Ka Fat Chow - Academia.edu (original) (raw)
Thesis Chapters by Ka Fat Chow
This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applicati... more This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applications to scalar reasoning. In Chapter 1, I introduce the basic notions of Generalized Quantifier Theory (GQT) and survey the major types of right-oriented GQs traditionally studied under GQT (including both monadic and iterated GQs). I also expand the scope of this theory to the analysis of left-oriented GQs (including left conservative GQs such as “only” and left-iterated GQs manifested as quantified statements with relative clauses).
In Chapter 2, I introduce the major aspects of scalar reasoning to be studied in this thesis and summarize the major findings in the literature. After reviewing different notions of scales, I introduce other essential concepts and review the various theories and schools on the two main types of scalar reasoning, i.e. scalar entailments (SEs) and scalar implicatures (SIs). I then introduce four types of scalar lexical items studied under the Scalar Model Theory and Chinese grammar and discuss how their semantics / pragmatics are related to SEs and/or SIs. These include scalar operators (SOs), climax construction connectives (CCCs), subjective quantity operators (SQOs) and lexical items denoting extreme values. In the final part of this chapter, some outstanding problems in the studies on scalar reasoning are identified.
In Chapter 3, I study four main types of quantifier inferences. They are monotonicity inferences, argument structure inferences, opposition inferences and (non-classical) syllogistic inferences. The major findings are summarized in tables and theorems. Special emphasis is put on devising general principles and methods that enable us to derive valid inferential patterns of iterated GQs from the inferential properties of their constituent monadic GQs.
In Chapter 4, I apply the major findings worked out in the previous chapter to resolve the outstanding problems identified in Chapter 2. I first develop a basic formal framework that is based on the notions of generalized fractions and I-function. This basic framework can deal with the various aspects of scalar reasoning in a uniform way. I then enrich the basic framework by adding specific ingredients to deal with the phenomena of SEs and SIs. To deal with SEs, I add a relation connecting the I-function and SEs to the basic framework, so that the derivation of SEs is reduced to comparison between the I-function values of propositions. Moreover, by capitalizing on a parallelism between SEs and monotonicity inferences, I combine findings of the two types of inferences and discover new inferential patterns, such as Proportionality Calculus and scalar syllogisms. To deal with SIs, I add the ingredients of question under discussion (QUD) foci, answer exhaustification and opposition inferences to the basic framework, so that it can account for the various types of SIs and related phenomena introduced in Chapter 2 in a uniform way. I then use the framework to conduct a cross-linguistic study on the English and Chinese scalar lexical items introduced in Chapter 2. The I-function is used to formulate the conditions of use for these lexical items. The association of SEs and SIs with different types of scalar lexical items is also explored.
Finally, Chapter 5 discusses the significance of the major findings of this thesis and possible extensions of the study.
Papers by Ka Fat Chow
New Dimensions of the Square of Opposition
This paper develops a theory on opposition inferences – quantifier inferences involving the contr... more This paper develops a theory on opposition inferences – quantifier inferences involving the contradictory, contrary and subcontrary relations. After the basic notions associated with opposition inferences, including opposition properties (OPs), o-sensitivities, etc., are defined as generalizations of the notions associated with monotonicity inferences, a number of theorems for determining the o-sensitivities of various types of monadic generalized quantifiers (GQs), including determiners, type <1> GQs and structured GQs, are proposed and proved, resulting in a classification of the most commonly used monadic GQs according to their OPs. For iterated polyadic GQs, the notion of OP-chain is defined. A principle that enables one to determine the o-sensitivities of an iterated GQ according to the o-sensitivities of its constituent monadic GQs is then proposed. The o-sensitivities of GQs viewed as sets and arguments of other GQs and logical operators, particularly the negation operator, are also discussed. Finally, opposition inferences are compared and contrasted with monotonicity inferences. It is finally concluded that o-sensitivities are independent of monotonicities, and opposition inferences are not subsumable under monotonicity inferences.
New Frontiers in Artificial Intelligence, 2019
This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive... more This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive Semantics (IS). After discussing the difficulty in treating quantifiers under the existing IS framework, I propose a new treatment of quantifiers that combines features of IS and the Generalized Quantifier Theory (GQT). My proposal comprises two main points: (i) assuming that the outputs of all quantifiers are non-inquisitive; and (ii) deriving a predicate X * of type s→(e n →t) corresponding to each predicate X of type e n →T. By using X * , we can then restore the traditional treatment of GQT under the IS framework. I next point out that to properly handle the pair list reading of some questions with "every", we have to revert to the old treatment of "every". I also introduce (and prove) a theorem that shows that the new treatment of "every" is just a special case of the old treatment, and conclude that the new treatment of all quantifiers other than "every" plus the old treatment of "every" is sufficient for the general purpose of treating quantified statements and questions.
Opposition inferences constitute an important type of immediate inferences studied in Classical L... more Opposition inferences constitute an important type of immediate inferences studied in Classical Logic. These are inferences involving 4 types of relations defined on the classical square of opposition: subalternation, contradictoriness, contrariety and subcontrariety. Based on the definitions of these relations, one can immediately obtain certain opposition inferences, such as the following: (1) (Given that there is some student.) No student sang. ╞ It is not the case that every student sang. However, the applicability of classical opposition inferences is limited because Classical Logic only studied quantified statements headed by the 4 classical quantifiers: “every”, “no”, “some” and “not every”. The advent of modern Generalized Quantifier Theory (GQT) has opened up possible ways to extend the classical opposition inferences. Not only can we consider opposition inferences of quantified statements headed by non-classical quantifiers such as “most”, “at least 3/4”, but we can now co...
This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applicati... more This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applications to scalar reasoning. In Chapter 1, I introduce the basic notions of Generalized Quantifier Theory (GQT) and survey the major types of right-oriented GQs traditionally studied under GQT (including both monadic and iterated GQs). I also expand the scope of this theory to the analysis of left-oriented GQs (including left conservative GQs such as “only” and left-iterated GQs manifested as quantified statements with relative clauses). In Chapter 2, I introduce the major aspects of scalar reasoning to be studied in this thesis and summarize the major findings in the literature. After reviewing different notions of scales, I introduce other essential concepts and review the various theories and schools on the two main types of scalar reasoning, i.e. scalar entailments (SEs) and scalar implicatures (SIs). I then introduce four types of scalar lexical items studied under the Scalar Model Theory and Chinese grammar and discuss how their semantics / pragmatics are related to SEs and/or SIs. These include scalar operators (SOs), climax construction connectives (CCCs), subjective quantity operators (SQOs) and lexical items denoting extreme values. In the final part of this chapter, some outstanding problems in the studies on scalar reasoning are identified. In Chapter 3, I study four main types of quantifier inferences. They are monotonicity inferences, argument structure inferences, opposition inferences and (non-classical) syllogistic inferences. The major findings are summarized in tables and theorems. Special emphasis is put on devising general principles and methods that enable us to derive valid inferential patterns of iterated GQs from the inferential properties of their constituent monadic GQs. In Chapter 4, I apply the major findings worked out in the previous chapter to resolve the outstanding problems identified in Chapter 2. I first develop a basic formal framework that is based on the notions of generalized fractions and I-function. This basic framework can deal with the various aspects of scalar reasoning in a uniform way. I then enrich the basic framework by adding specific ingredients to deal with the phenomena of SEs and SIs. To deal with SEs, I add a relation connecting the I-function and SEs to the basic framework, so that the derivation of SEs is reduced to comparison between the I-function values of propositions. Moreover, by capitalizing on a parallelism between SEs and monotonicity inferences, I combine findings of the two types of inferences and discover new inferential patterns, such as Proportionality Calculus and scalar syllogisms. To deal with SIs, I add the ingredients of question under discussion (QUD) foci, answer exhaustification and opposition inferences to the basic framework, so that it can account for the various types of SIs and related phenomena introduced in Chapter 2 in a uniform way. I then use the framework to conduct a cross-linguistic study on the English and Chinese scalar lexical items introduced in Chapter 2. The I-function is used to formulate the conditions of use for these lexical items. The association of SEs and SIs with different types of scalar lexical items is also explored. Finally, Chapter 5 discusses the significance of the major findings of this thesis and possible extensions of the study.
Journal of Logic, Language and Information, 2021
Journal of Logic, Language and Information, 2019
We present a Revised Projectivity Calculus (denoted RC) that extends the scope of inclusion and e... more We present a Revised Projectivity Calculus (denoted RC) that extends the scope of inclusion and exclusion inferences derivable under the Projectivity Calculus (denoted C) developed by Icard (2012). After pointing out the inadequacies of C, we introduce four opposition properties (OPs) which have been studied by Chow (2012, 2017) and are more appropriate for the study of exclusion reasoning. Together with the monotonicity properties (MPs), the OPs will form the basis of RC instead of the additive/multiplicative properties used in C. We also prove some important results of the OPs and their relation with the MPs. We then introduce a set of projectivity signatures together with the associated operations and conditions for valid inferences, and develop RC by inheriting the key features of C. We then show that under RC, we can derive some inferences that are not derivable under C. We finally discuss some properties of RC and point to possible directions of further studies.
Lecture Notes in Computer Science, 2011
This paper introduces a semantic model for vague quantifiers (VQs) combining Fuzzy Theory (FT) an... more This paper introduces a semantic model for vague quantifiers (VQs) combining Fuzzy Theory (FT) and Supervaluation Theory (ST), which are the two main theories on vagueness, a common source of uncertainty in natural language. After comparing FT and ST, I will develop the desired model and a numerical method for evaluating truth values of vague quantified statements, called the Modified Glöckner's Method, that combines the merits and overcomes the demerits of the two theories. I will also show how the model can be applied to evaluate truth values of complex quantified statements with iterated VQs.
Lecture Notes in Computer Science, 2013
In this paper, I will develop a semantic model for interrogatives, an important sentence type exp... more In this paper, I will develop a semantic model for interrogatives, an important sentence type expressing a special aspect of uncertainty. The model is based on the notions of generalized quantifiers and bilattices, and is used to model several aspects of interrogative semantics, including resolvedness conditions, answerhood, exhaustivity and interrogative inferences. It will be shown that the semantic model satisfies a number of adequacy criteria.
Lecture Notes in Computer Science, 2012
This paper generalizes the notion of monotonicities to opposition properties (OPs). Some proposit... more This paper generalizes the notion of monotonicities to opposition properties (OPs). Some propositions regarding the OPs of determiners will be proposed and proved. We will also define the notion of OP-chain and deduce a condition that enables us to determine the OPs of an iterated quantifier in its predicates based on the OPs of its constituent determiners.
Around and Beyond the Square of Opposition, 2012
Volume of Abstracts Non-classical Modal and …
The studies on interrogatives in logic and formal semantics have been a difficult task because th... more The studies on interrogatives in logic and formal semantics have been a difficult task because there is not an intuitive and uncontroversial notion of truth values for interrogatives. Thus we see different frameworks for interrogatives with different merits and demerits. In this paper, I will formulate a theoretical framework that combines Gutierrez-Rexach 's GQT-based framework (in [4, 5]) and Nelken and Francez's bilattice-based framework (in [7, 8]) for interrogatives and derive certain valid inferential patterns involving interrogatives based on this framework. Gutierrez-Rexach's framework is based on Generalized Quantifier Theory (GQT) and treats a WH-word as an interrogative quantifier (IQ) that requires, in addition to the ordinary arguments, an "answer argument" to make a complete proposition. For instance, the truth condition of "who" is represented by "who(Y)(X) = 1 iff P ERSON ∩ Y = X", where X is the answer argument. Thus, under this approach the question "Who sang" is semantically equivalent to the noun phrase "person(s) who sang". Nelken and Francez's framework assumes that interrogatives are of the same semantic type as that of propositions. The denotation of declaratives and interrogatives are thus both truth values. However, to distinguish the two types of sentences, they adopt 5 truth values which are arranged in 2 lattices (hence a "bilattice"). For declaratives, there are 3 truth values: t ("known to be true"), f ("known to be false") and uk ("unknown whether true or false"). For interrogatives, they borrow the concept of "resolvedness" from [1] and assume 2 truth values: r ("resolved") and ur ("unresolved"). The two groups of truth values are related by the resolvedness conditions of interrogatives. For illustration, consider the polar question "Did Mary kiss John" whose formal representation and resolvedness condition is " ?(KISS(m, j)) = r iff KISS(m, j) ∈ {t, f }" (where p denotes the truth value of p), meaning that "Did Mary kiss John" is resolved iff it is known whether Mary kissed John. In this paper, I will develop a formal framework for interrogatives that is based on Nelken and Francez's framework but with substantial modification. The reason for choosing Nelken and Francez's framework as the basis is that their
New Frontiers in Artificial Intelligence. JSAI-isAI 2018., 2019
This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive... more This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive Semantics (IS). After discussing the difficulty in treating quantifiers under the existing IS framework, I propose a new treatment of quantifiers that combines features of IS and the Generalized Quantifier Theory (GQT). My proposal comprises two main points: (i) assuming that the outputs of all quantifiers given non-inquisitive inputs are non-inquisitive; and (ii) deriving a predicate X * of type s→(e n →t) corresponding to each predicate X of type e n →T. By using X * , we can then restore the traditional treatment of GQT under the IS framework. I next point out that to properly handle the pair list reading of some questions with ''every'', we have to revert to the old treatment of every. I also introduce (and prove) a theorem that shows that the new treatment of every is just a special case of the old treatment, and conclude that the new treatment of all quantifiers other than every plus the old treatment of every is sufficient for the general purpose of treating quantified statements and questions.
This paper develops a theory on opposition inferences – quantifier inferences involving the contr... more This paper develops a theory on opposition inferences – quantifier inferences involving the contradictory, contrary and subcontrary relations. After the basic notions associated with opposition inferences, including opposition properties (OPs), o-sensitivities, etc., are defined as generalizations of the notions associated with monotonicity inferences, a number of theorems for determining the o-sensitivities of various types of monadic generalized quantifiers (GQs), including determiners, type <1> GQs and structured GQs, are proposed and proved, resulting in a classification of the most commonly used monadic GQs according to their OPs. For iterated polyadic GQs, the notion of OP-chain is defined. A principle that enables one to determine the o-sensitivities of an iterated GQ according to the o-sensitivities of its constituent monadic GQs is then proposed. The o-sensitivities of GQs viewed as sets and arguments of other GQs and logical operators, particularly the negation operator, are also discussed. Finally, opposition inferences are compared and contrasted with monotonicity inferences. It is finally concluded that o-sensitivities are independent of monotonicities, and opposition inferences are not subsumable under monotonicity inferences.
This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applicati... more This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applications to scalar reasoning. In Chapter 1, I introduce the basic notions of Generalized Quantifier Theory (GQT) and survey the major types of right-oriented GQs traditionally studied under GQT (including both monadic and iterated GQs). I also expand the scope of this theory to the analysis of left-oriented GQs (including left conservative GQs such as “only” and left-iterated GQs manifested as quantified statements with relative clauses).
In Chapter 2, I introduce the major aspects of scalar reasoning to be studied in this thesis and summarize the major findings in the literature. After reviewing different notions of scales, I introduce other essential concepts and review the various theories and schools on the two main types of scalar reasoning, i.e. scalar entailments (SEs) and scalar implicatures (SIs). I then introduce four types of scalar lexical items studied under the Scalar Model Theory and Chinese grammar and discuss how their semantics / pragmatics are related to SEs and/or SIs. These include scalar operators (SOs), climax construction connectives (CCCs), subjective quantity operators (SQOs) and lexical items denoting extreme values. In the final part of this chapter, some outstanding problems in the studies on scalar reasoning are identified.
In Chapter 3, I study four main types of quantifier inferences. They are monotonicity inferences, argument structure inferences, opposition inferences and (non-classical) syllogistic inferences. The major findings are summarized in tables and theorems. Special emphasis is put on devising general principles and methods that enable us to derive valid inferential patterns of iterated GQs from the inferential properties of their constituent monadic GQs.
In Chapter 4, I apply the major findings worked out in the previous chapter to resolve the outstanding problems identified in Chapter 2. I first develop a basic formal framework that is based on the notions of generalized fractions and I-function. This basic framework can deal with the various aspects of scalar reasoning in a uniform way. I then enrich the basic framework by adding specific ingredients to deal with the phenomena of SEs and SIs. To deal with SEs, I add a relation connecting the I-function and SEs to the basic framework, so that the derivation of SEs is reduced to comparison between the I-function values of propositions. Moreover, by capitalizing on a parallelism between SEs and monotonicity inferences, I combine findings of the two types of inferences and discover new inferential patterns, such as Proportionality Calculus and scalar syllogisms. To deal with SIs, I add the ingredients of question under discussion (QUD) foci, answer exhaustification and opposition inferences to the basic framework, so that it can account for the various types of SIs and related phenomena introduced in Chapter 2 in a uniform way. I then use the framework to conduct a cross-linguistic study on the English and Chinese scalar lexical items introduced in Chapter 2. The I-function is used to formulate the conditions of use for these lexical items. The association of SEs and SIs with different types of scalar lexical items is also explored.
Finally, Chapter 5 discusses the significance of the major findings of this thesis and possible extensions of the study.
New Dimensions of the Square of Opposition
This paper develops a theory on opposition inferences – quantifier inferences involving the contr... more This paper develops a theory on opposition inferences – quantifier inferences involving the contradictory, contrary and subcontrary relations. After the basic notions associated with opposition inferences, including opposition properties (OPs), o-sensitivities, etc., are defined as generalizations of the notions associated with monotonicity inferences, a number of theorems for determining the o-sensitivities of various types of monadic generalized quantifiers (GQs), including determiners, type <1> GQs and structured GQs, are proposed and proved, resulting in a classification of the most commonly used monadic GQs according to their OPs. For iterated polyadic GQs, the notion of OP-chain is defined. A principle that enables one to determine the o-sensitivities of an iterated GQ according to the o-sensitivities of its constituent monadic GQs is then proposed. The o-sensitivities of GQs viewed as sets and arguments of other GQs and logical operators, particularly the negation operator, are also discussed. Finally, opposition inferences are compared and contrasted with monotonicity inferences. It is finally concluded that o-sensitivities are independent of monotonicities, and opposition inferences are not subsumable under monotonicity inferences.
New Frontiers in Artificial Intelligence, 2019
This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive... more This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive Semantics (IS). After discussing the difficulty in treating quantifiers under the existing IS framework, I propose a new treatment of quantifiers that combines features of IS and the Generalized Quantifier Theory (GQT). My proposal comprises two main points: (i) assuming that the outputs of all quantifiers are non-inquisitive; and (ii) deriving a predicate X * of type s→(e n →t) corresponding to each predicate X of type e n →T. By using X * , we can then restore the traditional treatment of GQT under the IS framework. I next point out that to properly handle the pair list reading of some questions with "every", we have to revert to the old treatment of "every". I also introduce (and prove) a theorem that shows that the new treatment of "every" is just a special case of the old treatment, and conclude that the new treatment of all quantifiers other than "every" plus the old treatment of "every" is sufficient for the general purpose of treating quantified statements and questions.
Opposition inferences constitute an important type of immediate inferences studied in Classical L... more Opposition inferences constitute an important type of immediate inferences studied in Classical Logic. These are inferences involving 4 types of relations defined on the classical square of opposition: subalternation, contradictoriness, contrariety and subcontrariety. Based on the definitions of these relations, one can immediately obtain certain opposition inferences, such as the following: (1) (Given that there is some student.) No student sang. ╞ It is not the case that every student sang. However, the applicability of classical opposition inferences is limited because Classical Logic only studied quantified statements headed by the 4 classical quantifiers: “every”, “no”, “some” and “not every”. The advent of modern Generalized Quantifier Theory (GQT) has opened up possible ways to extend the classical opposition inferences. Not only can we consider opposition inferences of quantified statements headed by non-classical quantifiers such as “most”, “at least 3/4”, but we can now co...
This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applicati... more This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applications to scalar reasoning. In Chapter 1, I introduce the basic notions of Generalized Quantifier Theory (GQT) and survey the major types of right-oriented GQs traditionally studied under GQT (including both monadic and iterated GQs). I also expand the scope of this theory to the analysis of left-oriented GQs (including left conservative GQs such as “only” and left-iterated GQs manifested as quantified statements with relative clauses). In Chapter 2, I introduce the major aspects of scalar reasoning to be studied in this thesis and summarize the major findings in the literature. After reviewing different notions of scales, I introduce other essential concepts and review the various theories and schools on the two main types of scalar reasoning, i.e. scalar entailments (SEs) and scalar implicatures (SIs). I then introduce four types of scalar lexical items studied under the Scalar Model Theory and Chinese grammar and discuss how their semantics / pragmatics are related to SEs and/or SIs. These include scalar operators (SOs), climax construction connectives (CCCs), subjective quantity operators (SQOs) and lexical items denoting extreme values. In the final part of this chapter, some outstanding problems in the studies on scalar reasoning are identified. In Chapter 3, I study four main types of quantifier inferences. They are monotonicity inferences, argument structure inferences, opposition inferences and (non-classical) syllogistic inferences. The major findings are summarized in tables and theorems. Special emphasis is put on devising general principles and methods that enable us to derive valid inferential patterns of iterated GQs from the inferential properties of their constituent monadic GQs. In Chapter 4, I apply the major findings worked out in the previous chapter to resolve the outstanding problems identified in Chapter 2. I first develop a basic formal framework that is based on the notions of generalized fractions and I-function. This basic framework can deal with the various aspects of scalar reasoning in a uniform way. I then enrich the basic framework by adding specific ingredients to deal with the phenomena of SEs and SIs. To deal with SEs, I add a relation connecting the I-function and SEs to the basic framework, so that the derivation of SEs is reduced to comparison between the I-function values of propositions. Moreover, by capitalizing on a parallelism between SEs and monotonicity inferences, I combine findings of the two types of inferences and discover new inferential patterns, such as Proportionality Calculus and scalar syllogisms. To deal with SIs, I add the ingredients of question under discussion (QUD) foci, answer exhaustification and opposition inferences to the basic framework, so that it can account for the various types of SIs and related phenomena introduced in Chapter 2 in a uniform way. I then use the framework to conduct a cross-linguistic study on the English and Chinese scalar lexical items introduced in Chapter 2. The I-function is used to formulate the conditions of use for these lexical items. The association of SEs and SIs with different types of scalar lexical items is also explored. Finally, Chapter 5 discusses the significance of the major findings of this thesis and possible extensions of the study.
Journal of Logic, Language and Information, 2021
Journal of Logic, Language and Information, 2019
We present a Revised Projectivity Calculus (denoted RC) that extends the scope of inclusion and e... more We present a Revised Projectivity Calculus (denoted RC) that extends the scope of inclusion and exclusion inferences derivable under the Projectivity Calculus (denoted C) developed by Icard (2012). After pointing out the inadequacies of C, we introduce four opposition properties (OPs) which have been studied by Chow (2012, 2017) and are more appropriate for the study of exclusion reasoning. Together with the monotonicity properties (MPs), the OPs will form the basis of RC instead of the additive/multiplicative properties used in C. We also prove some important results of the OPs and their relation with the MPs. We then introduce a set of projectivity signatures together with the associated operations and conditions for valid inferences, and develop RC by inheriting the key features of C. We then show that under RC, we can derive some inferences that are not derivable under C. We finally discuss some properties of RC and point to possible directions of further studies.
Lecture Notes in Computer Science, 2011
This paper introduces a semantic model for vague quantifiers (VQs) combining Fuzzy Theory (FT) an... more This paper introduces a semantic model for vague quantifiers (VQs) combining Fuzzy Theory (FT) and Supervaluation Theory (ST), which are the two main theories on vagueness, a common source of uncertainty in natural language. After comparing FT and ST, I will develop the desired model and a numerical method for evaluating truth values of vague quantified statements, called the Modified Glöckner's Method, that combines the merits and overcomes the demerits of the two theories. I will also show how the model can be applied to evaluate truth values of complex quantified statements with iterated VQs.
Lecture Notes in Computer Science, 2013
In this paper, I will develop a semantic model for interrogatives, an important sentence type exp... more In this paper, I will develop a semantic model for interrogatives, an important sentence type expressing a special aspect of uncertainty. The model is based on the notions of generalized quantifiers and bilattices, and is used to model several aspects of interrogative semantics, including resolvedness conditions, answerhood, exhaustivity and interrogative inferences. It will be shown that the semantic model satisfies a number of adequacy criteria.
Lecture Notes in Computer Science, 2012
This paper generalizes the notion of monotonicities to opposition properties (OPs). Some proposit... more This paper generalizes the notion of monotonicities to opposition properties (OPs). Some propositions regarding the OPs of determiners will be proposed and proved. We will also define the notion of OP-chain and deduce a condition that enables us to determine the OPs of an iterated quantifier in its predicates based on the OPs of its constituent determiners.
Around and Beyond the Square of Opposition, 2012
Volume of Abstracts Non-classical Modal and …
The studies on interrogatives in logic and formal semantics have been a difficult task because th... more The studies on interrogatives in logic and formal semantics have been a difficult task because there is not an intuitive and uncontroversial notion of truth values for interrogatives. Thus we see different frameworks for interrogatives with different merits and demerits. In this paper, I will formulate a theoretical framework that combines Gutierrez-Rexach 's GQT-based framework (in [4, 5]) and Nelken and Francez's bilattice-based framework (in [7, 8]) for interrogatives and derive certain valid inferential patterns involving interrogatives based on this framework. Gutierrez-Rexach's framework is based on Generalized Quantifier Theory (GQT) and treats a WH-word as an interrogative quantifier (IQ) that requires, in addition to the ordinary arguments, an "answer argument" to make a complete proposition. For instance, the truth condition of "who" is represented by "who(Y)(X) = 1 iff P ERSON ∩ Y = X", where X is the answer argument. Thus, under this approach the question "Who sang" is semantically equivalent to the noun phrase "person(s) who sang". Nelken and Francez's framework assumes that interrogatives are of the same semantic type as that of propositions. The denotation of declaratives and interrogatives are thus both truth values. However, to distinguish the two types of sentences, they adopt 5 truth values which are arranged in 2 lattices (hence a "bilattice"). For declaratives, there are 3 truth values: t ("known to be true"), f ("known to be false") and uk ("unknown whether true or false"). For interrogatives, they borrow the concept of "resolvedness" from [1] and assume 2 truth values: r ("resolved") and ur ("unresolved"). The two groups of truth values are related by the resolvedness conditions of interrogatives. For illustration, consider the polar question "Did Mary kiss John" whose formal representation and resolvedness condition is " ?(KISS(m, j)) = r iff KISS(m, j) ∈ {t, f }" (where p denotes the truth value of p), meaning that "Did Mary kiss John" is resolved iff it is known whether Mary kissed John. In this paper, I will develop a formal framework for interrogatives that is based on Nelken and Francez's framework but with substantial modification. The reason for choosing Nelken and Francez's framework as the basis is that their
New Frontiers in Artificial Intelligence. JSAI-isAI 2018., 2019
This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive... more This paper proposes a new treatment of quantifiers under the theoretical framework of Inquisitive Semantics (IS). After discussing the difficulty in treating quantifiers under the existing IS framework, I propose a new treatment of quantifiers that combines features of IS and the Generalized Quantifier Theory (GQT). My proposal comprises two main points: (i) assuming that the outputs of all quantifiers given non-inquisitive inputs are non-inquisitive; and (ii) deriving a predicate X * of type s→(e n →t) corresponding to each predicate X of type e n →T. By using X * , we can then restore the traditional treatment of GQT under the IS framework. I next point out that to properly handle the pair list reading of some questions with ''every'', we have to revert to the old treatment of every. I also introduce (and prove) a theorem that shows that the new treatment of every is just a special case of the old treatment, and conclude that the new treatment of all quantifiers other than every plus the old treatment of every is sufficient for the general purpose of treating quantified statements and questions.
This paper develops a theory on opposition inferences – quantifier inferences involving the contr... more This paper develops a theory on opposition inferences – quantifier inferences involving the contradictory, contrary and subcontrary relations. After the basic notions associated with opposition inferences, including opposition properties (OPs), o-sensitivities, etc., are defined as generalizations of the notions associated with monotonicity inferences, a number of theorems for determining the o-sensitivities of various types of monadic generalized quantifiers (GQs), including determiners, type <1> GQs and structured GQs, are proposed and proved, resulting in a classification of the most commonly used monadic GQs according to their OPs. For iterated polyadic GQs, the notion of OP-chain is defined. A principle that enables one to determine the o-sensitivities of an iterated GQ according to the o-sensitivities of its constituent monadic GQs is then proposed. The o-sensitivities of GQs viewed as sets and arguments of other GQs and logical operators, particularly the negation operator, are also discussed. Finally, opposition inferences are compared and contrasted with monotonicity inferences. It is finally concluded that o-sensitivities are independent of monotonicities, and opposition inferences are not subsumable under monotonicity inferences.