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Taking ScopeThe Natural Semantics of Quantifiers$
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Mark Steedman

Print publication date: 2011

Print ISBN-13: 9780262017077

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262017077.001.0001

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Model Theory (with Stephen Isard)

Model Theory (with Stephen Isard)

Chapter:
(p.61) Chapter 5 Model Theory (with Stephen Isard)
Source:
Taking Scope
Author(s):

Mark Steedman

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262017077.003.0005

This chapter describes a model theory based on a standard statically scoped model theory for first-order logic and generalizes it to the case of relations whose arguments name propositions. It first discusses the nonstandard features of the model theory, with an emphasis on semantics and syntax, before turning to Skolem terms and negation, Maximal Participant Condition, and natural logic. The chapter also presents some examples in which all polarities are nonnegative and can be suppressed, and shows that conjunction, conditionals, and disjunction are all “filters on presuppositions.”

Keywords:   model theory, first-order logic, semantics, syntax, Skolem terms, negation, polarities, conjunction, conditionals, disjunction

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