Concatenation theory - Revision history

78.133.210.58: Removed hatnote, nothing with “string” in title redirects here

2024-10-22T16:40:54Z

Removed hatnote, nothing with “string” in title redirects here

← Previous revision		Revision as of 16:40, 22 October 2024
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	{{for\|the theory of strings in physics\|String theory}}

	'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for [[formal linguistics]], computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.		'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for [[formal linguistics]], computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.

78.133.210.58: Category:String (computer science)

2024-10-22T16:39:16Z

Category:String (computer science)

← Previous revision		Revision as of 16:39, 22 October 2024
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	{{Reflist}}		{{Reflist}}

			[[Category:String (computer science)]]
	[[Category:Logic]]		[[Category:Logic]]
	[[Category:Syntax]]		[[Category:Syntax]]

FatalSubjectivities: spellling

2023-01-16T12:14:12Z

spellling

← Previous revision		Revision as of 12:14, 16 January 2023
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	The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

	In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[~~Pierce~~'s type-token distinction]].		In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Peirce's type-token distinction]].

	==References==		==References==

FrescoBot: Bot: link syntax

2022-09-27T20:50:28Z

Bot: link syntax

← Previous revision		Revision as of 20:50, 27 September 2022
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	The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

	In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[~~Hans Hermes\|~~Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]].		In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]].

	==References==		==References==

Chiswick Chap: /* top */ rm overlink (and uncited text)

2022-07-25T10:22:27Z

top: rm overlink (and uncited text)

← Previous revision		Revision as of 10:22, 25 July 2022
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	The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

	In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]]~~, not to be confused with similar distinctions underlying other [[type-token distinction]]s~~.		In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]].

	==References==		==References==

Zagreus99 at 19:01, 23 July 2022

2022-07-23T19:01:52Z

← Previous revision		Revision as of 19:01, 23 July 2022
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	The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

	In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[~~:de:~~Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.		In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.

	==References==		==References==

Weidorje at 18:11, 7 July 2020

2020-07-07T18:11:27Z

← Previous revision		Revision as of 18:11, 7 July 2020
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	{{for\|the theory of strings in physics\|String theory}}		{{for\|the theory of strings in physics\|String theory}}

	'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.		'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for [[formal linguistics]], computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.

	The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

I dream of horses: /* top */clean up, typo(s) fixed: Tarski’s → Tarski's

2018-12-19T08:21:30Z

top: clean up, typo(s) fixed: Tarski’s → Tarski's

← Previous revision		Revision as of 08:21, 19 December 2018
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	The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

	In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[:de:Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of ~~Tarski’s~~ 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.		In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[:de:Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.

	==References==		==References==

68.4.165.110 at 07:15, 7 February 2017

2017-02-07T07:15:36Z

← Previous revision		Revision as of 07:15, 7 February 2017
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	'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.		'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.

	The most basic operation on strings is [[concatenation]], ~~connecting~~ two strings to form a longer string whose length is the sum of the lengths of those two strings: ~~abcde~~ is the concatenation of ab with ~~cde~~, in symbols ~~abcde~~ = ab ^ ~~cde~~. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]]; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

	In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[:de:Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski’s 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.		In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[:de:Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski’s 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.

68.4.165.110: will probably be reverted but: Already referred to the "operands" a word I wasn't immediately familiar with as strings at least 3 times earlier in the same sentence (internal consistency).

2017-02-07T07:13:39Z

will probably be reverted but: Already referred to the "operands" a word I wasn't immediately familiar with as strings at least 3 times earlier in the same sentence (internal consistency).

← Previous revision		Revision as of 07:13, 7 February 2017
Line 3:		Line 3:
	'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.		'''Concatenation theory''', also called '''string theory''', '''character-string theory''', or '''theoretical [[syntax]]''', studies [[String (computer science)\|character strings]] over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory.<ref>John Corcoran and Matt Lavine, "Discovering string theory". ''Bulletin of Symbolic Logic''. 19 (2013) 253–4.</ref> A [[generative grammar]] can be seen as a recursive definition in string theory.

	The most basic operation on strings is [[concatenation]], connecting two strings to form a longer string whose length is the sum of the lengths of ~~the~~ ~~operands~~: abcde is the concatenation of ab with cde, in symbols abcde = ab ^ cde. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].		The most basic operation on strings is [[concatenation]], connecting two strings to form a longer string whose length is the sum of the lengths of those two strings: abcde is the concatenation of ab with cde, in symbols abcde = ab ^ cde. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a [[free monoid]].

	In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[:de:Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski’s 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.		In 1956 [[Alonzo Church]] wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".<ref>Alonzo Church, ''Introduction to Mathematical Logic'', Princeton UP, Princeton, 1956</ref> Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by [[:de:Hans Hermes\|Hans Hermes]] and one by [[Alfred Tarski]].<ref>[[John Corcoran (logician)\|John Corcoran]], William Frank and Michael Maloney, "String theory", ''Journal of Symbolic Logic'', vol. 39 (1974) pp. 625– 637</ref> Coincidentally, the first English presentation of Tarski’s 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations.<ref>Pages 173–4 of Alfred Tarski, ''The concept of truth in formalized languages'', reprinted in ''Logic, Semantics, Metamathematics'', Hackett, Indianapolis, 1983, pp. 152–278</ref> As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of [[Pierce's type-token distinction]], not to be confused with similar distinctions underlying other [[type-token distinction]]s.