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Design Transformations for Rule-based Procedural Modeling

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Construction grammar

Construction grammar (often abbreviated CxG) is a family of theories within the field of cognitive linguistics which posit that constructions, or learned pairings of linguistic patterns with meanings, are the fundamental building blocks of human language. Constructions include words (aardvark, avocado), morphemes (anti-, -ing), fixed expressions and idioms (by and large, jog X's memory), and abstract grammatical rules such as the passive voice (The cat was hit by a car) or the ditransitive (Mary gave Alex the ball).

Constructive solid geometry

Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, potentially generating visually complex objects by combining a few primitive ones. In 3D computer graphics and CAD, CSG is often used in procedural modeling. CSG can also be performed on polygonal meshes, and may or may not be procedural and/or parametric.

Transformational grammar

In linguistics, transformational grammar (TG) or transformational-generative grammar (TGG) is part of the theory of generative grammar, especially of natural languages. It considers grammar to be a system of rules that generate exactly those combinations of words that form grammatical sentences in a given language and involves the use of defined operations (called transformations) to produce new sentences from existing ones. The method is commonly associated with American linguist Noam Chomsky.

Formal grammar

In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language. Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics.

Code-switching

In linguistics, code-switching or language alternation occurs when a speaker alternates between two or more languages, or language varieties, in the context of a single conversation or situation. Code-switching is different from plurilingualism in that plurilingualism refers to the ability of an individual to use multiple languages, while code-switching is the act of using multiple languages together. Multilinguals (speakers of more than one language) sometimes use elements of multiple languages when conversing with each other.

Phrase structure rules

Phrase structure rules are a type of rewrite rule used to describe a given language's syntax and are closely associated with the early stages of transformational grammar, proposed by Noam Chomsky in 1957. They are used to break down a natural language sentence into its constituent parts, also known as , including both lexical categories (parts of speech) and phrasal categories. A grammar that uses phrase structure rules is a type of phrase structure grammar.

Merge (linguistics)

Merge (usually capitalized) is one of the basic operations in the Minimalist Program, a leading approach to generative syntax, when two syntactic objects are combined to form a new syntactic unit (a set). Merge also has the property of recursion in that it may apply to its own output: the objects combined by Merge are either lexical items or sets that were themselves formed by Merge. This recursive property of Merge has been claimed to be a fundamental characteristic that distinguishes language from other cognitive faculties.

Voice (grammar)

In grammar, the voice (aka diathesis) of a verb describes the relationship between the action (or state) that the verb expresses and the participants identified by its arguments (subject, object, etc.). When the subject is the agent or doer of the action, the verb is in the active voice. When the subject is the patient, target or undergoer of the action, the verb is said to be in the passive voice. When the subject both performs and receives the action expressed by the verb, the verb is in the middle voice.

Ambiguous grammar

In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule. A language that only admits ambiguous grammars is called an inherently ambiguous language. Deterministic context-free grammars are always unambiguous, and are an important subclass of unambiguous grammars; there are non-deterministic unambiguous grammars, however.

Affine variety

In algebraic geometry, an affine algebraic set is the set of the common zeros over an algebraically closed field k of some family of polynomials in the polynomial ring An affine variety or affine algebraic variety, is an affine algebraic set such that the ideal generated by the defining polynomials is prime. Some texts call variety any algebraic set, and irreducible variety an algebraic set whose defining ideal is prime (affine variety in the above sense).