Search results for "quantifier"

From Adjectives to Quantifiers. Evidence from Old and Modern Catalan

2011

La història dels quantificadors indefinits de les llengües romàniques és la història del desenvolupament de nous trets distribucionals per un grup escollit d’adjectius llatins (Company 1991, 1997; Batllori 1998). Aquesta distribució serà responsable de la constitució posterior de la nova subclasse de determinants que anomenem quantificadors. Com s’explica a Zamparelli (2000), l’augment de la complexitat estructural del marge esquerre del SDet suposa l’especialització de paraules que pertanyien a antigues categories per aquestes noves posicions. És així com la posició de quantificador genera la categoria quantificador. Estem devant un procés de llarga durada amb conseqüències que encara són …

Fluted Logic with Counting

2021

The fluted fragment is a fragment of first-order logic in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that the fluted fragment possesses the finite model property. In this paper, we extend the fluted fragment by the addition of counting quantifiers. We show that the resulting logic retains the finite model property, and that the satisfiability problem for its (m+1)-variable sub-fragment is in m-NExpTime for all positive m. We also consider the satisfiability and finite satisfiability problems for the extension of any of these fragments in which the fluting requirement applies only to sub-form…

Quantifier Elimination and Rectilinearisation Theorem for Generalised Quasianalytic Algebras

2013

International audience; An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation result for generalised quasianalytic algebras.

Probabilistic inference and syllogisms

2014

Traditionally, syllogisms are arguments with two premises and one conclusion which are constructed by propositions of the form “All S are P ” and “At least one S is P ” and their respective negated versions. We will discuss probabilistic notions of the existential import and the basic sentences type. We will develop an intuitively plausible version of the syllogisms that is able to deal with uncertainty, exceptions and nonmonotonicity. We will develop a new semantics for categorical syllogisms that is based on subjective probability. Specifically, we propose de Finetti’s principle of coherence and its generalization to lower and upper conditional probabilities as the fundamental corner ston…

Square of Opposition Under Coherence

2016

Various semantics for studying the square of opposition have been proposed recently. So far, only (Gilio et al., 2016) studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized qu…

Probabilistic semantics for categorical syllogisms of Figure II

2018

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of \(\bar{P}|S\) from the premise set \(\{M|P,\bar{M}|S\}\) is not informative, we add \(p(S|(S \vee P))>0\) as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the…

Two-variable First-Order Logic with Counting in Forests

2018

We consider an extension of two-variable, first-order logic with counting quantifiers and arbitrarily many unary and binary predicates, in which one distinguished predicate is interpreted as the mother-daughter relation in an unranked forest. We show that both the finite satisfiability and the general satisfiability problems for the extended logic are decidable in NExpTime. We also show that the decision procedure for finite satisfiability can be extended to the logic where two distinguished predicates are interpreted as the mother-daughter relations in two independent forests.

Imprecise probability assessments and the Square of Opposition

There is a long history of investigations on the square of opposition spanning over two millenia. A square of opposition represents logical relations among basic sentence types in a diagrammatic way. The basic sentence types, traditionally denoted by A (universal affirmative: ''Every S is P''), E (universal negative: ''No S is P''), I (particular affirmative: ''Some S are P''), and O (particular negative: ''Some S are not P''), constitute the corners of the square, and the logical relations--contradiction, contrarity, subalternation, and sub-contrarity--form the diagonals and the sides of the square. We investigate the square of opposition from a probabilistic point of view. To manage impre…

Observacions sobre la posició dels subjectes postverbals en català i castellà

2007

This is a comparative study of the different positions of postverbal subjects in two closely related languages that nevertheless show clear differences in this respect. The comparative study will allow us to reject the idea that postverbal subjects in Romance languages are in a unique in situ position Spec VP as has been proposed recently (Motapayane1995, Ordóñez 1998, Costa 2000, Alexiadou i Anagnostopoulou 2001, Cardinaletti 2001). On the contrary, this study will show clearly that there is a need for two positions for postverbal subjects in order to understand the parametric differences between Catalan and Spanish. The general hypothesis will be that the subjects can access a higher Spec…

The article a(n) in English quantifying expressions: A default marker of cardinality

2020

Certain English quantificational expressions feature what appears to be an indefinite article, e.g. 'a bunch, a few, a hundred'. These can be divided into three types of quantifying expressions: pseudopartitives ('a lot, a bunch, a ton'), article-requiring quantifiers ('a few, a couple, a hundred'), and article-free quantifiers ('three, many, several'); article-free quantifiers have an article under certain circumstances, e.g. modification by an adjective ('a surprising 30 …'). While standard analyses would take the article in these expressions to be a D head, it is argued here that the article is not in D, nor is it singular or count, as evidenced by its (lack of an) interaction with verba…