Theory 16:347–385, 1998) analysis. (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 →.

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)

This paper analyzes a non-temporal interpretation of the adverb sempre “always” in European Portuguese and Italian, in which the adverb expresses persistence of the truth of a proposition over time and displays specific contextual constraints (TP-sempre). Despite an overlap in the contexts in which TP-sempre may occur in both languages, we provide data showing that its distribution is not exactly the same in European Portuguese and Italian. In view of these data, we propose that TP-sempre is a modal operator of (...) confirmation in both languages, but that it is more restricted in Italian in that it has a plan presupposition only in this language. (shrink)

This paper presents a novel semantic analysis of unit names and gradable adjectives, inspired by measurement theory (Krantz et al 1971). Based on measurement theory's typology of measures, I claim that different predicates are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases.

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.