When Compositionality Fails to Predict Systematicity Reinhard Blutner, Petra Hendriks, Helen de Hoop, Oren Schwartz

The immediate appeal of compositionality: Frege (1923) It is astonishing what language can do. With a few syllables it can express an incalculable number of thoughts, so that even a thought grasped by a terrestrial being for the first time can be put into a form of words which will be understood by someone to whom the thought is entirely new. This would be impossible, were we not able to distinguish parts in the thoughts corresponding to the parts of a sentence, so that the structure of the sentence serves as the image of the structure of the thoughts.

Compositionality The meaning of a complex expression is determined by its structure and the meanings of its constitutents. equivalently There is a homomorphism between the syntactic term algebra to the algebra of meanings.

Compositionality Compositionality is necessary to explain the productivity of language. Compositionality entails productivity.

Systematicity The term and empirical hypothesis was introduced by Fodor & Pylyshyn (1988), who didn’t attempt a precise definition of the concept or a complete description of the empirical phenomenon. Van Gelder & Niklasson (1994) summarize F&P’s notion of systematicity as: [the] ability to do some things of a given cognitive type (including at least “thinking a thought” and making an inference) is intrinsically connected with their ability to do other, structurally related things of that type.

Systematicity When an agent understands the expressions brown triangle and black square, she understands the expressions brown square and black triangle as well. Does compositionality entail systematicity?

A Classical Example Agent understands brown triangle and black square. She constructs the conceptual representations BROWN  TRIANGLE and BLACK  SQUARE (via compositionality). She knows the truth conditional impact of the corresponding constitutents, and she extracts the lexicon entries: brown -> BROWN, square- >SQUARE, etc. Using these, she constructs BROWN  SQUARE and BLACK  TRIANGLE (via compositionality) Thus compositionality may derive systematicity

Systematicity If an agent understands within an hour and without a watch, does she also understand within a watch and without an hour? (Szabo 2004)

Our View Language is (mostly) systematic and compositional, but not always. Traditional semantic analyses have difficulty with cases where the systematicity of meaning is weak or missing. Connectionist models are well suited to handling these types of cases, and can account for the semantic contribution of a constitutent that is both systematic (in general) and idiosyncratic (in certain cases).

Why compositionality fails to explain systsematicity In his “Grundlagen der Mathematik” Frege (1884) noticed the context- dependence of words (and took this as an argument against compositionality in NL) “One should ask for the meaning of a word only in the context of a sentence, and not in isolation.“

Empirical Phenomena Quine (1960) was the first who noted the contrast between red apple (red on the outside) and pink grapefruit (pink on the inside). Lahav (1993) argues that an adjective such as brown doesn’t make a simple and fixed contribution to any composite expression in which it appears: brown cow, brown crystal, brown book, brown newspaper

Empirical Phenomena Different colors typically denoted by red in red apple and red hair. the actual color value deviates in a systematic way from the prototypical color value that can be assigned to the color adjective in isolation – in dependency on the conceptual properties of the modified noun Similarly, the same color is often described with different adjectives In Japanese, brown sugar, aka-zatoo (lit. ‘red sugar’) comes in the same range of colors as shira-miso, (lit. ‘white bean paste’)

Three consequences Intersectivity, ||A(B)|| = ||A(x)||  ||B||, doesn’t hold, even for most ‘absolute’ adjectives Systematicity statements cannot be derived from compositionality in these cases Encyclopedic knowledge is required to determine the truth conditional content of an utterance (explicature in Relevance Theory).

A Related Phenomenon Typicality A specific instance of a red apple is more typical of a “red apple” than of an “apple” Incompatible Conjunctions The typicality effects are greater for “incompatible conjunctions” (striped apple) than for “compatible conjunctions” (green apple)

A Concrete Question How should we account for the semantic contribution of an (absolute) adjective to an (Adjective Noun) N complex expression in the face of these phenomena?

Radical underspecification with contextual enrichment small  x small(x,N) * small terrier  x [small(x,N) & terrier(x)] Analogously for red apple with place-holders for the relevant parts red  x [part(Y,x) & red(Y)] red apple  x [part(Y,x) & red(Y) & apple(x)] How to determine the proper values for N and Y, respectively? Contextual enrichment, as in Probabilistic Theory of Relevance (van Rooy 2000) * with small(x,N)  size(x) < N

Problems with underspecification Does not really clarify how to determine the border line between the underspecified representation and the contextual enrichment It is difficult to see how the available mechanisms account for the prototype effects found in adjectival modification

A connectionist approach Inspired by the (symbolic) selective modification model (Smith, Osherson, Rips & Keane 1988) Prototype representations consisting of Symbolic, structured concepts Attribute-value pairs, weighted by salience Modifiers act on prototypes by increasing salience of attribute and changing its value Tversky’s (1977) contrast rule for similarity

A connectionist approach AdjectiveNoun Conceptual Layer

A connectionist approach AdjectiveNoun Conceptual Layer Color

A connectionist approach AdjectiveNoun Conceptual Layer Taste

A connectionist approach AdjectiveNoun Conceptual Layer Peel

A connectionist approach AdjectiveNoun Conceptual Layer Pulp

A connectionist approach AdjectiveNoun Conceptual Layer Color Peel (Color x Peel)

A connectionist approach AdjectiveNoun Conceptual Layer red

A connectionist approach AdjectiveNoun Conceptual Layer white

A connectionist approach AdjectiveNoun Conceptual Layer red peel white pulp red

A connectionist approach AdjectiveNoun Conceptual Layer

A connectionist approach AdjectiveNoun Conceptual Layer

A connectinist approach Default uniform connections within conceptual layer In training, instances are presented at the conceptual layer and at the (localist) adjective and noun layers. The prototypes learned by the model are found by turning on units in the adjective and noun layers and letting the network settle into a representation at the conceptual layer.

Prototype effects Using Tversky's (1977) contrast rule (formulated for activation vectors) sim(s,t) =  i min(s i,t i )   i |s i  t i | sim(s red apple, t 1 ) > sim(s apple, t 1 ) sim(s purple apple,t 2 )  sim(s apple,t 2 ) > sim(s red apple,t 1 )  sim(s apple,t 1 ) t 1 = a red apple, t 2 = a purple apple

Conclusions 1. Compositionality alone is not formally restrictive enough to explain the type of productivity in NL 2. Semantic contributions of constituents to their complex expressions are more complex and less systematic than we might expect 3. Encyclopedic knowledge is necessary to account for the variability in the semantic contribution of constituents to complex phrases 4. Connectionist approaches easily handle the accumulation and application of this knowledge.