The Nature of Systematicity in Natural Language. 27 October, 2004Blutner & Spenader KNAW-Colloquium...

The Nature of Systematicity in Natural Language

27 October, 2004 Blutner & Spenader KNAW-Colloquium 2

Systematicity• Introduced in Fodor & Pylyshyn (1988):

– A feature of cognition, inferential coherence

– “The ability to produce/understand some sentences is intrinsically connected to the ability to produce/understand certain others.” (p. 37)

– Fodor & Pylyshyn give no clear definition (see van Gelder) and only two examples


The operationalization of systematicity

• When an agent understands the sentence Peter likes Maria, she understands the sentence Maria likes Peter as well.

• When an agent understands the expressions brown triangle and black square, she understands the expressions brown square and black triangle as well.


Outline• What is systematicity?

– and to what degree is our understanding systematic

• Does compositionality entail systematicity?– No, because

• context-dependence of meaning• intrusion of encyclopedic knowledge on language

understanding

• What are appropriate models of natural language understanding if systematicity is taken into account ?


Is our understanding systematic ?

(1) Do all who understand good writer and bad teacher also understand bad writer and good teacher?

(2) Do all who understand within an hour and without a watch also understand within a watch and without an hour? (Szabó 2004).

(3) Does a child who understands Mom drives me to kindergarten also understand I drive mom to kindergarten ?


Understanding is not Systematic• Language understanding is not completely

systematic.– This is because the world is not entirely systematic– A. Clark (1996) “Instead of treating [systematicity] as a property

to be directly induced by a canny choice of basic architecture, it may be fruitful to try to treat it as intrinsic to the knowledge we want a system to acquire.”

• A good model of language – explains the systematic patterns of our language understanding– gives an account of when and why we find patterns that are not

really predictable.


Does compositionality entail systematicity?

• Compositionality: The meaning of a compound expression is determined by the meanings of its constituents and the syntactic way these constituents are combined.

• Systematicity: there are predictable patterns among the sentences we understand.


The present position

• Compositionality does not entail systematicity

• Systematicity is possible without compositionality


How to derive systematicity?

• Fodor & Pylyshyn:

– in the presented case the systematicity of linguistic competence derives from the fact that the syntactic operation of modification relates to the semantic operation of conjunction (or intersection)


Understanding NL Expressions

• According to the classical view, the phrase 'understanding natural language expressions' means more than just fixing a denotation.

• We 'understand' a phrase as brown triangle if (i) we are able to grasp the corresponding conceptual representation (browntriangle)(ii) the corresponding conceptual components have an known truth functional content(iii) With the help of the involved logical operators it is possible to determine the truth conditions of the whole phrase under discussion


Sytematicity Clauses: A sample “derivation”

• understanding the expressions brown triangle and black square

• deriving browntriangle and blacksquare• extracting the lexicon entries

brown brown, black black, triangle triangle, square square.

• Calculating the corresponding conceptual representations for brown square and black triangle : brownsquare and blacktriangle

• calculating the truth-conditional impact of these forms• understanding the expressions brown square and black

triangle


But does this actually work?

• This proposal doesn’t work for even the simplest of adjective-noun combinations

• Intersection doesn’t give you the systematic inferences that you would expect or would desire


Why compositionality fails to explain systematicity


Context dependence• In his “Grundlagen der Mathematik” Frege (1884)

noticed the context-dependence of words (and took this as a 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“

• There are compositional models of semantics that take context dependence into account

• We can use the phenomenon of context-dependence for construing an argument against deriving systematicity from compositionality.


What is a white triangle?

A

A

The black triangle

The white triangle

From P. Bosch (2002) Explaining semantic productivity. Paper presented at the Symposium on Logic and Creativity: Integrating Categorial Rules and Experience, Osnabrück.


Context Dependence?Does the proposition expressed by ‘black triangle’ depend on the contrast set?

Answer 1: No. The contrast set is relevant only for choosing a good/appropriate/optimal referring expressionPROBLEM: ? Triangle 1 is black and white (in one and the same respect)

Answer 2: Yes. Context-dependency of utterance meaning is widely accepted and also applies here(Kaplan’s characters; Haas-Spohn’s ‘hidden indexicality’; e.g. in connection with natural kind terms like water; theories of underspecification, e.g. Carstons 2002; explicatures in relevance theory)


What is a red apple?(a) a red apple [red peel]

(b) a sweet apple [sweet pulp]

(c) a reddish grapefruit [reddish pulp]

(d) a white room/ a white house [inside/outside]

A red apple?A red apple?

No, it’s a green apple No, it’s a green apple but it’s red on the but it’s red on the insideinside


More examples

• Quine (1960) was the first who noted the contrast between red apple (red on the outside) and pink grapefruit (pink on the inside).

• In a similar vein, 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:

In order for a cow to be brown most of its body’s surface should be brown, though not its udders, eyes, or internal organs. A brown crystal, on the other hand, needs to be brown both inside and outside. A brown book is brown if its cover, but not necessarily its inner pages, are mostly brown, while a newspaper is brown only if all its pages are brown. For a potato to be brown it needs to be brown only outside, ... (Lahav 1993: 76).


Three consequences• Intersectivity, ||A(B)|| = ||A()||||B||, doesn’t hold for

most ‘absolute’ adjectives and Fodor & Pylyshyn's compositional analysis breaks down

• Systematicity statements cannot be derived from compositionality if intersectivity fails

• Encyclopedic knowledge is required to determine the truth conditional content of an utterance (explicature in Relevance Theory)

• When an agent understands the expressions red apple (RED PEEL) and sweet grapefruit (SWEET PULP), then it's likely that she understands red grapefruit (RED PULP) and sweet apple (SWEET PULP) as well.


The Theoretical Part


Approach 1: The underspecification view

• Radical underspecification augmented 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 partsred 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?

* with small(x,N) size(x) < N


A mechanism of contextual enrichment

• The variables are specified in a way that maximizes the relevance of the corresponding question

- Small Terrier: Is a (randomly selected) terrier smaller than N?

- Red Apple: What color is part Y (of a randomly selected apple)?

• Probabilistic Theory of Relevance, see Robert van Rooy (2000): Comparing Questions and Answers: A bit of Logic, a bit of Language, and some bits of Information


Entropy of a question

• The semantic value of a question Q is a partition {q1, ..., qn} of the domain Ω.

inf(q) = -log2 prob(q) information = measure of surprise

Entropy of a question Q• The entropy of a question expresses our

uncertainty about the answer. Good questions have high entropies

)inf(q)prob(qE(Q)i

ii


What is a black triangle?

What color is the inner part? E=1 E=0

What color is the outer part? E=0 E=1


What is a red apple?

A red apple?A red apple?What color is an apple?Q1 What color is its peel?Q2 What color is its pulp?

E(Q1) >> E(Q2) Color differences between apples are expected for the peel and not for the pulp.

Therefore, the presented apple is considered as a green apple (inside red) and not as a red apple (outside green).This can change if we update our probability distribution.


Problems with the underspecification view

• Requires rather clumsy lexical entries

• How much of the peel of an apple has to be red in order to call it a red peel?

• This theory does not really clarify how the border line between the underspecified representation and the contextual enrichment is ever to be determined


Approach 2: Adnominal functors

• Take Montague (1970) as its starting-point and take adjectives as adnominal functors.

• red(X) means roughly the property– (a) of having a red inner volume if X denotes

fruits only the inside of which is edible– (b) of having a red surface if X denotes fruits

with edible outside– (c) of having a functional part that is red if X

denotes tools, …


Montague and systematicity clauses

• We cannot derive the intended systematicity clauses if we realize compositionality via adnominal functors!

• f(a) = p, g(b) = q

f(b) = ?, g(a) = ?• Compositionality is often very simple to realize if (higher

order) functions are introduced• In many cases, this idea realizes generalizations to the

worst case• Unfortunately, we cannot derive interesting

systematicity clauses from this style of compositionality!


Constraining the models• Additional constraints are required that restrict

the set of possible models• I will assume that these constraints can be

extracted from a Bayesian picture of the mental encyclopedia

• This is not so different from assuming a system of violable constraints (ranked defaults instead of inviolable meaning postulates)

• Systematicity mainly results from these additional constraints!


Approach 3: Connectionst model of adjectival modification*• Overcoming the gap between compositionality

and systematicity• Modeling both the truth-functional aspects of

adjectival modification and the typicality effects (Kamp & Partee 1995)

• Connectionist variant of the selective modification model of Smith et al. (1988)

• It shares with this model the (localist) attribute-value representation for the prototypes (apple, grapefruit, …) and for the relevant instances.

* From Blutner, Hendriks, de Hoop, & Schwartz (to appear): When compositionality fails to predict systematicity


The simplified modelAdjective

FormTasteColor

Noun

Conceptual Layer


Conclusions(1) Systematicity of natural language

understanding is intimately related to knowledge about the world

(2) Systematicity clauses have to reflect this reality

(3) A compositional representational system doesn’t give you systematicity of understanding because context-dependency of lexical meaning and world-knowledge both affect understanding


Conclusions cont.(4) If lexical principles like “intersectivity” fail

(because of context dependency) systematicity clauses can no longer be derived from compositionality

(5) A Bayesian and/or connectionist picture of the mental encyclopedia is the key for deriving systematicity clauses!

(6) The principle of compositionality of meaning may be interesting not as part of cognitive architecture, but as a consequence of evolutionary learning (e.g. Kirby).

The Nature of Systematicity in Natural Language. 27 October, 2004Blutner & Spenader KNAW-Colloquium...

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