A Neural-Symbolic Approach to the Contemporary Theory of Metaphor - - PowerPoint PPT Presentation

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Philosophy and Machine Learning - Workshop

(@ Neural Information Processing Systems 2011)

A Neural-Symbolic Approach to the Contemporary Theory of Metaphor

Guido Boella - University of Turin, Italy Artur d’Avila Garcez - City University, London Alan Perotti - University of Turin, Italy

1 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

The Classical Theory of Metaphor

Do not go gentle into that good night. Dylan Thomas Dates back to Aristotle Metaphors: Instances of novel poetic language in which words (like go and night) are not used in their normal everyday sense. Defines metaphor as a matter of language Describes metaphorical expression as mutually exclusive with the realm of ordinary language

2 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

The Contemporary Theory of Metaphor

”The generalizations governing poetic metaphorical expressions are not in language, but in thought: they are general mappings across conceptual domains. Moreover, these general principles which take the form of conceptual mappings, apply not just to novel poetic expressions, but to much of ordinary everyday language. In short, the locus of metaphor is not in language at all, but in the way we conceptualize one mental domain in terms of another. The general theory of metaphor is given by characterizing such cross-domain

• mappings. And in the process, everyday abstract concepts like

time, states, change, causation, and purpose also turn out to be metaphorical.” [G. Lakoff, The Contemporary Theory of Metaphor]

3 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

The Contemporary Theory of Metaphor

Love IS A journey We’ve hit a dead-end street We can’t turn back now We‘re driving in the fast lane on the freeway of love Relationship AS vehicle Lovers AS passengers Alternatives AS crossroads

4 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Source and target domain

a b x y T S

fT(x)? fT? fS

5 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Mapping over domains a b x y

m n

T S a b x y T S

fT n(fS(m(x))=y fT(x) = y fS fS

6 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

The Mapping

Given two algebraic structures A and B, a function m is a monomorphism iff: m is injective ∀ n-ary operation f over the structures, ∀ n-tuple x1, .., xn of A, m(fA(x1, .., xn)) = fB(m(x1), .., m(xn))

where fA and fB represent f over A and B respectively.

In our setting, we can’t compute fA, and we wonder what could fA(x1, .., xn) be. Since m is injective, it can be inverted. Let n be the inverse function of m. The following transformations hold: fA(x1, .., xn) ≡1 n(m(fA(x1, .., xn))) ≡2 n(fB(m(x1), .., m(xn))) Where (≡1) is justified because m and n are inverse functions (and therefore n(m(x)) ≡ x) and (≡2) follows from the definition

• f monomorphism.

7 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Knowledge representation and Learning

The Neural-Symbolic paradigm We model the source and target domains as connectionist inductive learning and logic programming (CILP) system The CILP system ([1]) is a neural-symbolic system showing a

• ne-to-one correspondence between logic programming and neural

networks that are trainable by backpropagation. We model the mapping functions m and n as a single restricted Boltzmann machine (RBM). A RBM defines a probability distribution P(V=v,H=h) over pairs of vectors v and h encoded in these layers, where v encodes the input data in binary or real values and h encodes the posterior probability P(H|v).

8 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Architecture a b x y

m n

T S

n(fS(m(x))=y fS

?

9 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Source domain

Reverse Put gas Find other path R1 Dead-end road Wrong turn R2 Low on gas R3 R4

10 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Mapping

Dead-end road Reverse Wrong turn Find other path Low

• n gas

Put gas No promotions Apply for a job Resign Volunteer for

• vertime

Low salary

11 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Target domain

Resign Volunteer for overtime Apply for a job No promotions Low salary

?

12 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Step one: mapping

Dead-end road Reverse Wrong turn Find other path Low

• n gas

Put gas No promotions Apply for a job Resign Volunteer for

• vertime

Low salary

13 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Step two: computing

Reverse Put gas Find other path R1 Dead-end road Wrong turn R2 Low on gas R3 R4

14 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Step three: mapping back

Dead-end road Reverse Wrong turn Find other path Low

• n gas

Put gas No promotions Apply for a job Resign Volunteer for

• vertime

Low salary

15 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Step four: learning

Resign Volunteer for overtime Apply for a job No promotions Low salary

!

R1

16 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Applications

Knowledge (and reasoning patterns) recycling Software reuse and encapsulation Blackbox use via interfaces Commitment-based multiagent interaction

17 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Conclusions

In this work, we model the cognitive theory of metaphor, as defined by Lakoff, as a monomorphism. With this approach we are able to prove that local computation can be performed over a more familiar domain. We propose a framework that relies on the CILP system and RBMs and allows to perform learning and reasoning

• ver unknown domains.

18 / 19

Contemporary Theory of Metaphor Sets, Functions and Networks Example Applications and conclusion

Thank you.

References:

1 A. d’Avila Garcez, K. B. Broda, and D. M. Gabbay.

Neural-Symbolic Learning Systems. Per- spectives in Neural

• Computing. Springer, 2002.

2 L. de Penning, A. S. d’Avila Garcez, L. C. Lamb, and J.-J. C.

• Meyer. A neural-symbolic cogni- tive agent for online learning and
• reasoning. In IJCAI, pages 1653–1658, 2011.

3 G. E. Hinton. Training products of experts by minimizing contrastive

• divergence. Neural Com- put., 14:1771–1800, August 2002.

4 G. Lakoff. The Neural Theory of Metaphor and Thought, page

17–39. Cambridge University Press, Cambridge, 2008.

5 G. Lakoff and M. Johnson. Metaphors we Live by. University of

Chicago Press, Chicago, 1980.

6 P. Smolensky. Information processing in dynamical systems:

foundations of harmony theory, pages 194–281. MIT Press, Cambridge, MA, USA, 1986.

19 / 19