1592:
1497:
1401:
847:
Variations of DisCoCat have been proposed with a different choice for the grammar category. The main motivation behind this lies in the fact that pregroup grammars have been proved to be weakly equivalent to context-free grammars. One example of variation chooses
118:
There are multiple definitions of DisCoCat in the literature, depending on the choice made for the compositional aspect of the model. The common denominator between all the existent versions, however, always involves a
106:). As such, they both benefit from a graphical calculus, which allows a purely diagrammatic reasoning. Although the analogy with quantum mechanics was kept informal at first, it eventually led to the development of
570:
838:
hypothesis "A word is characterized by the company it keeps" is particularly relevant when assigning meaning to words like adjectives or verbs, whose semantic connotation is strongly dependent on context.
424:
146:. This approach has some shortcomings: all parallel arrows of a posetal category are equal, which means that pregroups cannot distinguish between different grammatical derivations for the same
1744:
Grefenstette, Edward; Dinu, Georgiana; Zhang, Yao-Zhong; Sadrzadeh, Mehrnoosh; Baroni, Marco (2013-01-30). "Multi-Step
Regression Learning for Compositional Distributional Semantics".
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777:
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681:
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224:
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476:
264:
244:
1106:
Coecke, Bob; de Felice, Giovanni; Meichanetzidis, Konstantinos; Toumi, Alexis (2020-12-07). "Foundations for Near-Term
Quantum Natural Language Processing".
123:
definition of DisCoCat as a structure-preserving functor from a category of grammar to a category of semantics, which usually encodes the distributional
1642:
Bradley, Tai-Danae; Lewis, Martha; Master, Jade; Theilman, Brad (2018). "Translating and
Evolving: Towards a Model of Language Change in DisCoCat".
1687:
Grefenstette, Edward; Sadrzadeh, Mehrnoosh (2011-06-20). "Experimental
Support for a Categorical Compositional Distributional Model of Meaning".
1032:
Coecke, Bob; Sadrzadeh, Mehrnoosh; Clark, Stephen (2010-03-23). "Mathematical
Foundations for a Compositional Distributional Model of Meaning".
150:
sentence. A more intuitive manner of saying the same is that one works with diagrams rather than with partial orders when describing grammar.
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481:
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982:
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35:
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23:
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1311:
de Felice, Giovanni; Meichanetzidis, Konstantinos; Toumi, Alexis (2020-09-15). "Functorial
Question Answering".
1923:
967:
868:
835:
827:
31:
1053:
Zeng, William; Coecke, Bob (2016-08-02). "Quantum
Algorithms for Compositional Natural Language Processing".
686:
269:
370:
103:
1765:
de Felice, Giovanni; Meichanetzidis, Konstantinos; Toumi, Alexis (2019). "Functorial
Question Answering".
1593:"A type-driven vector semantics for ellipsis with anaphora using lambek calculus with limited contraction"
901:
897:
878:
1717:
789:
605:
369:
With this definition of pregroup grammars as free rigid categories, DisCoCat models can be defined as
321:
945:
940:
930:
147:
131:
83:
1519:
Meyer, Francois; Lewis, Martha (2020-10-12). "Modelling
Lexical Ambiguity with Density Matrices".
1451:
Kartsaklis, Dimitri (2016). "Coordination in
Categorical Compositional Distributional Semantics".
738:
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159:
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has generating objects for the words and the basic types of the grammar, and generating arrows
1894:
1843:
1573:
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1195:
1150:
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1812:"Applying Distributional Compositional Categorical Models of Meaning to Language Translation"
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1661:
1614:
1563:
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1423:
1379:
Yeung, Richie; Kartsaklis, Dimitri (2021). "A CCG-based version of the DisCoCat framework".
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Selinger, Peter (2010). "A survey of graphical languages for monoidal categories".
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55:
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1145:
1133:
International Journal for Research in Applied Science and Engineering Technology
861:
47:
1619:
98:
and quantum processes shared a common mathematical structure: they both form a
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124:
79:
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1847:
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1342:
1199:
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1084:
1861:
Coecke, Bob; de Felice, Giovanni; Marsden, Dan; Toumi, Alexis (2018-11-08).
1540:
Coecke, Bob; de Felice, Giovanni; Marsden, Dan; Toumi, Alexis (2018-11-08).
883:
826:
as the category of semantics is that vector spaces are the usual setting of
67:
1366:
In International Conference on Logical Aspects of Computational Linguistics
860:
The DisCoCat framework has been used to study the following phenomena from
22:(Categorical Compositional Distributional) is a mathematical framework for
1191:
139:
1889:
1862:
1838:
1811:
1788:
1710:"Prior disambiguation of word tensors for constructing sentence vectors"
1665:
1568:
1541:
1474:
1334:
1076:
917:
The DisCoCat framework has been applied to solve the following tasks in
135:
1168:
Preller, Anne (2014-12-27). "From Logical to Distributional Models".
1879:
1828:
1779:
1656:
1609:
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1418:
1385:
1364:
Buszkowski, Wojciech (2001). "Lambek grammars based on pregroups".
1325:
1112:
1067:
565:{\displaystyle F(w)\in F(t)=F(t_{1})\otimes \dots \otimes F(t_{n})}
1750:
1693:
1270:
1182:
1038:
426:. Spelling things out in detail, they assign a finite dimensional
1005:
999:
1400:
Sadrzadeh, Mehrnoosh; Kartsaklis, Dimitri; BalkΔ±r, Esma (2018).
1496:
Bankova, Dea; Coecke, Bob; Lewis, Martha; Marsden, Dan (2018).
1402:"Sentence entailment in compositional distributional semantics"
1264:. Lecture Notes in Physics. Vol. 813. pp. 289β355.
1498:"Graded hyponymy for compositional distributional semantics"
1863:"Towards Compositional Distributional Discourse Analysis"
1542:"Towards Compositional Distributional Discourse Analysis"
1129:"A Review Article on Quantum Natural Language Processing"
58:
to produce the meaning of a sentence or a piece of text.
226:
for the dictionary entries which assign a pregroup type
648:(objects for words are sent to the monoidal unit, i.e.
1867:
Electronic Proceedings in Theoretical Computer Science
1816:
Electronic Proceedings in Theoretical Computer Science
1767:
Electronic Proceedings in Theoretical Computer Science
1644:
Electronic Proceedings in Theoretical Computer Science
1546:
Electronic Proceedings in Theoretical Computer Science
1453:
Electronic Proceedings in Theoretical Computer Science
1313:
Electronic Proceedings in Theoretical Computer Science
1170:
Electronic Proceedings in Theoretical Computer Science
1055:
Electronic Proceedings in Theoretical Computer Science
16:
Mathematical framework for natural language processing
1002:, a Python toolkit for computing with string diagrams
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162:
153:
This problem is overcome when one considers the free
419:{\displaystyle F:\mathbf {G} \to \mathbf {FinVect} }
1708:Kartsaklis, Dimitri; Sadrzadeh, Mehrnoosh (2013).
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594:
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470:
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1406:Annals of Mathematics and Artificial Intelligence
1591:Wijnholds, Gijs; Sadrzadeh, Mehrnoosh (2019).
779:which can be computed as the contraction of a
1221:Preller, Anne; Lambek, Joachim (2007-01-18).
318:are grammatical derivations for the sentence
8:
178:generated by the pregroup grammar. That is,
1227:Mathematical Structures in Computer Science
1597:Journal of Logic, Language and Information
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830:reading in computational linguistics and
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185:
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86:, and Stephen Clark as an application of
1233:(doi: 10.1017/S0960129506005901): 309.
1021:
728:{\displaystyle f:w_{1}\dots w_{n}\to s}
311:{\displaystyle f:w_{1}\dots w_{n}\to s}
94:. It started with the observation that
1726:
1715:
78:The framework was first introduced by
7:
1027:
1025:
1010:quantum natural language processing
988:Quantum natural language processing
108:quantum natural language processing
38:. The grammatical derivations in a
819:{\displaystyle \mathbf {FinVect} }
641:{\displaystyle t=t_{1}\dots t_{n}}
66:and reason about natural language
14:
812:
809:
806:
803:
800:
797:
794:
786:The reason behind the choice of
412:
409:
406:
403:
400:
397:
394:
386:
351:{\displaystyle w_{1}\dots w_{n}}
186:
164:
576:space to each dictionary entry
102:(also known as a non-symmetric
850:Combinatory categorial grammar
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760:
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1:
1810:Tyrrell, Brian (2018-11-08).
1502:Journal of Language Modelling
983:Categorical quantum mechanics
973:Principle of compositionality
683:). The meaning of a sentence
88:categorical quantum mechanics
36:principle of compositionality
1127:Rai, Anshuman (2022-01-31).
856:List of linguistic phenomena
772:{\displaystyle F(f)\in F(s)}
364:adjunction units and counits
358:which can be represented as
193:{\displaystyle \mathbf {G} }
171:{\displaystyle \mathbf {G} }
130:The original paper used the
1280:10.1007/978-3-642-12821-9_4
1223:"Free Compact 2-Categories"
1146:10.22214/ijraset.2022.40103
919:natural language processing
832:natural language processing
735:is then given by a vector
92:natural language processing
24:natural language processing
1940:
1620:10.1007/s10849-019-09293-4
1262:New Structures for Physics
852:as the grammar category.
1919:Computational linguistics
1429:10.1007/s10472-017-9570-x
1239:10.1017/S0960129506005901
926:Word-sense disambiguation
834:. The underlying idea of
362:with cups and caps, i.e.
968:Distributional semantics
371:strong monoidal functors
32:distributional semantics
1008:, a Python library for
148:syntactically ambiguous
104:compact closed category
1725:Cite journal requires
879:Hyponymy and hypernymy
820:
773:
729:
677:
676:{\displaystyle F(w)=1}
642:
596:
595:{\displaystyle w\to t}
566:
472:
452:
420:
352:
312:
260:
240:
220:
219:{\displaystyle w\to t}
194:
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62:are used to visualise
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46:) are interpreted as
1192:10.4204/EPTCS.171.11
790:
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451:{\displaystyle F(x)}
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1890:10.4204/EPTCS.283.1
1839:10.4204/EPTCS.283.3
1789:10.4204/EPTCS.323.6
1666:10.4204/EPTCS.283.4
1569:10.4204/EPTCS.283.1
1475:10.4204/EPTCS.221.4
1335:10.4204/EPTCS.323.6
1077:10.4204/EPTCS.221.8
946:Anaphora resolution
941:Machine translation
931:Semantic similarity
913:Applications in NLP
572:in the appropriate
458:to each basic type
132:categorical product
84:Mehrnoosh Sadrzadeh
936:Question answering
907:Language evolution
893:Discourse analysis
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40:categorial grammar
1289:978-3-642-12820-2
471:{\displaystyle x}
259:{\displaystyle w}
239:{\displaystyle t}
96:pregroup grammars
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1139:(1): 1588β1594.
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1103:
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1070:
1050:
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963:Pregroup grammar
888:density matrices
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144:posetal category
64:information flow
44:pregroup grammar
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1924:Category theory
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958:Lambek calculus
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360:string diagrams
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60:String diagrams
28:category theory
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1905:
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1802:
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1736:
1727:|journal=
1700:
1679:
1634:
1603:(2): 331β358.
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1532:
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1488:
1443:
1412:(4): 189β218.
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1303:
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994:External links
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836:distributional
828:distributional
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574:tensor product
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155:rigid category
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100:rigid category
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52:tensor product
50:acting on the
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1522:
1515:
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1508:(2): 225β260.
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428:vector space
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56:word vectors
19:
18:
1176:: 113β131.
862:linguistics
121:categorical
48:linear maps
42:(usually a
26:which uses
1913:Categories
1880:1811.03277
1829:1811.03274
1780:1905.07408
1657:1811.11041
1610:1905.01647
1559:1811.03277
1526:2010.05670
1466:1606.01515
1419:1512.04419
1386:2105.07720
1326:1905.07408
1113:2012.03755
1068:1608.01406
1016:References
869:Entailment
843:Variations
246:to a word
142:seen as a
125:hypothesis
114:Definition
80:Bob Coecke
1899:2075-2180
1848:2075-2180
1822:: 28β49.
1797:195874109
1773:: 84β94.
1751:1301.6939
1694:1106.4058
1650:: 50β61.
1629:146120631
1578:2075-2180
1459:: 29β38.
1351:195874109
1343:2075-2180
1319:: 84β94.
1271:0908.3347
1200:2075-2180
1183:1412.8527
1155:2321-9653
1085:2075-2180
1061:: 67β75.
1039:1003.4394
884:Ambiguity
755:∈
720:→
707:…
626:…
587:→
541:⊗
538:⋯
535:⊗
498:∈
391:→
336:…
303:→
290:…
211:→
68:semantics
34:with the
30:to unify
1873:: 1β12.
1674:53775637
1552:: 1β12.
1483:10842035
1247:10763735
1208:18631267
1093:14897915
952:See also
902:ellipsis
898:Anaphora
140:pregroup
20:DisCoCat
1438:5038840
1298:8477212
1000:DisCoPy
138:with a
136:FinVect
74:History
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602:where
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1670:S2CID
1652:arXiv
1625:S2CID
1605:arXiv
1554:arXiv
1521:arXiv
1479:S2CID
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1434:S2CID
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1294:S2CID
1266:arXiv
1243:S2CID
1204:S2CID
1178:arXiv
1108:arXiv
1089:S2CID
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1034:arXiv
886:with
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1844:ISSN
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1081:ISSN
900:and
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