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**1** | a | Krifka's puzzle | morphologically negated antonyms | *unhappy* < *not happy* < *not unhappy* < *happy* | RSA for gradable adjectives with compositional negation (fuzzy logic) and free $\theta_{\text{unhappy}}$ and $\theta_{\text{happy}}$
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1 | b | Krifka's puzzle | lexicalized antonyms | *short* < *not tall* < *not short* < *tall* | same as 1a
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**2** | a | Horn's puzzle | asymmetries negAnt | *unhappy* - *not happy* $<^?$ *happy* - *not unhappy*; **alt** var(*not happy*) $<^?$ var(*not unhappy*) | ? same as 1 but with politeness ?
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2 | b | Horns's puzzle | asymmetries lexical | same as 2a but for *tall* and *short* | same as 2a
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**3** | - | Horns's puzzle | asymmetries with intensifiers | *not very happy* $\leadsto$ *rather sad***but***not very sad* $\leadsto$ *still sad*| politeness for asymetry; $[\![\text{very A}]\!] = \theta_A + x$ or $[\![\text{very A}]\!] = \theta_A$ but more costly
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**4** | a | Kennedy's puzzle | scale structure collapse; morphological | *imperfect* = *not perfect* < *perfect* = *not imperfect* | single $\theta$ (free or fixed); or like in 1 but with different priors e.g., $d \sim Beta(1,10)$
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4 | b | Kennedy's puzzle | scale structure collapse; lexical | *clean* = *not dirty* < *dirty* = *not clean* | same as 4a
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**5** | b | Leffels's puzzle | "not very" | *not very tall* $\not\leadsto$ *tall*, **but***not very late* $\leadsto$ *late* | ? combine 3 and 4 ?
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