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Principle of compositionality

April 10, 2024

In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege,[1] and arguably it was already assumed by George Boole[2] decades before Frege's work.

The principle of compositionality is highly debated in linguistics. Among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations.[3]

History edit

Discussion of compositionality started to appear at the beginning of the 19th century, during which it was debated whether what was most fundamental in language was compositionality or contextuality, and compositionality was usually preferred.[4] Frege (1848-1925) never adhered to the principle of compositionality as it is known today, and the first to explicitly formulate it was Freges' student Rudolf Carnap in 1947.[4]

Overview edit

A common formulation[4] of the principle of compositionality comes from Barbara Partee, stating: "The meaning of a compound expression is a function of the meanings of its parts and of the way they are syntactically combined."[5]

It is possible to distinguish different levels of compositionality. Strong compositionality refers to compound expressions that are determined by the meaning of its immediate parts and a top-level syntactic function that describes their combination. Weak compositionality refers to compound expressions that are determined by the meaning of its parts as well as their complete syntactic combination.[6][7] However, there can also be further gradations in between these two extremes. This is possible, if one not only allows the meaning of immediate parts but also the meaning of the second-highest parts (third-highest parts, fourth-highest parts, etc.) together with functions that describes their respective combinations.[7]

On a sentence level, the principle claims that what remains if one removes the lexical parts of a meaningful sentence, are the rules of composition. The sentence "Socrates was a man", for example, becomes "S was a M" once the meaningful lexical items—"Socrates" and "man"—are taken away. The task of finding the rules of composition, then becomes a matter of describing what the connection between S and M is.

Among the most prominent linguistic problems that challenge the principle of compositionality are the issues of contextuality, the non compositionality of idiomatic expressions, and the non compositionality of quotations.[3]

It is frequently taken to mean that every operation of the syntax should be associated with an operation of the semantics that acts on the meanings of the constituents combined by the syntactic operation. As a guideline for constructing semantic theories, this is generally taken, as in the influential work on the philosophy of language by Donald Davidson, to mean that every construct of the syntax should be associated by a clause of the T-schema with an operator in the semantics that specifies how the meaning of the whole expression is built from constituents combined by the syntactic rule. In some general mathematical theories (especially those in the tradition of Montague grammar), this guideline is taken to mean that the interpretation of a language is essentially given by a homomorphism between an algebra of syntactic representations and an algebra of semantic objects.

The principle of compositionality also exists in a similar form in the compositionality of programming languages.

Critiques edit

The principle of compositionality has been the subject of intense debate. Indeed, there is no general agreement as to how the principle is to be interpreted, although there have been several attempts to provide formal definitions of it.[8]

Scholars are also divided as to whether the principle should be regarded as a factual claim, open to empirical testing; an analytic truth, obvious from the nature of language and meaning; or a methodological principle to guide the development of theories of syntax and semantics. The Principle of Compositionality has been attacked in all three spheres, although so far none of the criticisms brought against it have been generally regarded as compelling.[citation needed] Most proponents of the principle, however, make certain exceptions for idiomatic expressions in natural language.[8]

The principle of compositionality usually holds when only syntactic factors play in the increased complexity of sentence processing, while it becomes more problematic and questionable when the complexity increase is due to sentence or discourse context, semantic memory, or sensory cues.[9] Among the problematic phenomena for traditional theories of compositionality is that of logical metonymy, which has been studied at least since the mid 1990s by linguists James Pustejovsky and Ray Jackendoff.[10][11][12] Logical metonymies are sentences like John began the book, where the verb to begin requires (subcategorizes) an event as its argument, but in a logical metonymy an object (i.e. the book) is found instead, and this forces to interpret the sentence by inferring an implicit event ("reading", "writing", or other prototypical actions performed on a book).[10] The problem for compositionality is that the meaning of reading or writing is not present in the words of the sentence, neither in "begin" nor in "book".

Further, in the context of the philosophy of language, the principle of compositionality does not explain all of meaning. For example, you cannot infer sarcasm purely on the basis of words and their composition, yet a phrase used sarcastically means something completely different from the same phrase uttered straightforwardly. Thus, some theorists argue that the principle has to be revised to take into account linguistic and extralinguistic context, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.[8]

See also edit

Notes edit

  1. ^ Pelletier, Francis Jeffry (2001). "Did Frege Believe Frege's Principle?". Journal of Logic, Language and Information. 10 (1): 87–114. doi:10.1023/A:1026594023292.
  2. ^ Boole, G. (1854). An investigation of the laws of thought: on which are founded the mathematical theories of logic and probabilities. Walton and Maberly.
  3. ^ a b Pelletier (2016) section "12 This Chapter"
  4. ^ a b c Janssen, Theo (2012). "Compositionality: Its Historic Context". Oxford handbook of compositionality: 19–46. doi:10.1093/oxfordhb/9780199541072.013.0001.
  5. ^ Partee, Barbara (1984). "Compositionality". Varieties of formal semantics. 3: 281–311.
  6. ^ Coopmans, Cas W.; Kaushik, Karthikeya; Martin, Andrea E. (2023). "Hierarchical structure in language and action: A formal comparison". Psychological Review. 130 (4): 935–952. doi:10.1037/rev0000429. ISSN 1939-1471.
  7. ^ a b Pagin, Peter; Westerståhl, Dag (2010). "Compositionality I: Definitions and Variants". Philosophy Compass. 5 (3): 250–264. doi:10.1111/j.1747-9991.2009.00228.x.
  8. ^ a b c Szabó, Zoltán Gendler (2012) "". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. First published Thu Apr 8, 2004; substantive revision Fri Dec 7, 2012
  9. ^ Baggio et al. (2012), Conclusions.
  10. ^ a b Chersoni, E., Lenci, A., & Blache, P. (2017, August). Logical metonymy in a distributional model of sentence comprehension. In Sixth Joint Conference on Lexical and Computational Semantics (* SEM 2017) (pp. 168-177).
  11. ^ James Pustejovsky. 1995. The Generative Lexicon. The MIT Press, Cambridge, MA
  12. ^ Ray Jackendoff. 1997. The Architecture of the Language Faculty. The MIT Press, Cambridge, MA.

References edit

  • Baggio, G., Van Lambalgen, M., & Hagoort, P. (2012) The processing consequences of compositionality, in M. Werning, W. Hinzen, & E. Machery (Eds.), The Oxford handbook of compositionality (pp. 655–672).
  • Janssen, T. M. (2012) Compositionality: Its historic context, in M. Werning, W. Hinzen, & E. Machery (Eds.), The Oxford handbook of compositionality, pp. 19–46, Oxford University Press.
  • Pelletier, Francis Jeffry (2001) Did Frege believe Frege’s principle?, in Journal of Logic, Language, and Information 10:87–114.
  • Pelletier, Francis Jeffry (2016) Semantic Compositionality in M. Aronoff (ed) The Oxford Research Encyclopedia of Linguistics, Oxford UP.

Further reading edit

  • Ferreira, F., Bailey, K. G., & Ferraro, V. (2002). Good-enough representations in language comprehension in Current directions in psychological science, 11(1), 11-15.
  • Ferreira, F., & Patson, N. D. (2007). The ‘good enough’approach to language comprehension in Language and Linguistics Compass, 1(1‐2), 71-83.
  • Szabó, Zoltán Gendler. "Compositionality". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. (2004) revisions in , , , , .
  • Werning, Markus; & Edouard Machery, & Gerhard Schurz (Eds., 2004) The Compositionality of Meaning and Content, Vol. I & II, Ontos
  • Werning, Markus; & Wolfram Hinzen, & Edouard Machery (Eds., 2012) The Oxford Handbook of Compositionality, Oxford University Press

April 10, 2024
principle, compositionality, semantics, mathematical, logic, related, disciplines, principle, compositionality, principle, that, meaning, complex, expression, determined, meanings, constituent, expressions, rules, used, combine, them, principle, also, called, . In semantics mathematical logic and related disciplines the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them The principle is also called Frege s principle because Gottlob Frege is widely credited for the first modern formulation of it However the principle has never been explicitly stated by Frege 1 and arguably it was already assumed by George Boole 2 decades before Frege s work The principle of compositionality is highly debated in linguistics Among its most challenging problems there are the issues of contextuality the non compositionality of idiomatic expressions and the non compositionality of quotations 3 Contents 1 History 2 Overview 3 Critiques 4 See also 5 Notes 6 References 7 Further readingHistory editDiscussion of compositionality started to appear at the beginning of the 19th century during which it was debated whether what was most fundamental in language was compositionality or contextuality and compositionality was usually preferred 4 Frege 1848 1925 never adhered to the principle of compositionality as it is known today and the first to explicitly formulate it was Freges student Rudolf Carnap in 1947 4 Overview editA common formulation 4 of the principle of compositionality comes from Barbara Partee stating The meaning of a compound expression is a function of the meanings of its parts and of the way they are syntactically combined 5 It is possible to distinguish different levels of compositionality Strong compositionality refers to compound expressions that are determined by the meaning of its immediate parts and a top level syntactic function that describes their combination Weak compositionality refers to compound expressions that are determined by the meaning of its parts as well as their complete syntactic combination 6 7 However there can also be further gradations in between these two extremes This is possible if one not only allows the meaning of immediate parts but also the meaning of the second highest parts third highest parts fourth highest parts etc together with functions that describes their respective combinations 7 On a sentence level the principle claims that what remains if one removes the lexical parts of a meaningful sentence are the rules of composition The sentence Socrates was a man for example becomes S was a M once the meaningful lexical items Socrates and man are taken away The task of finding the rules of composition then becomes a matter of describing what the connection between S and M is Among the most prominent linguistic problems that challenge the principle of compositionality are the issues of contextuality the non compositionality of idiomatic expressions and the non compositionality of quotations 3 It is frequently taken to mean that every operation of the syntax should be associated with an operation of the semantics that acts on the meanings of the constituents combined by the syntactic operation As a guideline for constructing semantic theories this is generally taken as in the influential work on the philosophy of language by Donald Davidson to mean that every construct of the syntax should be associated by a clause of the T schema with an operator in the semantics that specifies how the meaning of the whole expression is built from constituents combined by the syntactic rule In some general mathematical theories especially those in the tradition of Montague grammar this guideline is taken to mean that the interpretation of a language is essentially given by a homomorphism between an algebra of syntactic representations and an algebra of semantic objects The principle of compositionality also exists in a similar form in the compositionality of programming languages Critiques editThe principle of compositionality has been the subject of intense debate Indeed there is no general agreement as to how the principle is to be interpreted although there have been several attempts to provide formal definitions of it 8 Scholars are also divided as to whether the principle should be regarded as a factual claim open to empirical testing an analytic truth obvious from the nature of language and meaning or a methodological principle to guide the development of theories of syntax and semantics The Principle of Compositionality has been attacked in all three spheres although so far none of the criticisms brought against it have been generally regarded as compelling citation needed Most proponents of the principle however make certain exceptions for idiomatic expressions in natural language 8 The principle of compositionality usually holds when only syntactic factors play in the increased complexity of sentence processing while it becomes more problematic and questionable when the complexity increase is due to sentence or discourse context semantic memory or sensory cues 9 Among the problematic phenomena for traditional theories of compositionality is that of logical metonymy which has been studied at least since the mid 1990s by linguists James Pustejovsky and Ray Jackendoff 10 11 12 Logical metonymies are sentences like John began the book where the verb to begin requires subcategorizes an event as its argument but in a logical metonymy an object i e the book is found instead and this forces to interpret the sentence by inferring an implicit event reading writing or other prototypical actions performed on a book 10 The problem for compositionality is that the meaning of reading or writing is not present in the words of the sentence neither in begin nor in book Further in the context of the philosophy of language the principle of compositionality does not explain all of meaning For example you cannot infer sarcasm purely on the basis of words and their composition yet a phrase used sarcastically means something completely different from the same phrase uttered straightforwardly Thus some theorists argue that the principle has to be revised to take into account linguistic and extralinguistic context which includes the tone of voice used common ground between the speakers the intentions of the speaker and so on 8 See also editComponential analysis Context principle Semantics computer science Semantics of logic Garden path sentence Initial algebra Levels of Processing model Opaque context another problem for compositionality Referential transparency in programming languages Semantic decomposition natural language processing Notes edit Pelletier Francis Jeffry 2001 Did Frege Believe Frege s Principle Journal of Logic Language and Information 10 1 87 114 doi 10 1023 A 1026594023292 Boole G 1854 An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities Walton and Maberly a b Pelletier 2016 section 12 This Chapter a b c Janssen Theo 2012 Compositionality Its Historic Context Oxford handbook of compositionality 19 46 doi 10 1093 oxfordhb 9780199541072 013 0001 Partee Barbara 1984 Compositionality Varieties of formal semantics 3 281 311 Coopmans Cas W Kaushik Karthikeya Martin Andrea E 2023 Hierarchical structure in language and action A formal comparison Psychological Review 130 4 935 952 doi 10 1037 rev0000429 ISSN 1939 1471 a b Pagin Peter Westerstahl Dag 2010 Compositionality I Definitions and Variants Philosophy Compass 5 3 250 264 doi 10 1111 j 1747 9991 2009 00228 x a b c Szabo Zoltan Gendler 2012 Compositionality In Zalta Edward N ed Stanford Encyclopedia of Philosophy First published Thu Apr 8 2004 substantive revision Fri Dec 7 2012 Baggio et al 2012 Conclusions a b Chersoni E Lenci A amp Blache P 2017 August Logical metonymy in a distributional model of sentence comprehension In Sixth Joint Conference on Lexical and Computational Semantics SEM 2017 pp 168 177 James Pustejovsky 1995 The Generative Lexicon The MIT Press Cambridge MA Ray Jackendoff 1997 The Architecture of the Language Faculty The MIT Press Cambridge MA References editBaggio G Van Lambalgen M amp Hagoort P 2012 The processing consequences of compositionality in M Werning W Hinzen amp E Machery Eds The Oxford handbook of compositionality pp 655 672 Janssen T M 2012 Compositionality Its historic context in M Werning W Hinzen amp E Machery Eds The Oxford handbook of compositionality pp 19 46 Oxford University Press Pelletier Francis Jeffry 2001 Did Frege believe Frege s principle in Journal of Logic Language and Information 10 87 114 Pelletier Francis Jeffry 2016 Semantic Compositionality in M Aronoff ed The Oxford Research Encyclopedia of Linguistics Oxford UP Further reading editFerreira F Bailey K G amp Ferraro V 2002 Good enough representations in language comprehension in Current directions in psychological science 11 1 11 15 Ferreira F amp Patson N D 2007 The good enough approach to language comprehension in Language and Linguistics Compass 1 1 2 71 83 Szabo Zoltan Gendler Compositionality In Zalta Edward N ed Stanford Encyclopedia of Philosophy 2004 revisions in 2005 2007 2012 2017 2020 Werning Markus amp Edouard Machery amp Gerhard Schurz Eds 2004 The Compositionality of Meaning and Content Vol I amp II Ontos Werning Markus amp Wolfram Hinzen amp Edouard Machery Eds 2012 The Oxford Handbook of Compositionality Oxford University Press Retrieved from https en wikipedia org w index php title Principle of compositionality amp oldid 1216584600, wikipedia, wiki, book, books, library,

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