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43
Boolean Connection Algebras: A New Approach to the RegionConnection Calculus
 Artificial Intelligence
, 1999
"... The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and prove ..."
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Cited by 43 (7 self)
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The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and proves that these structures are equivalent to models of the RCC axioms. BCAs permit a wealth of results from the theory of lattices and boolean algebras to be applied to RCC. This is demonstrated by two theorems which provide constructions for BCAs from suitable distributive lattices. It is already well known that regular connected topological spaces yield models of RCC, but the theorems in this paper substantially generalize this result. Additionally, the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions. Keywords: RegionConnection Calculus, Qualitative Spatial Reasoning, Boolean Connection Algebra, Mer...
Type construction and the logic of concepts
 The Syntax of Word Meaning
, 2001
"... I would like to pose a set of fundamental questions regarding the constraints we can place on the structure of our concepts, particularly as revealed through language. I will outline a methodology for the construction of ontological types based on the dual concerns of capturing linguistic generaliza ..."
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Cited by 25 (7 self)
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I would like to pose a set of fundamental questions regarding the constraints we can place on the structure of our concepts, particularly as revealed through language. I will outline a methodology for the construction of ontological types based on the dual concerns of capturing linguistic generalizations and satisfying metaphysical considerations. I discuss what “kinds of things ” there are, as reflected in the models of semantics we adopt for our linguistic theories. I argue that the flat and relatively homogeneous typing models coming out of classic Montague Grammar are grossly inadequate to the task of modelling and describing language and its meaning. I outline aspects of a semantic theory (Generative Lexicon) employing a ranking of types. I distinguish first between natural (simple) types and functional types, and then motivate the use of complex types (dot objects) to model objects with multiple and interdependent denotations. This approach will be
Genitive Modifiers, Sorts, and Metonymy
, 2001
"... Our longterm goal is to contribute to the integration of formal and lexical semantics. Our more immediate theoretical starting point is the idea of text as theory, within a modeltheoretic semantic framework. We describe a set of empirical problems in the domain of genitive modifiers which offer ..."
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Cited by 10 (1 self)
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Our longterm goal is to contribute to the integration of formal and lexical semantics. Our more immediate theoretical starting point is the idea of text as theory, within a modeltheoretic semantic framework. We describe a set of empirical problems in the domain of genitive modifiers which offer a challenge to theories of the integration of lexical, compositional, and contextual information. After sketching a solution, we raise the issue of metonymy in the interpretation of genitives, and examine the role of sortal information in the specification of underspecified meanings and in processes of typeshifting and sortshifting, including metonymy.
Dependent plurals and plural meaning
, 2008
"... While writing this thesis, there were many things I wanted to get right. I wanted to get the data right. I wanted to get my analysis of the data right. I certainly wanted to get all my citations right, which can get pretty tricky when one is trying to finish a chapter at 2am. But if an error did cre ..."
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Cited by 3 (0 self)
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While writing this thesis, there were many things I wanted to get right. I wanted to get the data right. I wanted to get my analysis of the data right. I certainly wanted to get all my citations right, which can get pretty tricky when one is trying to finish a chapter at 2am. But if an error did creep in somewhere in the body of the thesis, that is not a disaster. Sooner or later, I will get a chance to correct it in a future publication. However, this part of the thesis, which sits right at the beginning but was among the last to be written, is different. I only have one opportunity to express, in print, how thankful I am to the people whose assistance was so important to me over the past years. Which is unfortunate, since if I were to truly elaborate all I am thankful for, these acknowledgements would be the lengthiest chapter of the thesis. But I hope this brief version will suffice in its stead. Nearly six years ago, when choosing among graduate programs, I picked NYU because I wanted to work with Anna Szabolcsi. Ever since, I had countless reasons to be thankful for that choice. Anna has consistently shown me incredible support and attention, and at the same time always demanded the highest standards from
LogAB: An algebraic logic of belief
 Proceedings of the Workshop on Relational Approaches to Knowledge Representation and Learning: Workshop of the 32nd German Conference on Artificial Intelligence. (2009) 2–18 Conditional Reasoning: The Monotonic Case 13
"... Abstract. LogAB is a family of logics of belief. It holds a middle ground between the expressive, but prone to paradox, syntactical firstorder theories and the often inconvenient, but safe, modal approaches. In this report, the syntax and semantics of LogAB are presented. LogAB is algebraic in the ..."
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Cited by 1 (1 self)
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Abstract. LogAB is a family of logics of belief. It holds a middle ground between the expressive, but prone to paradox, syntactical firstorder theories and the often inconvenient, but safe, modal approaches. In this report, the syntax and semantics of LogAB are presented. LogAB is algebraic in the sense that it is a language of only terms; there is no notion of a formula, only propositiondenoting terms. The domain of propositions is taken to be a Boolean lattice, which renders classical truth conditions and definitions of consequence and validity theorems about LogAB structures. LogAB is shown to be sufficiently expressive to accommodate complex patterns of reasoning about belief while remaining paradoxfree. A number of results are proved regarding paradoxical selfreference. They are shown to strengthen previous results, and to point to possible new approaches to circumventing paradoxes in syntactical theories of belief. 1
Superplurals in English
"... It is now widely believed among philosophers and logicians that ordinary English contains plural terms and plural predicates. For instance, (1a) Alice, Bob and Charlie cooperate should be seen as having the logical form (1b) F(aa) where ‘aa ’ is a plural term, and ‘F ’ a plural predicate. Following ..."
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Cited by 1 (0 self)
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It is now widely believed among philosophers and logicians that ordinary English contains plural terms and plural predicates. For instance, (1a) Alice, Bob and Charlie cooperate should be seen as having the logical form (1b) F(aa) where ‘aa ’ is a plural term, and ‘F ’ a plural predicate. Following George Boolos (1984) and others, many philosophers and logicians also think that plural expressions should be analysed as not introducing any new ontological commitments to some sort of ‘plural entities’, but rather as involving a new form of reference to objects to which we are already committed (for an overview and further details, see Linnebo 2004). For instance, the plural term ‘aa ’ refers to Alice, Bob and Charlie simultaneously, and the plural predicate ‘F ’ is true of some things just in case these things cooperate. A natural question that arises is whether the step from the singular to the plural can be iterated. Are there terms that stand to ordinary plural terms the way ordinary plural terms stand to singular terms? Let’s call such terms superplural. A superplural term would thus, loosely