Vector Semantics

Preface............................................................... vii

1 Foundations of non-compositionality.................................

1.1 Background ...................................................

1.2 Lexicographic principles ........................................

1.3 The syntax of definitions ........................................

1.4 The geometry of definitions......................................

1.5 The algebra of definitions .......................................

2 From morphology to syntax ........................................ 23

2.1 Lexical categories and subcategories .............................. 23

2.2 Bound morphemes ............................................. 25

2.4 Linking....................................................... 39

2.5 Naive grammar ................................................ 46

3 Time and space.................................................... 53

3.1 Space ........................................................ 54

3.2 Time ......................................................... 59

3.3 Indexicals, coercion ............................................ 62

3.4 Measure ...................................................... 65

4 Negation.......................................................... 69

4.1 Negation in the lexicon.......................................... 71

4.2 Quantifiers .................................................... 73

4.3 Negation in compositional constructions ........................... 74

4.4 Double negation ............................................... 77

4.5 Compositional quantifiers ....................................... 78

4.6 Disjunction ................................................... 80

4.7 Scope ambiguities.............................................. 81

4.8 Conclusions ................................................... 82

5 Valuations ........................................................ 83

5.1 Introduction ................................................... 83

5.2 The likeliness scale............................................. 84

5.3 Naive inference (likeliness update) ................................ 86

5.4 Learning...................................................... 89

6 Modality ......................................................... 93

6.1 The deontic world .............................................. 93

6.2 Epistemic and autoepistemic logic ................................ 93

6.3 Defaults ...................................................... 93

7 Adjectives, gradience, implicature ................................... 95

7.1 Adjectives .................................................... 95

7.2 Gradience..................................................... 96

7.3 Implicature.................................................... 96

7.4 The elementary pieces .......................................... 97

7.5 The mechanism ................................................ 100

7.6 Memory ...................................................... 103

7.7 Conclusions ................................................... 104

8 Trainability and real-world knowledge............................... 107

8.1 Proper names.................................................. 107

8.2 Trainability ................................................... 109

9 Dynamic