Information about Algebraic Syntax
Recursive categorical syntax is an algebraic theory of syntax developed by Michael Brame as an alternative to transformational-generative grammar. Brame formulated an algebra (technically a nonassociative groupoid with inverses) of lexical items (words and phrases), or lexes for short. A lex is a string representation of a word or phrase together with a string of directed types. A directed type is a symbol representing a syntactic type together with a direction (up, down, left, right) usually given by an arrow beside or above the symbol. In this article left and down arrows will be placed to the left and right and up arrows to the right of symbols.
Lexical composition of two lexes is performed by concatenating the phonetic or orthographic representations and composing the directed type strings. Thus [A, B] [C, D] = [AC, BD]. In our groupoid of directed type strings we define X→←X = X↑↓X = ←X↓X = X↑X→ = 1 for all X so that these strings "cancel."
With these definitions we can consider the subgroupoid generated by a lexicon of primitive lexes. For example, our lexicon might contain the words [We, ←SV→], [went, ←VN→], and [home, ←N], from which we can construct [We, ←SV→] [went, ←VN→] [home, ←N] = [We went home, ←S]. Given a correct lexicon to begin with, the theory of algebraic syntax claims that the grammatical sentences will be precisely those with directed type ←S.
Lexical composition of two lexes is performed by concatenating the phonetic or orthographic representations and composing the directed type strings. Thus [A, B] [C, D] = [AC, BD]. In our groupoid of directed type strings we define X→←X = X↑↓X = ←X↓X = X↑X→ = 1 for all X so that these strings "cancel."
With these definitions we can consider the subgroupoid generated by a lexicon of primitive lexes. For example, our lexicon might contain the words [We, ←SV→], [went, ←VN→], and [home, ←N], from which we can construct [We, ←SV→] [went, ←VN→] [home, ←N] = [We went home, ←S]. Given a correct lexicon to begin with, the theory of algebraic syntax claims that the grammatical sentences will be precisely those with directed type ←S.
References
- Brame, Michael. "Universal Word Induction vs Move &alpha" in Linguistic Analysis, Vol. 14, No. 4, 1984.
- Brame, Michael. "Recursive Categorical Syntax I: Semigroups, Monoids, Lattices, and Categories" in Linguistic Analysis, Vol. 14, No. 1.
- Brame, Michael. "Recursive Categorical Syntax II: n-arity and Variable Continuation" in Linguistic Analysis, Vol. 15, No. 2-3, 1985.
- Brame, Michael. "Recursive Categorical Syntax III: dl-Induction" in Linguistic Analysis.
In computer science, SYNTAX is a system used to generate lexical and syntactic analyzers (parsers) (both deterministic and non-deterministic) for all kind of context-free grammars
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In linguistics, a transformational grammar, or transformational-generative grammar (TGG), is a grammar, especially of a natural language, that has been developed in a Chomskian tradition.
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Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. Most authors nowadays simply write algebra instead of abstract algebra.
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groupoid is a simultaneous generalisation of a group, a setoid (a set equipped with an equivalence relation), and a -set (a set equipped with an action of a group ). Groupoids are often used to capture information about geometrical objects such as manifolds.
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