Boolean Semantics for Natural Language

Keenan, Edward L.; Faltz, Leonard M.

doi:10.1007/978-94-009-6404-4

Cited by 140 publications

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“…Observe that (92) and (94) This allows for a definition of conjunction and disjunction across different types of questions, and even across questions and that-clauses, using the techniques of typelifting of Boolean structures developed in Keenan & Faltz (1985). Cross-categorial versions of conjunction, disjunction, and negation can be defined as follows: Here, f ranges over functions whose domains include M and M'.…”

Section: Embedded Questionsmentioning

confidence: 99%

For a Structured Meaning Account of Questions and Answers

Krifka¹

2001

Audiatur Vox Sapientiae

152

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Section: Embedded Questionsmentioning

confidence: 99%

For a Structured Meaning Account of Questions and Answers

Krifka¹

2001

Audiatur Vox Sapientiae

152

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“…We arrive at such interpretations by applying the well-known boolean analysis of conjunction, according to which it behaves as set-theoretic intersection (Keenan and Faltz 1985;Partee and Rooth 1983), and combining it with a distributivity operator that shifts a VP into one that holds of a plural individual such as the boys iff that VP holds of each atomic part of that individual, i.e. each boy (Link 1983).…”

Section: Introductionmentioning

confidence: 99%

Concept Typicality and the Interpretation of Plural Predicate Conjunction

Poortman

2017

Language, Cognition, and Mind

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This chapter studies the interpretations of plural sentences with conjoined predicates, e.g. The boys are sitting and cooking and The boys are waving and smiling. Such sentences are sometimes interpreted intersectively, sometimes non-intersectively (or 'split'), and sometimes both interpretations appear to be allowed. This is surprising, since the logical structure of these sentences is identical, i.e. they differ only with respect to content words (e.g. sitting, cooking vs. waving, smiling). I propose that the logical interpretation of these sentences is systematically affected by lexical information tied to the complex predicate in the sentences, specifically their so-called typicality effects. With a set of experiments, I show that (a) the acceptability of a sentence in a non-intersective situation can be expressed in terms of a continuum and (b) each acceptability proportion is predicted by the typicality of the two conjoined predicates applying simultaneously. This way, I specify at least one of the relevant pragmatic considerations that determine the interpretation of a plural sentence with conjunctive predicates. More generally, these results stress the importance of conceptual structure of predicates in semantic theories of language.

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“…As the linguist Hurford (1987) pointed out, ''the commonest indicators of addition" across languages such as Arabic (wa), English (and), French (et) and German (und), ''are words which also happen to indicate the logical conjunction of propositions" (p. 226). Moreover, several linguists have proposed distinguishing two ands in English (Partee & Rooth, 1983;Keenan & Faltz, 1985). Keenan and Faltz, for instance, proposed a distinction between the ''lower order and we have been using which forms intersections and a higher order one which (roughly) forms sets" (p. 270).…”

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The conjunction fallacy and the many meanings of and

2008

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a b s t r a c tAccording to the conjunction rule, the probability of A and B cannot exceed the probability of either single event. This rule reads and in terms of the logical operator^, interpreting A and B as an intersection of two events. As linguists have long argued, in natural language ''and" can convey a wide range of relationships between conjuncts such as temporal order (''I went to the store and bought some whisky"), causal relationships (''Smile and the world smiles with you"), and can indicate a collection of sets rather than their intersection (as in ''He invited friends and colleagues to the party"). When ''and" is used in word problems researching the conjunction fallacy, the conjunction rule, which assumes the logical operator^, therefore cannot be mechanically invoked as a norm. Across several studies, we used different methods of probing people's understanding of and-conjunctions, and found evidence that many of those respondents who violated the conjunction rule in their probability or frequency judgments inferred a meaning of and that differs from the logical operator^. We argue that these findings have implications for whether judgments involving ambiguous and-conjunctions that violate the conjunction rule should be considered manifestations of fallacious reasoning or of reasonable pragmatic and semantic inferences.Ó 2008 Elsevier B.V. All rights reserved.. . .it is a mistake to analyze natural language words like and as being identical to entities of the man-made logical terminology which so clearly derives from natural language (rather than the other way around) and so clearly has needs and purposes distinct from those of natural language (Sweetser, 1990, p. 92).One of the most frequent words in the English language is and. In Leech, Rayson, and Wilson's (2001) analysis of word frequencies in a 100 million word collection of samples of written and spoken language (the British National Corpus) the unremarkable three-letter word ''and" is the third most frequent word. Its commonness and plainness, however, do not mean that the most general connective in the English language lacks the ability to convey a wide range of relationships between the states of affairs described by the conjuncts. In fact, one reason for linguists' enduring fascination with and is that among all coordinating conjunctions (e.g., or, but, nor) it has the least semantic and syntactic limits, the least specific meaning, and the highest context dependency (Lang, 1991).Take, for instance, the use of and in (1): (1) Her husband is in hospital and she is seeing other men.As Kitis (2000) pointed out, the and in (1) does much more than conjoin the two clauses. Rather, it functions as an ''emotional device" that communicates the speaker's emotional attitude, surprise, or even outrage.The notion of and's context dependency stands in stark contrast with the highly constrained meaning of the logical and operator (^). The logical^represents the Boolean intersection of two sets. For illustration, if set A contains all even numbers (mu...

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Boolean Semantics for Natural Language

Cited by 140 publications

References 0 publications

For a Structured Meaning Account of Questions and Answers

For a Structured Meaning Account of Questions and Answers

Concept Typicality and the Interpretation of Plural Predicate Conjunction

The conjunction fallacy and the many meanings of and

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