Difference between revisions of "Models of metaphor in NLP"
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=== Met* System (Fass, 1991) === | === Met* System (Fass, 1991) === | ||
− | + | * Shutova thought it's the first attempt, but actually it's not the first one who explored this area. | |
− | - | + | * Using selectional preference and hand-coded knowledge base |
− | - | + | * 3-Stage Approaches |
+ | # Detect selectional preference violation | ||
+ | # If find violations, tested for being a metonymic relation using hand-coded patterns | ||
+ | # If not metonymy, search the knowledge base for a relevant analogy in order to discriminate metaphorical relations | ||
+ | * Problem | ||
+ | # Detects any kind of non-literalness in language (metaphors, metonymies and others), and not only metaphors | ||
+ | # Fail to detect high conventionality of metaphor | ||
=== Goatly (1997) === | === Goatly (1997) === | ||
+ | * Identify a set of linguistic cues indicate metaphor | ||
+ | ** ''metaphorically speaking, utterly, completely, so to speak and, surprisingly, literally. | ||
+ | '' | ||
=== Peters & Peters (2000) === | === Peters & Peters (2000) === | ||
− | + | * Detect figurative language in the WordNet | |
+ | * Search for '''systematic polysemy''', which allows to capture metonymic and metaphorical relations | ||
=== CorMet System (Mason, 2004) === | === CorMet System (Mason, 2004) === | ||
+ | * The '''first attempt for source-target domain mapping''' | ||
+ | * A corpus-based approach to find systematic variations in '''domain-specific selectional preferences''' | ||
+ | * Take Master Metaphor List (Lakoff et al., 1991) as baseline, and achieve an accuracy of 77% (judged by human) | ||
− | === TroFi System(Birke & Sarkar, 2006) === | + | === TroFi System (Birke & Sarkar, 2006) === |
+ | * Sentence clustering approach for non-literal language recognition | ||
+ | * Inspired by a similarity-based word sense disambiguation method | ||
+ | * Approach | ||
+ | # Use a set of seed sentences (human annotated) | ||
+ | # Compute similarity between (1) the sentence containing the word to be disambiguated and (2) all of the seed sentences | ||
+ | # Select the sense corresponding to the annotation in the most similar seed sentences | ||
+ | * F1-score = 0.538. But the task is not clearly defined. | ||
=== Gedigan et al. (2006) === | === Gedigan et al. (2006) === | ||
+ | * A survey-like work about literal and metaphorical uses of verbs | ||
+ | * Method | ||
+ | # Extract the lexical items whose frames are related to MOTION and CURE from FrameNet (Fillmore et al., 2003). | ||
+ | # Search the PropBank Wall Street Journal corpus (Kingsbury and Palmer, 2002) for sentences containing such lexical items and annotated them with respect to metaphoricity (by hand). | ||
+ | # Used PropBank annotation as features to train the maximum entropy classifier | ||
+ | * Accuracy = 95.12% | ||
+ | ** Very close to majority baseline (92.90%) => 92.00% of the verbs of MOTION and CURE in the Wall Street Journal corpus are used metaphorically. | ||
=== Krishnakumaran & Zhu (2007) === | === Krishnakumaran & Zhu (2007) === | ||
+ | * Deal with not only verbs, but also '''nouns and adjectives'''. | ||
+ | * Use hyponymy relation in WordNet and word bigram counts to predict metaphors at sentence level. | ||
+ | * Approach | ||
+ | ** '''Noun-Noun''': Given an '''IS-A''' metaphor, verify if the two nouns involved are in hyponymy relation in WordNet, if not, tag as a metaphor | ||
+ | ** '''Verb-Noun and Adjective-Noun''': Calculate bigram probabilities of verb-noun and adj-noun pairs, if the pair has low frequency, tag as a metaphor | ||
+ | * Fail to capture conventionalized metaphors (loose information compared of parsed text) | ||
== Metaphor Interpretation == | == Metaphor Interpretation == | ||
=== MIDAS System (Martin, 1990) === | === MIDAS System (Martin, 1990) === | ||
+ | * A Metaphor Interpretation, Denotation and Acquisition System (MIDAS) | ||
+ | * Capture hierarchical organization of '''conventional metaphors''' | ||
+ | * Idea | ||
+ | ** More specific conventional metaphors descend from the general ones | ||
+ | * Approach (modeling how novel metaphors are acquired) | ||
+ | # Given a metaphor example, search for a corresponding metaphor that would explain the anomaly. | ||
+ | # If not find: abstract it from the example to more general concepts and repeats search. | ||
+ | # If find a suitable general metaphor: create a mapping for its descendant (a more specific metaphor) based on this example. | ||
+ | * MIDAS has been integrated with the Unix Consultant (UC), the system that answers questions about Unix. | ||
=== KARMA System (Narayanan, 1997), ATT-Meta (Barnden and Lee, 2002) === | === KARMA System (Narayanan, 1997), ATT-Meta (Barnden and Lee, 2002) === | ||
+ | * Performing inferences about entities and events in the source and target domains for metaphor interpretation. | ||
+ | * Metaphor-based reasoning framework | ||
+ | * Approach | ||
+ | # Reasoning process relies on manually coded knowledge of the source domain. | ||
+ | # The results are then projected onto the target domain (using the conceptual mapping representation). | ||
+ | * Problems | ||
+ | # ATT-Meta concerns metaphorical and metonymic description of mental states and reasoning about mental states using '''first order logic'''. But they can not take natural language sentences as input. | ||
+ | # KARMA doesn't have this problem, it takes parsed text as input. | ||
− | === Veale and Hao | + | === Talking Points (Veale and Hao, 2008) === |
+ | * '''Fluid knowledge representation''' for metaphor interpretation and generation | ||
+ | * Approach | ||
+ | # From WordNet and from the web, extract a set of characteristics of (1) concepts belonging to source and target domains and (2) related facts about the world. | ||
+ | # Talking Points are then organized in Slipnet, a framework that allows for a number of insertions, deletions and substitutions in definitions of such characteristics in order to establish a connection between the target and the source concepts. | ||
+ | * Problem <br> Not evaluate to which extent their knowledge base are useful. | ||
=== Shutova (2010) === | === Shutova (2010) === | ||
+ | * Defines metaphor interpretation as a paraphrasing task | ||
+ | * Derive literal paraphrases for metaphorical expression | ||
+ | * Approach | ||
+ | # Given a context, apply a probabilistic model to rank all possible paraphrases for the metaphorical expression | ||
+ | # Use automatically induced selectional preferences to discriminate between figurative and literal paraphrases | ||
+ | * Tested on metaphors expressed by a verb, and achieve an accuracy of '''0.81'''. | ||
== Metaphor Resources == | == Metaphor Resources == | ||
+ | * '''Metaphor is a knowledge-hungry phenomenon.''' | ||
+ | * Two type of resources are needed | ||
+ | # Extensive manually-created knowledge-base (easier, most work is of this type) | ||
+ | # Robust knowledge acquisition system for interpretation of metaphorical expressions (much harder) | ||
+ | *Although hand-coded knowledge is useful for metaphor interpretation, it has a very limited coverage. | ||
+ | |||
+ | === Master Metaphor List (Lakoff et al., 1991) === | ||
+ | * Includes a classification of metaphorical mappings (mainly those related to mind, feelings and emotions) with the corresponding examples of language use. | ||
+ | * Problem: lack of clear structuring principles of the mapping ontology | ||
+ | # The taxonomical levels are often confused | ||
+ | # The same classes are referred to by different class labels | ||
+ | # (Consquence) Not suitable for computational use. | ||
+ | * The idea and its actual mappings ontology inspired a lot of other work | ||
+ | === MetaBank (Martin, 1994) & Mental Metaphor Databank === | ||
+ | * Created in the framework of the ATT-meta project | ||
+ | * A knowledge-base of English metaphorical conventions | ||
+ | * Represented in the form of metaphor maps (Martin, 1988) which contains detailed information about source-target concept mappings | ||
+ | |||
+ | === Other Language === | ||
+ | * There has been a wealth of research on metaphor in '''Spanish, Chinese, Russian, German, French and Italian.''' | ||
+ | * '''German and French''': Hamburg Metaphor Database (L¨onneker, 2004; Reining and L¨onneker-Rodman,2007) | ||
+ | ** Contain examples of metaphorical expressions which are mapped to senses from EuroWordNet and annotated with source–target domain mappings (taken from the Master Metaphor List.) | ||
+ | * '''Italian''': Alonge and Castelli (2003) | ||
+ | ** Discuss how metaphors can be represented in ItalWordNet | ||
== Metaphor Annotation in Corpora == | == Metaphor Annotation in Corpora == | ||
− | + | * Two distinct aspects of the phenomenon, two stages of metaphor annotation | |
+ | # Identify metaphorical senses in text (akin word sense disambiguation) | ||
+ | # Annotating source–target domain mappings of it | ||
+ | * Traditional approaches to metaphor annotation is manually search for: | ||
+ | # Lexical items used metaphorically | ||
+ | # Source and target domain vocabulary | ||
+ | # Linguistic markers of metaphor | ||
=== Metaphor & Polysemy === | === Metaphor & Polysemy === | ||
+ | * Two kinds of metaphorical language | ||
+ | # '''Novel (or poetic) metaphors''' (surprise our imagination) | ||
+ | # '''Conventionalized metaphors''' (become a part of an ordinary discourse) | ||
+ | * '''Over time some of the aspects of the target domain are added to the meaning of a term in a source domain''', resulting in a (metaphorical) sense extension of this term. | ||
+ | * It is often unclear that if a metaphorical instance is: | ||
+ | # A case of broadening of the sense in context due to general vagueness, or | ||
+ | # It manifests a formation of a new distinct metaphorical sense | ||
=== Metaphor Identification === | === Metaphor Identification === | ||
− | ==== Pragglejaz Procedure ==== | + | ==== Pragglejaz Procedure (2007) ==== |
+ | * A metaphor identification procedure (MIP) | ||
+ | * Metaphor annotation at the '''word level''' | ||
+ | * Annotators guidelines | ||
+ | # For each verb establish its meaning in context and try to imagine a more basic meaning of this verb on other contexts. Basic meanings normally are: (1) more concrete; (2) related to bodily action; (3) more precise (as opposed to vague); (4) historically older. | ||
+ | # If you can establish the basic meaning that is distinct from the meaning of the verb in this context, the verb is likely to be used metaphorically. | ||
==== Source - Target Domain Vocabulary ==== | ==== Source - Target Domain Vocabulary ==== | ||
+ | * Lists of '''source and target domain vocabulary''' | ||
+ | * Support the metaphor extraction technique that search for sentences containing lexical items from the source domain, the target domain, or both. | ||
+ | * Martin (2006) | ||
+ | ** A corpus study in order to confirm that metaphorical expressions occur in text in contexts containing such lexical items. | ||
+ | ** Goal | ||
+ | *# Evaluate predictive ability of contexts containing vocabulary from source domain and target domain | ||
+ | *# Estimate the likelihood of a metaphorical expression following another metaphorical expression described by the same mapping | ||
+ | ** Data: Wall Street Journal (WSJ) corpus | ||
+ | ** Focus on four conceptual metaphors | ||
+ | *# NUMERICAL VALUE AS LOCATION | ||
+ | *# COMMERCIAL ACTIVITY AS CONTAINER | ||
+ | *# COMMERCIAL ACTIVITY AS PATH FOLLOWING | ||
+ | *# COMMERCIAL ACTIVITY AS WAR | ||
+ | ** Method | ||
+ | *# Manually compile the lists of terms characteristic for each domain by examining sampled metaphors of these types | ||
+ | *# Augment them through the use of thesaurus | ||
+ | *# Search the WSJ for sentences containing vocabulary from these lists | ||
+ | *# Checked whether the sentences contain metaphors of the above types | ||
+ | ** Result <br> NUMERICAL-VALUE-AS-LOCATION type has the best result, P(Metaphor|Source) = 0.069, P(Metaphor|Target) = 0.677, P(Metaphor|Metaphor) = 0.703 | ||
=== Annotating Source and target Domains === | === Annotating Source and target Domains === | ||
+ | * Wallington et al. (2003) | ||
+ | ** Two teams of annotators: | ||
+ | *# Team A <br> Asked to annotate '''“interesting stretches”''', whereby a phrase was considered '''interesting''' if | ||
+ | *## its significance in the document was non-physical | ||
+ | *## it could have a physical significance in another context with a similar syntactic frame | ||
+ | *## this physical significance was related to the abstract one. | ||
+ | *# Team B <br> Annotate phrases according to '''their own intuitive definition''' of metaphor | ||
+ | ** Also annotate the source – target domain mappings <br> Annotators were given a set of mappings from the Master Metaphor List, and were asked to assign the most suitable ones. | ||
+ | ** Problem | ||
+ | *# Not report the level of inter-annotator agreement | ||
+ | *# Not report the coverage of the mappings in the Master Metaphor List | ||
+ | * Shutova and Teufel (2010) | ||
+ | ** Different approach to the annotation of source – target domain mappings | ||
+ | *** Not rely on predefined mappings | ||
+ | *** Derive independent sets of most common source and target categories | ||
+ | ** 2-stage Procedure | ||
+ | *# Metaphors are first identified using MIP | ||
+ | *# The source domain and the target domain are selected from the lists of categories | ||
+ | ** Inter-annotator agreement (Kappa) = 0.61 | ||
+ | == Conclusion and Future Direction == | ||
+ | * There is still a '''clear need''' in: | ||
+ | *#'''Unified metaphor annotation procedure''' | ||
+ | *#'''Large publicly available metaphor corpus''' | ||
+ | * Some future directions | ||
+ | *# Automatic acquisition of an extensive set of valid metaphorical associations from linguistic data via statistical pattern matching | ||
+ | *# Using the knowledge of these associations for metaphor recognition in the unseen unrestricted text | ||
+ | *# Interpretation of the identified metaphorical expressions by deriving the closest literal paraphrase | ||
== Related papers == | == Related papers == | ||
− | + | * Birte Loenneker-Rodman and Srini Narayanan (2012). Computational Models of Figurative Language, Cambridge Encyclopedia of Psycholinguistics (2012). Spivey, M., Joannisse, M., McRae, K. (eds.), Cambridge Univeristy Press, Cambridge. http://www1.icsi.berkeley.edu/~snarayan/CompFig.pdf | |
− | |||
− | |||
− |
Latest revision as of 10:45, 11 October 2012
Contents
Citation
E. Shutova. 2010. Models of Metaphor in NLP. In Proceedings of ACL 2010, Uppsala, Sweden.
Online version
Introduction
This is a review paper of modeling metaphors in NLP. The author devised it into two main tasks: "metaphor recognition" and "metaphor interpretation".
Metaphor Recognition
Met* System (Fass, 1991)
- Shutova thought it's the first attempt, but actually it's not the first one who explored this area.
- Using selectional preference and hand-coded knowledge base
- 3-Stage Approaches
- Detect selectional preference violation
- If find violations, tested for being a metonymic relation using hand-coded patterns
- If not metonymy, search the knowledge base for a relevant analogy in order to discriminate metaphorical relations
- Problem
- Detects any kind of non-literalness in language (metaphors, metonymies and others), and not only metaphors
- Fail to detect high conventionality of metaphor
Goatly (1997)
- Identify a set of linguistic cues indicate metaphor
- metaphorically speaking, utterly, completely, so to speak and, surprisingly, literally.
Peters & Peters (2000)
- Detect figurative language in the WordNet
- Search for systematic polysemy, which allows to capture metonymic and metaphorical relations
CorMet System (Mason, 2004)
- The first attempt for source-target domain mapping
- A corpus-based approach to find systematic variations in domain-specific selectional preferences
- Take Master Metaphor List (Lakoff et al., 1991) as baseline, and achieve an accuracy of 77% (judged by human)
TroFi System (Birke & Sarkar, 2006)
- Sentence clustering approach for non-literal language recognition
- Inspired by a similarity-based word sense disambiguation method
- Approach
- Use a set of seed sentences (human annotated)
- Compute similarity between (1) the sentence containing the word to be disambiguated and (2) all of the seed sentences
- Select the sense corresponding to the annotation in the most similar seed sentences
- F1-score = 0.538. But the task is not clearly defined.
Gedigan et al. (2006)
- A survey-like work about literal and metaphorical uses of verbs
- Method
- Extract the lexical items whose frames are related to MOTION and CURE from FrameNet (Fillmore et al., 2003).
- Search the PropBank Wall Street Journal corpus (Kingsbury and Palmer, 2002) for sentences containing such lexical items and annotated them with respect to metaphoricity (by hand).
- Used PropBank annotation as features to train the maximum entropy classifier
- Accuracy = 95.12%
- Very close to majority baseline (92.90%) => 92.00% of the verbs of MOTION and CURE in the Wall Street Journal corpus are used metaphorically.
Krishnakumaran & Zhu (2007)
- Deal with not only verbs, but also nouns and adjectives.
- Use hyponymy relation in WordNet and word bigram counts to predict metaphors at sentence level.
- Approach
- Noun-Noun: Given an IS-A metaphor, verify if the two nouns involved are in hyponymy relation in WordNet, if not, tag as a metaphor
- Verb-Noun and Adjective-Noun: Calculate bigram probabilities of verb-noun and adj-noun pairs, if the pair has low frequency, tag as a metaphor
- Fail to capture conventionalized metaphors (loose information compared of parsed text)
Metaphor Interpretation
MIDAS System (Martin, 1990)
- A Metaphor Interpretation, Denotation and Acquisition System (MIDAS)
- Capture hierarchical organization of conventional metaphors
- Idea
- More specific conventional metaphors descend from the general ones
- Approach (modeling how novel metaphors are acquired)
- Given a metaphor example, search for a corresponding metaphor that would explain the anomaly.
- If not find: abstract it from the example to more general concepts and repeats search.
- If find a suitable general metaphor: create a mapping for its descendant (a more specific metaphor) based on this example.
- MIDAS has been integrated with the Unix Consultant (UC), the system that answers questions about Unix.
KARMA System (Narayanan, 1997), ATT-Meta (Barnden and Lee, 2002)
- Performing inferences about entities and events in the source and target domains for metaphor interpretation.
- Metaphor-based reasoning framework
- Approach
- Reasoning process relies on manually coded knowledge of the source domain.
- The results are then projected onto the target domain (using the conceptual mapping representation).
- Problems
- ATT-Meta concerns metaphorical and metonymic description of mental states and reasoning about mental states using first order logic. But they can not take natural language sentences as input.
- KARMA doesn't have this problem, it takes parsed text as input.
Talking Points (Veale and Hao, 2008)
- Fluid knowledge representation for metaphor interpretation and generation
- Approach
- From WordNet and from the web, extract a set of characteristics of (1) concepts belonging to source and target domains and (2) related facts about the world.
- Talking Points are then organized in Slipnet, a framework that allows for a number of insertions, deletions and substitutions in definitions of such characteristics in order to establish a connection between the target and the source concepts.
- Problem
Not evaluate to which extent their knowledge base are useful.
Shutova (2010)
- Defines metaphor interpretation as a paraphrasing task
- Derive literal paraphrases for metaphorical expression
- Approach
- Given a context, apply a probabilistic model to rank all possible paraphrases for the metaphorical expression
- Use automatically induced selectional preferences to discriminate between figurative and literal paraphrases
- Tested on metaphors expressed by a verb, and achieve an accuracy of 0.81.
Metaphor Resources
- Metaphor is a knowledge-hungry phenomenon.
- Two type of resources are needed
- Extensive manually-created knowledge-base (easier, most work is of this type)
- Robust knowledge acquisition system for interpretation of metaphorical expressions (much harder)
- Although hand-coded knowledge is useful for metaphor interpretation, it has a very limited coverage.
Master Metaphor List (Lakoff et al., 1991)
- Includes a classification of metaphorical mappings (mainly those related to mind, feelings and emotions) with the corresponding examples of language use.
- Problem: lack of clear structuring principles of the mapping ontology
- The taxonomical levels are often confused
- The same classes are referred to by different class labels
- (Consquence) Not suitable for computational use.
- The idea and its actual mappings ontology inspired a lot of other work
MetaBank (Martin, 1994) & Mental Metaphor Databank
- Created in the framework of the ATT-meta project
- A knowledge-base of English metaphorical conventions
- Represented in the form of metaphor maps (Martin, 1988) which contains detailed information about source-target concept mappings
Other Language
- There has been a wealth of research on metaphor in Spanish, Chinese, Russian, German, French and Italian.
- German and French: Hamburg Metaphor Database (L¨onneker, 2004; Reining and L¨onneker-Rodman,2007)
- Contain examples of metaphorical expressions which are mapped to senses from EuroWordNet and annotated with source–target domain mappings (taken from the Master Metaphor List.)
- Italian: Alonge and Castelli (2003)
- Discuss how metaphors can be represented in ItalWordNet
Metaphor Annotation in Corpora
- Two distinct aspects of the phenomenon, two stages of metaphor annotation
- Identify metaphorical senses in text (akin word sense disambiguation)
- Annotating source–target domain mappings of it
- Traditional approaches to metaphor annotation is manually search for:
- Lexical items used metaphorically
- Source and target domain vocabulary
- Linguistic markers of metaphor
Metaphor & Polysemy
- Two kinds of metaphorical language
- Novel (or poetic) metaphors (surprise our imagination)
- Conventionalized metaphors (become a part of an ordinary discourse)
- Over time some of the aspects of the target domain are added to the meaning of a term in a source domain, resulting in a (metaphorical) sense extension of this term.
- It is often unclear that if a metaphorical instance is:
- A case of broadening of the sense in context due to general vagueness, or
- It manifests a formation of a new distinct metaphorical sense
Metaphor Identification
Pragglejaz Procedure (2007)
- A metaphor identification procedure (MIP)
- Metaphor annotation at the word level
- Annotators guidelines
- For each verb establish its meaning in context and try to imagine a more basic meaning of this verb on other contexts. Basic meanings normally are: (1) more concrete; (2) related to bodily action; (3) more precise (as opposed to vague); (4) historically older.
- If you can establish the basic meaning that is distinct from the meaning of the verb in this context, the verb is likely to be used metaphorically.
Source - Target Domain Vocabulary
- Lists of source and target domain vocabulary
- Support the metaphor extraction technique that search for sentences containing lexical items from the source domain, the target domain, or both.
- Martin (2006)
- A corpus study in order to confirm that metaphorical expressions occur in text in contexts containing such lexical items.
- Goal
- Evaluate predictive ability of contexts containing vocabulary from source domain and target domain
- Estimate the likelihood of a metaphorical expression following another metaphorical expression described by the same mapping
- Data: Wall Street Journal (WSJ) corpus
- Focus on four conceptual metaphors
- NUMERICAL VALUE AS LOCATION
- COMMERCIAL ACTIVITY AS CONTAINER
- COMMERCIAL ACTIVITY AS PATH FOLLOWING
- COMMERCIAL ACTIVITY AS WAR
- Method
- Manually compile the lists of terms characteristic for each domain by examining sampled metaphors of these types
- Augment them through the use of thesaurus
- Search the WSJ for sentences containing vocabulary from these lists
- Checked whether the sentences contain metaphors of the above types
- Result
NUMERICAL-VALUE-AS-LOCATION type has the best result, P(Metaphor|Source) = 0.069, P(Metaphor|Target) = 0.677, P(Metaphor|Metaphor) = 0.703
Annotating Source and target Domains
- Wallington et al. (2003)
- Two teams of annotators:
- Team A
Asked to annotate “interesting stretches”, whereby a phrase was considered interesting if- its significance in the document was non-physical
- it could have a physical significance in another context with a similar syntactic frame
- this physical significance was related to the abstract one.
- Team B
Annotate phrases according to their own intuitive definition of metaphor
- Also annotate the source – target domain mappings
Annotators were given a set of mappings from the Master Metaphor List, and were asked to assign the most suitable ones. - Problem
- Not report the level of inter-annotator agreement
- Not report the coverage of the mappings in the Master Metaphor List
- Shutova and Teufel (2010)
- Different approach to the annotation of source – target domain mappings
- Not rely on predefined mappings
- Derive independent sets of most common source and target categories
- 2-stage Procedure
- Metaphors are first identified using MIP
- The source domain and the target domain are selected from the lists of categories
- Inter-annotator agreement (Kappa) = 0.61
- Different approach to the annotation of source – target domain mappings
Conclusion and Future Direction
- There is still a clear need in:
- Unified metaphor annotation procedure
- Large publicly available metaphor corpus
- Some future directions
- Automatic acquisition of an extensive set of valid metaphorical associations from linguistic data via statistical pattern matching
- Using the knowledge of these associations for metaphor recognition in the unseen unrestricted text
- Interpretation of the identified metaphorical expressions by deriving the closest literal paraphrase
Related papers
- Birte Loenneker-Rodman and Srini Narayanan (2012). Computational Models of Figurative Language, Cambridge Encyclopedia of Psycholinguistics (2012). Spivey, M., Joannisse, M., McRae, K. (eds.), Cambridge Univeristy Press, Cambridge. http://www1.icsi.berkeley.edu/~snarayan/CompFig.pdf