Numerical Quantifiers Research Articles

Why are L2 learners not always sensitive to subject-verb agreement?

This study investigates whether intermediate Japanese learners of English (JLE) show any variability in sensitivity to the overuse of 3rd person singular (3sg) -s and if they do, what the causes may be. The results of the experiment indicate that JLE do exhibit variability: JLE showed sensitivity to ungrammaticality caused by a discrepancy in person features between subjects and verbs. In addition, they were sensitive to number feature disagreement when the plurality of subjects was expressed syntactically, namely, by using the conjunction and (e.g., Tim and Paul), by the demonstrative these and by a numeral quantifier (e.g., these two secretaries). However, they were not sensitive to such disagreement when subjects were marked only by plural -s (e.g., The chefs). Based on these results, we suggest that the failure of JLE to use 3sg -s may not lie in the difficulty of subject–verb agreement, but in the detection of the number feature of sentential subjects. We suggest that intermediate JLE have problems both with the number feature at the lexicon/syntax level and with its morphological mapping at the level of morphology.

On the Computational Complexity of the Numerically Definite Syllogistic and Related Logics

AbstractThenumerically definite syllogisticis the fragment of English obtained by extending the language of the classical syllogism with numerical quantifiers. Thenumerically definite relational syllogisticis the fragment of English obtained by extending the numerically definite syllogistic with predicates involving transitive verbs. This paper investigates the computational complexity of the satisfiability problem for these fragments. We show that the satisfiability problem (= finite satisfiability problem) for the numerically definite syllogistic is strongly NP-complete, and that the satisfiability problem (= finite satisfiability problem) for the numerically definite relational syllogistic is NEXPTIME-complete, but perhaps not strongly so. We discuss the related problem of probabilistic (propositional) satisfiability, and thereby demonstrate the incompleteness of some proof-systems that have been proposed for the numerically definite syllogistic.

Evaluation of qualitative attributes of forest ecosystems by means of numerical quantifiers

This paper presents a proposal of four variants of quantifiers for the numerical expression of qualitative attributes of forest ecosystems, for example site, naturalness, biodiversity, ecological stability, threat of injurious agents, status of forest biotopes of European significance in the NATURA 2000 network and so on. Quantifiers enable to completely characterise the whole set of these qualitative attributes of the ecosystem by one number which directly indicates the relative approximation of the ecosystem (in %) to the required most favourable status. They have more advantages: different numerical operations can be done with them, it is possible to aggregate evaluated units of the ecosystem to larger entities, to determine average value, variability and confidence limits of the final evaluation and to compare resulting statuses mutually or very objectively on the principle of biometric monitoring in a longer time. The construction of quantifiers is opened and it arbitrarily enables to choose input parameters at need (numerical quantifications of ecosystem quality statuses and weights of their criteria and indicators) and to search for optimal solutions. The reaction of quantifiers to different input situations is analysed on model examples and suggestions for their introduction into practice are presented. Special PC software was elaborated for the automated calculation of quantifiers.

Locality in Syntax and Floating Numeral Quantifiers

We defend the idea that a floating quantifier observes syntactic locality with its associated noun phrase. This idea has given rise to a number of important empirical insights, including the VP-internal subject position, intermediate traces, and NP-traces. Recently, this syntactic locality of floating quantifiers has been questioned in a number of languages. We take up evidence from Japanese that purports to disprove the locality requirements on floating numeral quantifiers and their associated NP, and we demonstrate that the arguments in fact give evidence for syntactic locality, not against it. Our conclusions suggest that evidence against the locality of floating quantifiers given in other languages should be reexamined.

Individual-denoting classifiers

This paper discusses Japanese numeral quantifiers that are used to count individuals, rather than quantities, of a substance, and which may occur either as floated or non-floated quantifiers. It is argued that such morphologically complex numeral quantifiers (NQs) are semantically complex as well: The numeral within the NQ is the quantifier itself, the classifier its domain of quantification. The proposed analysis offers a unified semantic account of floated and non-floated NQs that adheres closely to their surface morphology and syntax. It explains why floated NQs generally force a distributive reading. It covers both classifiers construed with objects and classifiers construed with events. In addition, it captures the fact that the classifier must agree with the NP it is construed with.

Floating numerals and floating quantifiers

This paper investigates the basic licensing conditions of the floating quantifier, e.g. all in The boys all took a card. It proposes a new analysis in which the quantificational operation of the floating quantifier is distinct from that of the quantifier local to a DP, e.g. all in All boys took a card, in the sense that the former takes place within the verbal domain while the latter takes place within the nominal domain. Under this view, floatable quantifiers are associated with an (often) inaudible nominal element that functions as the domain of quantification. Furthermore, this nominal element is taken to be either a lexical or a morphological component of the floatable quantifier. Observations such as that English all, each and both and Japanese numeral quantifiers are licensed to be floating quantifiers, while English every as well as English numeral quantifiers and Chinese numeral quantifiers are not, can be seen to follow from the circumstance that the former satisfy the proposed conditions while the latter do not.

The Quantificational Function of the Japanese Numeral Classifier

This paper presents a new quantificational analysis of the Japanese numeral quantifier (NQ) construction. It is proposed that the classifier within the NQ functions as the domain of quantification for the numeral, denoting a set of atomic individuals. This accounts for the predominant distributive reading of the floating NQ sentence, both with object classifiers and event classifiers, as a direct consequence of the atomicity condition of the classifier denotation. The analysis correctly predicts that, unlike the floating NQ, the non-floating NQ will show a collective/distributive ambiguity because it forms a plural term, which can always be interpreted as a group individual or as a sum of individuals. The analysis also provides a semantic account of the well-known classifier-NP agreement phenomenon.

Toward a comprehensive treatment of temporal constraints about periodic events

In this article, we propose an Allen-like approach to deal with different types of temporal constraints about periodic events. We consider the different components of such constraints (thus, unlike Allen, we also take into account quantitative constraints) including frame times, user-defined periods, qualitative temporal constraints, and numeric quantifiers and the interactions between such components. We propose a specialized high-level formalism to represent temporal constraints about periodic events; temporal reasoning on the formalism is performed by a path-consistency algorithm repeatedly applying our operations of inversion, intersection, and composition and by a specialized reasoner about periods and numeric quantification. The high-level formalism has been designed in such a way that different types of temporal constraints about periodic events can be represented in a compact and (hopefully) user-friendly way and path-consistency-based temporal reasoning on the formalism can be performed in polynomial time. We also prove that our definitions of inversion, intersection, and composition and, thus, of our path-consistency algorithm, are correct. This article also sketches the general architecture of the temporal manager for periodic events (TeMP+), that has been designed on the basis of our approach. As a working example, we show an application of our approach to scheduling in a school. © 2003 Wiley Periodicals, Inc.

Assessment of AIDS risks: effects of different scale ranges and preventive knowledge

In a sample of 552 respondents effects of different scale ranges and respondents' knowledge about AIDS for answering questions about AIDS-risks were examined. Knowledge was assessed with 12 items related to risks for HIV infections and preventive measures. AIDS hazards for different groups (prostitutes, fixers, hospital personnel, homosexuals, and haemophiliacs) had to be rated with five items, one for each group. Response variations were assessed in three parallel questionnaire versions with different ranges of risk assignments. Estimations had to be performed in comparison with the average population. Some groups were consistently rated to be at high risk, others were assigned low risks for becoming infected with the HIV-virus. The analysis of response patterns revealed that the three versions of numeric quantifiers determined the risk ratings only to some extent. The distribution patterns suggest that our subjects had an ordinal risk ordering in mind that might better be expressed in verbal terms. The knowledge about AIDS had no systematic effects on response behavior.

On the relative expressiveness of description logics and predicate logics

It is natural to view concept and role definitions in description logics as expressing monadic and dyadic predicates in predicate calculus. We show that the descriptions built using the constructors usually considered in the DL literature are characterized exactly as the predicates definable by formulas in \\ ̈ tL 3, the subset of first-order predicate calculus with monadic and dyadic predicates which allows only three variable symbols. In order to handle “number bounds”, we allow numeric quantifiers, and for transitive closure of roles we use infinitary disjunction. Using previous results in the literature concerning languages with limited numbers of variables, we get as corollaries the existence of formulas of FOPC which cannot be expressed as descriptions. We also show that by omitting role composition, descriptions express exactly the formulas in \\ ̈ tL 2, which is known to be decidable.

Learning Relations: An Evaluation of Search Strategies

Inducing concept descriptions in first order logic is inherently a complex task; then, heuristics are needed to keep the problem to manageable size. In this paper we explore the effect of alternative search strategies, including the use of information gain and of a-priori knowledge, on the quality of the acquired relations, intended as the ability to reconstruct the rule used to generate the examples. To this aim, an artificial domain has been created, in which the experimental conditions can be kept under control, the “solulion” of the learning problem is known and a perfect theory is available. Another investigated aspect is the impact of more complex description languages, such as, for instance, including numerical quantifiers. The resultS show that the information gain criterion is too greedy to be useful when the concepts have a complex internal structure; however, this drawback is more or less shared with any purely statistical evaluation criterion. The addition of parts of the available domain theory increases the obtained performance level. Similar results have been previously obtained on a number of real applications and of test-cases taken from standard machine learning data bases.

Pragmatic and semantic constraints on numeral quantifier position in Japanese

Japanese, like many other languages, permits numeral expressions to appear in several positions relative to the argument whose number they specify. This article concentrates on just two of the possibilities, the ‘Pre-Nominal’ and the ‘Q-Float’ numeral positions, describing a number of semantic, syntactic and pragmatic differences between them.

Papers from the Second International Workshop on Japanese Syntax

Preface 1. Subcategorization and word order Takao Gunji 2. Discourse factors in the binding of Zibun Masayo Iida and Peter Sells 3. Japanese zero pronominal binding: where syntax and discourse meet Megumi Kameyama 4. Blended quasi-direct discourse in Japanese Susumu Kuno 5. Whether we agree or not: a comparative syntax of English and Japanese Shige-Yuki Kuroda 6. Case deletion and discourse context Kiyoko Masunaga 7. Predication and numeral quantifier Shigeru Miyagawa 8. Readjustment and compound formation Masayoshi Shibatani and Taro Kageyama.

Remarks on Japanese subjects

It has been proposed that subjects are base-generated under VP (VP internal subjects hypothesis). In this paper, we argue that the VP internal subject hypothesis that allows the subject to be base-generated under VP and move above VP at S-structure is not warranted in Japanese. Four pieces of evidence are discussed: floating numeral quantifiers; pseudo-cleft constructions; temporal phrases; and secondary depictive predicates. These collectively indicate that the subjects of unergative and transitive verbs are base-generated above VP while the subjects of unaccusatives and direct passives are base-generated under VP (i.e., the object position) in Japanese. The unaccusatives and the direct passives are different in that the subjects of the direct passives must be above VP at S-structure while the subject of the unaccusative can be at the object position.

Numerical Quantifiers in game‐theoretical semantics

Numerical Quantifiers in game‐theoretical semantics

Reasoning under incomplete information in artificial intelligence: A comparison of formalisms using a single example

Man is capable of reasoning when the available information is incomplete. the conclusions obtained are based on knowledge considered as “generally true.” These conclusions are temporary as they are liable to be challenged by the arrival of new pieces of information which will refine the information previously available (without necessarily contradicting it). Numerous studies have independently dealt with the formalization of this kind of revisable reasoning over the last ten years. the approaches used have been very diverse: some are purely symbolic, others make use of numbers to quantify the uncertainty; some are close to formal logic, and others are much less formalized; some only deal with exceptions, a smaller number which are somewhat more ambitious tackle the problem of knowledge base revision. This work presents the above approaches and compares them on a single example in order to better evaluate their similarities, their differences, their abilities to formalize certain aspects of so-called “commonsense” reasoning, and also in order to try to lay bare the fundamental principles that underlie the different approaches. the logics considered in this work are default logic, nonmonotonic modal logics, including autoepistemic logic, circumscription, circumscription-like approaches, supposition-based logic, conditional logics, logics of uncertainty, i.e., probabilistic, and possibilistic logics as well as belief functions, numerical quantifier logic, and fuzzy logics. We also consider formalisms oriented towards causal reasoning and analogical reasoning. Lastly, we study the contribution of works on truth maintenance, action logic, as well as recent attempts to formalize the process of revision of a set of formulae closed by deduction. the systematic use of a single example and of the same evaluation criteria for each formalism, will enable the reader to better perceive the rationale behind the various approaches as well as to appreciate their interest.

Reasoning under incomplete information in artificial intelligence: A comparison of formalisms using a single example

Man is capable of reasoning when the available information is incomplete. the conclusions obtained are based on knowledge considered as “generally true.” These conclusions are temporary as they are liable to be challenged by the arrival of new pieces of information which will refine the information previously available (without necessarily contradicting it). Numerous studies have independently dealt with the formalization of this kind of revisable reasoning over the last ten years. the approaches used have been very diverse: some are purely symbolic, others make use of numbers to quantify the uncertainty; some are close to formal logic, and others are much less formalized; some only deal with exceptions, a smaller number which are somewhat more ambitious tackle the problem of knowledge base revision. This work presents the above approaches and compares them on a single example in order to better evaluate their similarities, their differences, their abilities to formalize certain aspects of so-called “commonsense” reasoning, and also in order to try to lay bare the fundamental principles that underlie the different approaches. the logics considered in this work are default logic, nonmonotonic modal logics, including autoepistemic logic, circumscription, circumscription-like approaches, supposition-based logic, conditional logics, logics of uncertainty, i.e., probabilistic, and possibilistic logics as well as belief functions, numerical quantifier logic, and fuzzy logics. We also consider formalisms oriented towards causal reasoning and analogical reasoning. Lastly, we study the contribution of works on truth maintenance, action logic, as well as recent attempts to formalize the process of revision of a set of formulae closed by deduction. the systematic use of a single example and of the same evaluation criteria for each formalism, will enable the reader to better perceive the rationale behind the various approaches as well as to appreciate their interest.

Reasoning under incomplete information in artificial intelligence: A comparison of formalisms using a single example

Man is capable of reasoning when the available information is incomplete. the conclusions obtained are based on knowledge considered as “generally true.” These conclusions are temporary as they are liable to be challenged by the arrival of new pieces of information which will refine the information previously available (without necessarily contradicting it). Numerous studies have independently dealt with the formalization of this kind of revisable reasoning over the last ten years. the approaches used have been very diverse: some are purely symbolic, others make use of numbers to quantify the uncertainty; some are close to formal logic, and others are much less formalized; some only deal with exceptions, a smaller number which are somewhat more ambitious tackle the problem of knowledge base revision. This work presents the above approaches and compares them on a single example in order to better evaluate their similarities, their differences, their abilities to formalize certain aspects of so-called “commonsense” reasoning, and also in order to try to lay bare the fundamental principles that underlie the different approaches. the logics considered in this work are default logic, nonmonotonic modal logics, including autoepistemic logic, circumscription, circumscription-like approaches, supposition-based logic, conditional logics, logics of uncertainty, i.e., probabilistic, and possibilistic logics as well as belief functions, numerical quantifier logic, and fuzzy logics. We also consider formalisms oriented towards causal reasoning and analogical reasoning. Lastly, we study the contribution of works on truth maintenance, action logic, as well as recent attempts to formalize the process of revision of a set of formulae closed by deduction. the systematic use of a single example and of the same evaluation criteria for each formalism, will enable the reader to better perceive the rationale behind the various approaches as well as to appreciate their interest.

On fuzzy syllogisms

This paper provides a systematic treatment of possibly imprecisely or vaguely specified numerical quantifiers in default syllogisms, following an approach initiated by Zadeh. The obtained propagation rules are derived from simple properties of relative cardinality or, equivalently, conditional probability. Uncertainty in the description of numerical quantifiers is handled using possibility theory and, particularly, fuzzy arithmetic. The advantages of this default reasoning method are its ability to model any kind of quantifier and to build new defaults by chaining existing ones, in a rigorous manner. This approach also emphasizes the difference between two types of uncertain pieces of knowledge, i.e., conjectures versus general rules.

The effects of verbal and numerical quantifiers on questionnaire responses

Three experiments are described which assess the effects of responding to different sets of verbal quantifiers (e g, always, often, sometimes). In Experiment 1, participants were asked to give percentage equivalents to three sets of supposedly equivalent quantifiers. The responses differed significantly. In Experiment 2, participants completed different versions of a questionnaire in order to see if the three sets of quantifiers produced equivalent responses in a more concrete situation. The results again showed that the three sets were not equivalent. In Experiment 3, participants completed one version of the questionnaire with a set of verbal quantifiers and two versions of the questionnaire with numerical quantifiers (e g, I do this about 75% of the time). The verbal quantifiers produced virtually the same results as before: the numerical quantifiers produced different but quite consistent results. It is concluded that numerical quantifiers are probably more useful than verbal ones, and should be used if possible.