ContentsPreface............................................................... 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 2.3 Relations ..................................................... 30 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 5.5 Conclusions ................................................... 91 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 
