OT and HG From HG to OT Cluster simplification Sum: learning & maturation Harmonic Grammar growing into Optimality Theory Maturation as the strict domination limit (or vice-versa) including joint work with Klaas Seinhorst (University of Amsterdam) Tamás Biró ELTE Eötvös Loránd University BLINC @ ELTE, June 2, 2017 Tamás Biró Harmonic Grammar growing into Optimality Theory 1
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Learning and maturation A standard idea in contemporary linguistics: Children learning a language: setting parameters or re-ranking constraints. Hence / because: children speak a typologically different language that resides in the typology of adult languages. Is it really so? Goal of this talk: to show how maturation (as opposed to learning ) can be included into OT. Tamás Biró Harmonic Grammar growing into Optimality Theory 2
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Learning and maturation A standard idea in contemporary linguistics: Children learning a language: setting parameters or re-ranking constraints. Hence / because: children speak a typologically different language that resides in the typology of adult languages. Is it really so? Goal of this talk: to show how maturation (as opposed to learning ) can be included into OT. Tamás Biró Harmonic Grammar growing into Optimality Theory 2
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Overview Optimality Theory and Harmonic Grammar 1 From HG to OT: the strict domination limit 2 Consonant cluster simplification in Dutch 3 Summary: learning and maturation 4 Tamás Biró Harmonic Grammar growing into Optimality Theory 3
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Overview Optimality Theory and Harmonic Grammar 1 From HG to OT: the strict domination limit 2 Consonant cluster simplification in Dutch 3 Summary: learning and maturation 4 Tamás Biró Harmonic Grammar growing into Optimality Theory 4
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Optimality Theory in a broad sense Underlying representation �→ candidate set. Surface representation = optimal element of candidate set. Optimality: most harmonic. What is “harmony”? Tamás Biró Harmonic Grammar growing into Optimality Theory 5
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Optimality Theory in a narrow sense Gen ( σσσσ ) = { [suuu], [usuu], [uusu], [uuus] } . / σσσσ / E ARLY L ATE N ON F INAL [s u u u ] 0 3 0 ☞ [u s u u ] 1! 2 0 [u u s u ] 2! 1 0 [u u u s ] 3! 0 1 SF ( σσσσ ) = [suuu]. Tamás Biró Harmonic Grammar growing into Optimality Theory 6
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Optimality Theory in a narrow sense Gen ( σσσσ ) = { [suuu], [usuu], [uusu], [uuus] } . / σσσσ / N ON F INAL L ATE E ARLY [s u u u] 0 3! 0 [u s u u] 0 2! 1 [u u s u] 0 1 2 ☞ [u u u s] 1! 0 3 SF ( σσσσ ) = [uusu]. Tamás Biró Harmonic Grammar growing into Optimality Theory 7
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Optimality Theory in a narrow sense Gen ( σσσσ ) = { [suuu], [usuu], [uusu], [uuus] } . / σσσσ / N ON F INAL L ATE E ARLY [u u s u] 0 1 2 ☞ [u s u u] 0 2 1 [s u u u] 0 3 0 [u u u s] 1 0 3 Harmony in terms of lexicographic order : [uusu] ≻ [usuu] ≻ [suuu] ≻ [uuus]. Hence, SF ( σσσσ ) = [uusu]. Tamás Biró Harmonic Grammar growing into Optimality Theory 8
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Harmonic Grammar, symbolic approach Gen ( σσσσ ) = { [suuu], [usuu], [uusu], [uuus] } . Constraint C k is assigned weight w k . Harmony H ( A ) of cand. A : / σσσσ / N ON F INAL L ATE E ARLY − H ( A ) = w k = 9 3 1 � k w k · C k [ A ] [u u s u] 0 1 2 5 ☞ 9 · 0 + 3 · 1 + 1 · 2 = [u s u u] 0 2 1 7 9 · 0 + 3 · 2 + 1 · 1 = [s u u u] 0 3 0 9 9 · 0 + 3 · 3 + 1 · 0 = [u u u s] 1 0 3 9 · 1 + 3 · 0 + 1 · 3 = 12 By comparing the integer/real numbers in H : [uusu] ≻ [usuu] ≻ [suuu] ≻ [uuus]. Hence, SF ( σσσσ ) = [uusu]. Tamás Biró Harmonic Grammar growing into Optimality Theory 9
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Harmonic Grammar, connectionist approach Boltzmann machine: The “energy” (negative harmony) of the network: N � − H ( A ) = s i · W i , j · s j i , j = 1 s i : activation of node i . Input nodes clamped (fixed). W i , j : connection strength Output nodes read between nodes i and j . after optimization of H ( A ) . Tamás Biró Harmonic Grammar growing into Optimality Theory 10
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Harmonic Grammar, connectionist approach Constraint C k has weight w k : n � w k · W k W i , j = i , j k = 1 The “energy” (negative harmony) of the network: N Constraint C k is a set of W k � − H ( A ) = s i · W i , j · s j = i , j partial connection strengths. i , j = 1 N n n N n � � w k · W k � � s i · W k � = s i · i , j · s j = w k · i , j · s j = w k · C k [ A ] . i , j = 1 k = 1 k = 1 i , j = 1 k = 1 Tamás Biró Harmonic Grammar growing into Optimality Theory 11
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Harmonic Grammar, connectionist approach Constraint C k has weight w k : n � w k · W k W i , j = i , j k = 1 The “energy” (negative harmony) of the network: N Constraint C k is a set of W k � − H ( A ) = s i · W i , j · s j = i , j partial connection strengths. i , j = 1 N n n N n � � w k · W k � � s i · W k � = s i · i , j · s j = w k · i , j · s j = w k · C k [ A ] . i , j = 1 k = 1 k = 1 i , j = 1 k = 1 Tamás Biró Harmonic Grammar growing into Optimality Theory 11
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Summary thus far: We have three approaches: Optimality Theory: symbolic, optimization w.r.t. lexicographic order. Symbolic Harmonic Grammar: optimization w.r.t. ≥ relation among real numbers. Connectionist Harmonic Grammar: optimization w.r.t. ≥ relation among real numbers. Typological predictions? Learnability? Cognitive plausibility? Question: how to get OT in a “connectionist brain”? (A major issue for Smolensky’s Integrated Connectionist/Symbolic Architecture.) Tamás Biró Harmonic Grammar growing into Optimality Theory 12
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Summary thus far: We have three approaches: Optimality Theory: symbolic, optimization w.r.t. lexicographic order. Symbolic Harmonic Grammar: optimization w.r.t. ≥ relation among real numbers. Connectionist Harmonic Grammar: optimization w.r.t. ≥ relation among real numbers. Typological predictions? Learnability? Cognitive plausibility? Question: how to get OT in a “connectionist brain”? (A major issue for Smolensky’s Integrated Connectionist/Symbolic Architecture.) Tamás Biró Harmonic Grammar growing into Optimality Theory 12
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Summary thus far: We have three approaches: Optimality Theory: symbolic, optimization w.r.t. lexicographic order. Symbolic Harmonic Grammar: optimization w.r.t. ≥ relation among real numbers. Connectionist Harmonic Grammar: optimization w.r.t. ≥ relation among real numbers. Typological predictions? Learnability? Cognitive plausibility? Question: how to get OT in a “connectionist brain”? (A major issue for Smolensky’s Integrated Connectionist/Symbolic Architecture.) Tamás Biró Harmonic Grammar growing into Optimality Theory 12
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Overview Optimality Theory and Harmonic Grammar 1 From HG to OT: the strict domination limit 2 Consonant cluster simplification in Dutch 3 Summary: learning and maturation 4 Tamás Biró Harmonic Grammar growing into Optimality Theory 13
OT and HG From HG to OT Cluster simplification Sum: learning & maturation Exponential Harmonic Grammar, or q -HG Optimality Theory minimizes a vector of violations: C n C n − 1 . . . C i . . . C 1 r n (= n ) r n − 1 r i r 1 (= 1 ) H ( A ) = C 1 [ A ] C 2 [ A ] . . . C i [ A ] . . . C n [ A ] Harmonic Grammar minimizes a weighted sum of violations: n � H ( A ) = w i · C i [ A ] . i = 1 “Standard” HG: weights w i = ranks r i . Exponential HG: weights are ranks exponentiated, fixed base w i = e r i . ( e = 2 . 7182 . . . ) q -HG: weights are ranks exponentiated, with (variable) base q w i = q r i . Tamás Biró Harmonic Grammar growing into Optimality Theory 14
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