Harmonic grammar

Key takeaways

Harmonic grammar belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Harmonic grammar to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Harmonic grammar from memory before moving on to harder problems.

Reference excerpt

Harmonic grammar is a linguistic model proposed by Geraldine Legendre, Yoshiro Miyata, and Paul Smolensky in 1990. It is a connectionist approach to modeling linguistic well-formedness. During the late 2000s and early 2010s, the term "harmonic grammar" has been used to refer more generally to models of language that use weighted constraints, including ones that are not explicitly connectionist – see e.g. Pater (2009) and Potts et al. (2010).

See also Optimality theory

Bibliography Keller, Frank. (2000). Gradience in grammar: Experimental and computational aspects of degrees of grammaticality. (Doctoral dissertation, University of Edinburgh). (Online: homepages.inf.ed.ac.uk/keller/papers/phd.html). Keller, Frank. (2006). "Linear Optimality Theory as a model of gradience in grammar." In G. Fanselow, C. Fery, R. Vogel, & M. Schlesewsky (Eds.), Gradience in grammar: Generative perspectives. Oxford: Oxford University Press. (Online: homepages.inf.ed.ac.uk/keller/papers/oup06a.html). Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1990). "Can connectionism contribute to syntax?: Harmonic Grammar, with an application." In M. Ziolkowski, M. Noske, & K. Deaton (Eds.), Proceedings of the 26th regional meeting of the Chicago Linguistic Society (pp. 237–252). Chicago: Chicago Linguistic Society. Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1990). Can connectionism contribute to syntax?: Harmonic grammar, with an application. Report CU-CS-485-90. Computer Science Department, University of Colorado at Boulder. (Online: www.cs.colorado.edu/department/publications/reports/docs/CU-CS-485-90.pdf.) Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1990). "Harmonic Grammar: A formal multi-level connectionist theory of linguistic well-formedness: Theoretical foundations." In Proceedings of the twelfth annual conference of the Cognitive Science Society (pp. 388–395). Cambridge, MA: Lawrence Erlbaum. Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1990). Harmonic Grammar: A formal multi-level connectionist theory of linguistic well-formedness: Theoretical foundations. Report CU-CS-465-90. Computer Science Department, University of Colorado at Boulder. (Online: www.cs.colorado.edu/department/publications/reports/docs/CU-CS-465-90.pdf.) Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1990). "Harmonic Grammar: A formal multi-level connectionist theory of linguistic well-formedness: An application." In Proceedings of the twelfth annual conference of the Cognitive Science Society (pp. 884–891). Cambridge, MA: Lawrence Erlbaum. Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1990). Harmonic Grammar: A formal multi-level connectionist theory of linguistic well-formedness: An application. Report CU-CS-464-90; ICS technical report 90-4. Computer Science Department, University of Colorado at Boulder. (Online: www.cs.colorado.edu/department/publications/reports/docs/CU-CS-464-90.pdf.) Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1991). Distributed recursive structure processing. Report CU-CS-514-91. Computer Science Department, University of Colorado at Boulder. (Online: www.cs.colorado.edu/department/publications/reports/docs/CU-CS-514-91.pdf.) Legendre, Géraldine; Miyata, Yoshiro; & Smolensky, Paul. (1991). "Unifying syntactic and semantic approaches to unaccusativity: A connectionist approach." In Proceedings of the 17th Annual Meeting of the Berkeley Linguistics Society (pp. 388–395). Berkeley. (Online: www.cs.colorado.edu/department/publications/reports/docs/CU-CS-532-91.pdf). Legendre, Géraldine; Sorace, Antonella; & Smolensky, Paul. (2006). "The Optimality Theory–Harmonic Grammar connection." In P. Smolensky & G. Legendre (Eds.), The harmonic mind: From neural computation to Optimality-Theoretic grammar (pp. 339–402). (Online: uit.no/getfile.php?PageId=874&FileId=187). Pater, Joe. (2009). "Weighted Constraints in Generative Linguistics". Cognitive Science 33: 999-1035. Potts, Christopher, Joe Pater, Karen Jesney, Rajesh Bhatt and Michael Becker. (2010). Harmonic Grammar with Linear Programming: From linear systems to linguistic typology. Phonology 27: 77–117. Prince, Alan. (2002). Anything goes. In ed. T. Honma, M. Okazaki, T. Tabata, & S. Tanaka (Eds.), New century of phonology and phonological theory (pp. 66–90). Tokyo: Kaitakusha. (Online: roa.rutgers.edu/view.php3?id=697). Prince, Alan; & Smolensky, Paul. (1991). Connectionism and harmony theory in linguistics. Report CU-CS-600-92. Computer Science Department, University of Colorado at Boulder. (Online: www.cs.colorado.edu/department/publications/reports/docs/CU-CS-533-91.pdf.) Prince, Alan; & Smolensky, Paul. (1993). Optimality Theory: Constraint interaction in generative grammar. RuCCS Technical Report 2, Rutgers University. Piscateway, NJ: Rutgers University Center for Cognitive Science. (Revised version published 2004). (Online: roa.rutgers.edu/view.php3?id=845). Smolensky, Paul. (1988). "On the proper treatment of connectionism". The Behavioral and Brain Sciences, 11, 1–23. Smolensky, Paul. (1990). "Tensor product variable binding and the representation of symbolic structures in connectionist networks". Artificial Intelligence, 46, 159–216. Smolensky, Paul; & Legendre, Géraldine. (2006). The harmonic mind: From neural computation to Optimality-Theoretic grammar (Vols. 1–2). Cambridge, MA: MIT Press. Smolensky, Paul; Legendre, Géraldine; & Miyata, Yoshiro. (1992). Principles for an integrated connectionist/symbolic theory of higher cognition. Report CU-CS-600-92. Computer Science Department, University of Colorado at Boulder. Smolensky, Paul; Legendre, Géraldine; & Miyata, Yoshiro. (1992). Integrating connectionist and symbolic computation for the theory of language. Computer Science Department Report CU-CS-628-92; Institute of Cognitive Science Report 92-16. Computer Science Department, University of Colorado at Boulder. (Online: www.cs.colorado.edu/department/publications/reports/docs/CU-CS-628-92.pdf). Smolensky, Paul; Legendre, Géraldine; & Miyata, Yoshiro. (1993). "Integrating connectionist and symbolic computation for the theory of language." Current Science, 64, 381–391. Tesar, Bruce. (2007). "A comparison of lexicographic and linear numeric optimization using violation difference ratios." Rutgers University. (Online: roa.rutgers.edu/view.php3?id=1351[link removed]).

Worked examples

Example 1 — a first encounter with Harmonic grammar

Start with the simplest possible case. Write down what Harmonic grammar claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Harmonic grammar before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Harmonic grammar ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Harmonic grammar

In research: Harmonic grammar appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Harmonic grammar in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Harmonic grammar is common in secondary-school and first-year university syllabi. It links to neighbouring topics Phonology, so understanding it makes those chapters shorter.
In everyday life: Look for Harmonic grammar outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Harmonic grammar in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Harmonic grammar means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Harmonic grammar out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Harmonic grammar in simple terms?

Harmonic grammar is a linguistic model proposed by Geraldine Legendre, Yoshiro Miyata, and Paul Smolensky in 1990. It is a connectionist approach to modeling linguistic well-formedness.

Why does Harmonic grammar matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Harmonic grammar?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Harmonic grammar.