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.

CompositionalityThe 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

BROWNTRIANGLE and BLACKSQUARE (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 BROWNSQUARE and BLACKTRIANGLE (via compositionality)

Thus compositionality may derive systematicity

SystematicityIf 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 ConjunctionsThe 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 underspecificationwith 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 approachAdjective Noun

Conceptual Layer

A connectionist approachAdjective Noun

Conceptual Layer

Color

A connectionist approachAdjective Noun

Conceptual Layer

Taste

A connectionist approachAdjective Noun

Conceptual Layer

Peel

A connectionist approachAdjective Noun

Conceptual Layer Pulp

A connectionist approachAdjective Noun

Conceptual Layer

Color

Peel

(Color x Peel)

A connectionist approachAdjective Noun

Conceptual Layer

red

A connectionist approachAdjective Noun

Conceptual Layer

white

A connectionist approachAdjective Noun

Conceptual Layer red peelwhite pulp

red

A connectionist approachAdjective Noun

Conceptual Layer

A connectionist approachAdjective Noun

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(si,ti) i |si ti|

sim(sred apple, t1) > sim(sapple, t1)

sim(spurple apple,t2)sim(sapple,t2) > sim(sred apple,t1)sim(sapple,t1)

t1= a red apple, t2 = a purple apple

Conclusions1. Compositionality alone is not formally restrictive

enough to explain the type of productivity in NL2. 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.