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Information theory and artificial grammar learning: inferring grammaticality from redundancy

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Abstract

In artificial grammar learning experiments, participants study strings of letters constructed using a grammar and then sort novel grammatical test exemplars from novel ungrammatical ones. The ability to distinguish grammatical from ungrammatical strings is often taken as evidence that the participants have induced the rules of the grammar. We show that judgements of grammaticality are predicted by the local redundancy of the test strings, not by grammaticality itself. The prediction holds in a transfer test in which test strings involve different letters than the training strings. Local redundancy is usually confounded with grammaticality in stimuli widely used in the literature. The confounding explains why the ability to distinguish grammatical from ungrammatical strings has popularized the idea that participants have induced the rules of the grammar, when they have not. We discuss the judgement of grammaticality task in terms of attribute substitution and pattern goodness. When asked to judge grammaticality (an inaccessible attribute), participants answer an easier question about pattern goodness (an accessible attribute).

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Notes

  1. Collapsing ratings over participants, the correlation between mean ratings and zero-order redundancy was r(38) = 0.47, p < 0.01, whereas the correlation between mean ratings and first-order redundancy was r(38) = 0.45, p < 0.01. Although the correlations computed in this way are more impressive, they are subject to an overestimation bias (see Lorch & Myers, 1990).

  2. We made the change because letters H and N looked similar to one another.

  3. Collapsing over participants, the correlation between ratings and zero-order redundancy was r(38) = 0.77, p < 0.01, whereas the correlation with first-order redundancy was r(38) = 0.68, p < 0.01. Although the correlations computed in this way are more impressive, they are subject to an overestimation bias (see Lorch & Myers, 1990).

  4. Demonstrations of grammatical string completion and serial reaction time learning are reported using a standard version of the MINERVA 2 model. However, those demonstrations are reproducible using the holographic representation scheme in the HEM.

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Acknowledgments

The research was supported by grants from the Natural Sciences and Engineering Research Council of Canada to RKJ and DJKM.

Author information

Authors and Affiliations

  1. Department of Psychology, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    Randall K. Jamieson & Uliana Nevzorova

  2. Department of Psychology, Queen’s University at Kingston, Kingston, Canada

    Graham Lee & D. J. K. Mewhort

Authors
  1. Randall K. Jamieson
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  2. Uliana Nevzorova
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  3. Graham Lee
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  4. D. J. K. Mewhort
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Corresponding author

Correspondence to Randall K. Jamieson.

Appendices

Appendix 1: materials in Experiment 1

Training strings

 BFBFFBKK

KGDKGDFF

CCJHJHFF

GDFFBFFB

 DKKGKGKG

DFBKGDKG

JKKGDFFB

KGKKGDKK

 KKKGDKKG

DFFFFBKG

HFBKKKKK

BFFBFBKG

 JKKGDFBK

BKKKGDFF

BFBKGKKK

GDFBFFFB

 CCJKGKKG

BKGKKGDK

DKGKKKKG

CCCCJHJH

 FFFFBKKG

BKKKGKKK

CCCJHJKG

HFBKGDKK

 HFBFFBKK

KKGKGDKG

CCCCJHJK

GDFBKKGK

 BFBKKKKK

CCJKKGDK

HFFFFFFF

GKGKKKKG

 GDKKGDFB

KKGDFFFB

DFBKGDKK

KGDKKKGK

 JHFBFBFB

HFBKKKKG

DFBFBKGK

BKKKGDKK

Test strings

 Grammatical

  TTTLLLRN

TLRTLLLL

SLRTLLRT

SZTTTLLL

  ZTLLRTTL

SLLLLLLR

LLRNRNZT

RNRTTTLL

  SLRNRNZT

YRNZTTLL

YRTTTTTT

LLLRNRTT

  RNZPNZTL

TLLLLLRT

NZTLLLRN

LLRNRNRN

  ZTTLLRTL

RTTLRNZT

YRNRNRTT

SZTTTLLR

 Ungrammatical

  SZPNRNZP

YRSTZYSN

TYLLNRYR

LPNPPYPP

  PRSRNYST

NSZPNTPT

PZLRZTTY

NRZNTYYS

  NYNLTSNP

ZZYYZZNY

SLTSZPRS

SLYPLSTZ

  ZLRPRRLL

YTSTPNRR

PRZLSTRR

TLNLPTYS

  YNZPSRLP

PTLTYZYT

PRLTPRPS

PSZSYYNZ

Appendix 2: materials in Experiment 2

Training strings

 BFGCFGKD

DGCDGCFD

GCDGCFDG

HKFDCDGK

 BKDGKFGK

DGCFDGKD

GKDCDCFD

HKFDGKFD

 CDCFDGCD

DGCFGKFG

GKDCDGCF

HKFGCDCF

 CDCFGKDG

FDCFDCDC

GKDCDGKD

KFDGCFDG

 CFDCDGCF

FDCFGCDC

GKDCFDGC

KFDGKFGK

 CFGKDGCF

FGCDGKDC

GKFDGCDC

KFGCDGKD

 DCDCDGCF

FGCDGKDG

GKFGKFDG

NCDCDGCD

 DCDCFGKD

FGKFDGCF

HDCDCFDG

NCDCFGCF

 DCDGCDCD

FGKFGCDC

HDCFDGKF

NCDCFGKD

 DCFGCDGC

GCDGCDGK

HKDCFGKF

NGKFDGKD

Test strings

 Grammatical

  JXRXSPSP

LPSPSTRX

JXSPSTXS

PJTRWLJT

  JXRXSTXR

RWJXSTXS

SPSTRWLP

SPJTXSTX

  LPSTXRWL

STRWJXST

STRWJXST

TRXRWLJX

  PSPSTRXS

WLJTXRWL

XRXSPSPJ

RWLPSPJX

  STRXRXRW

XSPSTRXS

LPJXRWJT

LJTXRWJT

 Ungrammatical

  TLRJTSRJ

RXTJWJRL

WLPRPXWS

JRLXWSXS

  XLPWXJXR

XPWRSJSP

XJXJWXTX

PJTXSJXP

  WSTLJLRP

PRLPJPWL

XSRXLRXJ

RSRSRJLP

  SPXWJPXW

WPRSJWXL

PWPWPTXW

JWRPTXTR

  SPSXLPLS

TWSPSRSR

XWLSTSXJ

RWJXLWXS

Appendix 3: materials in Experiment 3

Training strings

 

 Standard condition

    

  ZLBF

ZLBFJBJF

BJFJZ

BFJBF

ZLBFJBFL

ZFJBFJZ

  ZLBJL

BFJBJL

ZFJBF

ZLBJLBF

ZLBJLBFL

BJLBJLBF

  BJLBFJZ

ZLBJLZ

ZFJBJL

ZLBJLBFJ

BJLBJFJZ

ZLBJLBJL

  ZLBFJBJL

ZFJBFL

BFJBJF

BJFJBJLZ

BJFJBFJZ

BFJBFJBF

  BFJBJFL

BFJBJLZ

ZFJBFJ

BFJBJLBF

BJLBJL

BJFJBJFJ

 Transfer condition

  DMXQ

DMXQHXHQ

XHQHD

XQHXQ

DMXQHXQM

DQHXQHD

  DMXHM

XQHXHM

DQHXQ

DMXHMXQ

DMXHMXQM

XHMXHMXQ

  XHMXQHD

DMXHMD

DQHXHM

DMXHMXQH

XHMXHQHD

DMXHMXHM

  DMXQHXHM

DQHXQM

XQHXHQ

XHQHXHMD

XHQHXQHD

XQHXQHXQ

  XQHXHQM

XQHXHMD

DQHXQH

XQHXHMXQ

XHMXHM

XHQHXHQH

Test strings

 

 Grammatical

Low

Medium

High

   

BJLZ

BFJBFL

BJLBJLZ

   

ZLBJF

BJLBJF

ZLBJLBJF

   

ZLBFL

ZLBFJBF

BFJBFJ

   

ZFJBJLZ

BJLBJFL

ZLBFJBFJ

   

BJLBFL

ZFJBJFJ

BFJBFJZ

   

ZFJBJLBF

BJLBJFJ

BJFJBJF

   

BJFJBFL

BJFJBFJ

BJFJBJFL

   

BJFJBF

ZFJBJFJZ

ZFJBFJBF

   

 Ungrammatical

Low

Medium

High

   

JLBZ

BFLBFJ

BJLZBJL

   

BJFLZ

LBJFBJ

ZFLBJLBJ

   

ZBLFL

ZBFLJBF

JBFJBF

   

ZJBLJFZ

BJFLBJL

BFJLZBFJ

   

JBLFLB

BFJZJFJ

ZBFJBFJ

   

FBLJBJFZ

FLBJFBJ

FJBJFJB

   

BLFJFBJ

FJBFJBJ

JBJFLBJF

   

JFBFJB

ZBFJZJFJ

FBJFZBJF

   

Appendix 4: materials in Experiment 4

Training strings

 Standard condition

  BJFL

ZLBJLBFJ

BFJBFJBF

BFJBJFJZ

ZLBFJ

ZLBJLBJL

  ZFJBFJZ

ZLBFJBJF

BFJBF

BJFJBJFJ

BJFJBJL

ZFJBJL

  ZLBF

BJFJ

ZLBJFL

BFJBJFJ

ZFJZ

ZLBJFJZ

  ZLBJL

ZFJBFJ

BJLBF

BJFJBJLZ

ZLBJFJBF

BFJZ

  BFJBJL

ZLBFJBFL

ZLBFJZ

BJFJZ

BJLBFJ

BFJBJLZ

Transfer condition

 XHQM

DMXHMXQH

XQHXQHXQ

XQHXHQHD

DMXQH

DMXHMXHM

 DQHXQHD

DMXQHXHQ

XQHXQ

XHQHXHQH

XHQHXHM

DQHXHM

 DMXQ

XHQH

DMXHQM

XQHXHQH

DQHD

DMXHQHD

 DMXHM

DQHXQH

XHMXQ

XHQHXHMD

DMXHQHXQ

XQHD

 XQHXHM

DMXQHXQM

DMXQHD

XHQHD

XHMXQH

XQHXHMD

Test strings

 Grammatical

Low

Medium

High

   

BJLZ

BFJBFL

BJLBJLZ

   

ZLBJF

BJLBJF

ZLBJLBJF

   

ZLBFL

ZLBFJBF

BFJBFJ

   

ZFJBJLZ

BJLBJFL

ZLBFJBFJ

   

BJLBFL

ZFJBJFJ

BFJBFJZ

   

ZFJBJLBF

BJLBJFJ

BJFJBJF

   

BJFJBFL

BJFJBFJ

BJFJBJFL

   

BJFJBF

ZFJBJFJZ

ZFJBFJBF

   

 Ungrammatical

Low

Medium

High

   

JLBZ

BFLBFJ

BJLZBJL

   

BJFLZ

LBJFBJ

ZFLBJLBJ

   

ZBLFL

ZBFLJBF

JBFJBF

   

ZJBLJFZ

BJFLBJL

BFJLZBFJ

   

JBLFLB

BFJZJFJ

ZBFJBFJ

   

FBLJBJFZ

FLBJFBJ

FJBJFJB

   

BLFJFBJ

FJBFJBJ

JBJFLBJF

   

JFBFJB

ZBFJZJFJ

FBJFZBJF

   

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Jamieson, R.K., Nevzorova, U., Lee, G. et al. Information theory and artificial grammar learning: inferring grammaticality from redundancy. Psychological Research 80, 195–211 (2016). https://doi.org/10.1007/s00426-015-0660-2

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