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Model theory and the content of OT constraints
, 2002
"... We develop an extensible description logic for stating the content of optimalitytheoretic constraints in phonology, and specify a class of structures for interpreting it. The aim is a transparent formalisation of OT. We show how to state a wide range of constraints, including markedness, input–outpu ..."
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Cited by 19 (3 self)
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We develop an extensible description logic for stating the content of optimalitytheoretic constraints in phonology, and specify a class of structures for interpreting it. The aim is a transparent formalisation of OT. We show how to state a wide range of constraints, including markedness, input–output faithfulness and base–reduplicant faithfulness. However, output–output correspondence and ‘intercandidate’ sympathy are revealed to be problematic: it is unclear that any reasonable class of structures can reconstruct their proponents’ intentions. But our contribution is positive. Proponents of both output–output correspondence and sympathy have offered alternatives that fit into the general OT picture. We show how to state these in a reasonable extension of our formalism. The problematic constraint types were developed to deal with opaque phenomena. We hope to shed new light on the debate about how to handle opacity, by subjecting some common responses to it within OT to critical investigation.
Visualizing WordNet structure
 In Proc. of the 1st International Conference on Global WordNet
, 2002
"... Representations in WordNet are not on the level of individual words or word forms, but on the level of word meanings (lexemes). A word meaning, in turn, is characterized by simply listing the word forms that can be used to express it in a synonym set (synset). As a result, the meaning a word in Word ..."
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Cited by 5 (0 self)
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Representations in WordNet are not on the level of individual words or word forms, but on the level of word meanings (lexemes). A word meaning, in turn, is characterized by simply listing the word forms that can be used to express it in a synonym set (synset). As a result, the meaning a word in WordNet is determined by its sets of synonyms. This is essentially a recursive definition of word meaning. Hence meaning in WordNet is a structural notion: the meaning of a concept is determined by its position relative to the other words in the larger WordNet structure. We have implemented a set of scripts that visualize the WordNet structure from the vantage point of a particular word in the database. 1
2002. Comparative economy conditions in natural language syntax. Paper presented at the North
 Stanford University
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Definition 1.7
"... A tree T is a relational structure (T, S) where: (i) T, the set of nodes, contains a unique r ∈ T (called the root) such that ∀t ∈ T S ∗ rt. (ii) Every element of T distinct from r has a unique Spredecessor; that is, for every t = r there is a unique element t ′ ∈ T such that St ′ t. (iii) S is a ..."
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A tree T is a relational structure (T, S) where: (i) T, the set of nodes, contains a unique r ∈ T (called the root) such that ∀t ∈ T S ∗ rt. (ii) Every element of T distinct from r has a unique Spredecessor; that is, for every t = r there is a unique element t ′ ∈ T such that St ′ t. (iii) S is acyclic; that is, ∀t¬S + tt. (It follows that S is irreflexive.) Finite transitive trees: (Blackburn et al. 2001: p. 6) A transitive tree is an spo (T, <) such that (i) there is a root r ∈ T satisfying r < t for all t ∈ T and (ii) for each t ∈ T, the set {s ∈ T  s < t} of predecessors of t is finite and linearly ordered by <. Finite binary branching trees (Blackburn and MeyerViol 1997: p. 30) A tuple 〈W, ≻1, ≻2, root, Θ 〉 where “W is a finite, nonempty set, the set of tree nodes; Θ( ⊆ W) contains all and only the tree’s terminal nodes; and root is the (unique) root node of the tree. As for ≻1 and ≻2, there are binary relations defined as follows: (a) for all w, w ′ ∈ W, w ≻1 w ′ iff w ′ is the first daughter of w; and (b) w ≻2 w ′ iff w ′ is the second daughter of w. (c) Note that ≻1 and ≻2 are partial functions, for any node in an ordered binary tree has at most one first daughter and a most one second daughter. (d) Further note that if w ≻2 w ≻1 w ′ ′. (e) Moreover, w ′ ′ = w.” w ′ then there exists a unique w ′ ′ such that 1 Trees: (Carpenter 1997: p. 520523) “We construct trees from a set BasExp of basic expressions as well as a set Cat of categories, which are used to classify expressions. [...] The set Tree of trees over the basic set BasExp of basic expressions and the set Cat of categories is the least such satisfying the following: