Plugin: Lexicon

Plugin: Lexicon#

The Lexicon plugin contains additional symbols, relations and operators and their definitions. This plugin provides an expanded vocabulary.

Notation#

Constants#

  1. σ is used to represent delimiters, i.e. spaces.

  2. ε is used to represent null characters.

Variables#

These are general guidelines.

  1. x, y and z are general variables.

  2. π is used to represent indeterminate syllables, i.e. syllabe variables.

  3. ι is used to represent indeterminate characters, i.e. character variables.

  4. α is used to represent indeterminate words, i.e. word variables..

  5. ζ is used to represent indeterminant sentences, i.e. sentence variables.

  6. p, q and r are reserved for propositional variables.

  7. n and m are reserved for numerical variables.

  8. s and t are reserved for string variables.

Lowercase letters a, b, c, ... generally denote elements and uppercase letters A, B, C, ... generally denote sets. It should be clear from context when this convention is not applied.

Indexing#

  1. Character Indexing For a string x, x[i] refers to the character at the i:sup:th index, where the first character in a string is indexed at 0, e.g 'hello'[2] = 'l'.

  2. Word Indexing For a sentence ζ, ζ{i} refers to the word at the i:sup:th index, where the first word in a sentence is indexed at 0, e.g. 'hello person how are you'{2} = 'how'.

Sets#

  1. Language The symbol L refers to the set of all words in a language. If a language other than English is intended, it will be included in a subscript, e.g. L:sub:spanish.

  2. Corpus The symbol C:sub:L refers to the set of all sentences in a language L.

  3. Metric Words The symbol M:sub:S refers to the set of all words that satisfy the syllabic pattern S, where S is a concatenated sequence of syllabic stresses such that + means stressed and - means unstressed. For example, M:sub:-+ refers to the set of all iambic words.

  4. Reflective Words The symbol R refers to the set of all reflective words, i.e. words that are spelled the same forwards as backwards. Mathematically, if α[i] stands for the i:sup:th character in word α, then a reflective word is defined as the words which satisfy the relation α[i] = α[l(α)-i-1]. For example, nun is a reflective word.

  5. Invertible Words The symbol I refers to the set of invertible words. Mathematically, I is the set of word α that satisfy the definition, α ∈ I ↔  inv(α) \in L. For example, time is invertible word because inv(time) = emit and emit ∈ L whereas hello is not invertible because inv(hello) = olleh and olleh ∉ L.

  6. Palindromes The symbol P refers to the set of palindromes. Mathematically, a string x is palindromic if it satisfies the definition x ∈ P ↔ (ς(x) = inv(ς(x))). For example, borrow or rob is a palindrome because ς(borrow or rob) = inv(ς(borrow or rob)) = borroworrob.

Relations#

  1. Rhymes The geometric symbol for the relation of parallel ∥ (U+2225) is used to mean “rhymes with” in the context of linguistics.

  2. Synonymity and Antonymity The logical equivalence symbol ≡ (U+2261) is used to mean “has an equivalent meaning” in the context of linguistics. The logical nonequivalence symbol ≢ (U+2262) is used to mean “has an opposite meaning” in the context of linguistic. ≡ can be thought of as an extension of the relation of “synonym”. For example, “car” and “automobile” satisfy this relation, but even more complex sentences like “Venus is the Morning Star” and “Venus is the Evening Star” are equivalent. Taken to the extreme, “The man bought a sandwich” and “The sandwich, after being meticulously assembled by the delicatessen employee, was purchased by the man” are both linguistic objects that satisfy this relation. ≢ can be thought of as an extension of the relation of “antonym”. For example, “big” and “small” satisfy this relation, but even more complex sentences like “A bird flying high” and “a fish swimming deep” satisfy this relation.

  1. Hypernymity and Hyponymity The left bowtie symbol ⋉ (U+22C9) is used to represent the relation of hyponymity and the right bowtie symbol is used to represent the relation of hypernymity ⋊ (U+22CA). For example, man ⋉ animal and motion ⋊ running. Note that the relations of hyponymity and hypernymity are converses of one another, i.e. x ⋉ y if and only if y ⋊ x.

Operations#

  1. String Length The number of characters in a string x is denoted l(x).

  2. Word Length The number of non-overlapping words in a string x is denoted w(x).

  3. String Inversion A string inversion, inv(x), is an operation that reverses the order of characters in a string, e.g. inv(hello) = olleh.

  4. String Reduction A string reduction, ς(x), is an operation that removes all delimiters from a string, but preserves the relative order of characters, e.g. ς(hello gemini how are you) = hellogeminihowareyou.

  5. Selection A selection, [λx: f(x)], is understood to be any single indeterminate element x that satisfies f(x). In other words, [λx: f(x)] is a single object, not a set. For example, [λx: x ∈ M:sub:+-] refers to an iambic word, e.g. import.

  6. Concatenation For any two strings x and y, their concatenation is written xy. The operands of concatenation are often grouped with brackets, e.g. xy = [x][y].

  7. Succession For any two strings x and y, their succession, denoted, x.y is to mean the literal transcription of the strings on separate new lines. Exponents are used as shorthand for denoting multiple successions, e.g. line(x).line(x) = line(x)^2

  8. Separation For any two strings x and y, their separation, denoated x + y is to meant the literal transcriptions of the strings on separate new lines with a blank line in between them (i.e., separation creates stanzas). Summations are used as shorthand for denoting multiple separations, Σ:sub:`1`:sup`n` x.y denotes n stanzas of couplets (two lines).

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