| { | |
| "paper_id": "1991", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T07:35:04.481220Z" | |
| }, | |
| "title": "The Specification and Implementation of Constraint-Based Unification Grammars*", | |
| "authors": [ | |
| { | |
| "first": "Bob", | |
| "middle": [], | |
| "last": "Carpenter", | |
| "suffix": "", | |
| "affiliation": {}, | |
| "email": "" | |
| }, | |
| { | |
| "first": "Carl", | |
| "middle": [], | |
| "last": "Pollardt", | |
| "suffix": "", | |
| "affiliation": {}, | |
| "email": "" | |
| }, | |
| { | |
| "first": "Alex", | |
| "middle": [], | |
| "last": "Franz", | |
| "suffix": "", | |
| "affiliation": {}, | |
| "email": "" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
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| "abstract": "Our aim is to motivate and provide a specification for a unification-based natural language processing system where grammars are expressed in terms of principles which constrain linguis tic representations. Using typed feature structures with multiple inheritance for our linguistic representations and definite at tribute-value logic clauses to express constraints, we will develop the bare essenti a ls required for an implementation of a parser and generator for the Head-driven Phrase Structure Grammar (HPSG) formalism of Pollard and Sag (1987).", | |
| "pdf_parse": { | |
| "paper_id": "1991", | |
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| "abstract": [ | |
| { | |
| "text": "Our aim is to motivate and provide a specification for a unification-based natural language processing system where grammars are expressed in terms of principles which constrain linguis tic representations. Using typed feature structures with multiple inheritance for our linguistic representations and definite at tribute-value logic clauses to express constraints, we will develop the bare essenti a ls required for an implementation of a parser and generator for the Head-driven Phrase Structure Grammar (HPSG) formalism of Pollard and Sag (1987).", | |
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| "section": "Abstract", | |
| "sec_num": null | |
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| "text": "In the past decade, two competing approaches to the scientific study of natural language gram mar have become predominant, the rule-based approach and the principle/constraint-based approach. Within the rule-based approach, exemplified by Lexical Functional Grammar (LFG) (Bresnan 1982) and Generalized Phrase Structure Grammar (GPSG) (Gazdar et al. 1985) , rules are taken to correspond to grammatical constructions and are modeled as more or less schematic productions with the well-formed structures of the language generated over a finite set of lexical items by recursively applying the rules. Both LFG and GPSG are based upon context-free skeletons and explain syntactic dependencies in terms of informational consistency constraints that can be solved using feature structure unification. There has been a great deal of success in implementing these formalisms, in part due to their declarative nature and nat ural semantics, but also due to the existence of general unification-based grammar processing systems such as Fu nctional Unification Grammar (FUG) (Kay 1985) and PATR-II (Shieber et al. 1983) .", | |
| "cite_spans": [ | |
| { | |
| "start": 272, | |
| "end": 286, | |
| "text": "(Bresnan 1982)", | |
| "ref_id": "BIBREF4" | |
| }, | |
| { | |
| "start": 335, | |
| "end": 355, | |
| "text": "(Gazdar et al. 1985)", | |
| "ref_id": "BIBREF12" | |
| }, | |
| { | |
| "start": 1088, | |
| "end": 1109, | |
| "text": "(Shieber et al. 1983)", | |
| "ref_id": "BIBREF36" | |
| } | |
| ], | |
| "ref_spans": [], | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "Principle-based approaches to grammar have become predominant in theoretical linguistics, primarily due to the influence of Chomsky's (1981) Government-Binding (GB) framework. The novel aspect of GB considered as a grammar formalism is that it advocates the total abandonment of construction-specific rules in favor of a collection of interacting principles which serve to delimit the well-formed linguistic structures. Candidate structures are generated according to extremely general, universal, phrasal immediate dominance (ID) schemata (X Theory) and then iteratively transformed using movement rules (Move-a) in accordance with a number of highly tuned principles to deal with case (Case Theory), complementation (Projection Principle), pronominal and other coreference (Binding Theory), long-distance dependencies", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| "text": "\u2022The authors would like to thank Bob Kasper for a number of useful comments on an earlier draft of this paper. The research of Pollard and Franz was supported by a grant from the National Science Foundation .", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| { | |
| "text": "(Empty Category Principle and Subjacency) and so forth. Patterns of cross-linguistic variation are accounted for by means of the parametrization of these principles.", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| "text": "The methodological distinction between these two approaches is widely supposed to be that rules enumerate possibilities, while principles eliminate possibilities. But it is quite difficult to distinguish formally between a parametrized disjunctive principle and a collection of schematic rules only one of which can apply . \ufffdo a given structure. Consider, for example, the distinction between categorial grammar application schemata, basic ID rules of GPSG, and the C-structure con straints of LFG, on the one hand, and the disjunctive clauses of X Theory or the Empty Category Principle on the other. It should also be borne in mind that so-called rule-based approaches often employ not only rules but also global constraints on representations which behave similarly to principles, such as the Head Feature Convention and the Control Agreement Principle of GPSG or the Completeness and Function-Argument Biuniqueness Conditions of LFG.", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| "text": "HPSG belongs to the \"unification-based\" family of linguistic theories, but differs from LFG and GPSG in that grammars are formulated entirely in terms of universal and language-specific principles expressed as constraints on feature structures, which in turn are taken to represent possible linguistic objects. As shown by Pollard and Sag (1987) , constraints on feature struc tures can be used to do the same duty as many of the principles and rules of GPSG, LFG and GD. Unlike rule-based theories, in HPSG, immediate dominance and linear precedence condi tions ( traditional phrase-structure) are not modeled any differently than other constraints. But like the rule-based approaches, there is no appeal to derivational notions such as movement; th\ufffd work of transfor\ufffdations in GB is taken over by declarative constraints stated at a single level of representation.", | |
| "cite_spans": [ | |
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| "start": 323, | |
| "end": 345, | |
| "text": "Pollard and Sag (1987)", | |
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| "text": "Departing from more traditional formalisms which employ phrase-structure trees as the primary device for linguistic representation, we follow HPSG ( and to some extent LFG) in representing linguistic objects as fe ature structures. To this end, we show how a natural type discipline can be imposed on fe ature structures allowing for multiple inheritance and the speci fication of feature appropriateness and value restrictions. Our typing will be strong in the sense that every feature structure must be associated with a type. Strong typing carries with it the usual benefits of early error detection and enhanced control over crucial memory allocation, ac cess an<l reclamation functions. The use of multiple inheritance allows a sophisticated network of constraints to be expressed at the appropriate level of detail. This is especially important for the development of large lexicons (Flickinger et al. 1985) .", | |
| "cite_spans": [ | |
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| "start": 889, | |
| "end": 913, | |
| "text": "(Flickinger et al. 1985)", | |
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| "text": "Our types can be used to represent information that must be encoded by expensive structural unification or inference steps in untyped systems. In automatic deduction systems, this has been found to provide a significant run-time gain due to the fact that useless branches in the search space can be efficiently detected and pruned before the creation of expensive structural copies or binding frames (Walther 1985 (Walther , 1988 A1t-Kaci and Nasr 1986) .", | |
| "cite_spans": [ | |
| { | |
| "start": 400, | |
| "end": 413, | |
| "text": "(Walther 1985", | |
| "ref_id": "BIBREF38" | |
| }, | |
| { | |
| "start": 414, | |
| "end": 429, | |
| "text": "(Walther , 1988", | |
| "ref_id": "BIBREF39" | |
| }, | |
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| "start": 430, | |
| "end": 453, | |
| "text": "A1t-Kaci and Nasr 1986)", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| { | |
| "text": "In a constraint-based linguistic theory such as HPSG, parsing and generation reduces to solving constraints. We allow constraints to be expressed by a feature logic analogue of definite clauses. The benefit of this approach is that it admits a natural and effective method paralleling SLD-resolution (see Lloyd 1984) for enumerating the solutions to a system of constraints.", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| "text": "Type declarations in our system contain information concerning su btyping and appropriateness conditions which state the fe atures that are appropriate for each type and the values that they can take. If a \ufffd r we say that a subsumes, is more general than or a supertype of T. We refer to the least upper bound operation in our inheritance hierarchy as (type) unification since the least upper bound of a set of objects representing partial information is the object which represents the most general piece of information that is more specific than each member of the set. The least upper bound of the empty set is written J_, read \"bottom\", and is the unique universal or most general type. Our restrictions on appropriateness are analogous to the condition of regularity in the signatures of order-sorted algebras (Meseguer et al. 1987) ; taken together, the conditions on the inheritance hierarchy and appropriateness function will ensure that unification is well defined and produces a unique result, which is crucial for efficient and natural unification-based processing (Pereira 1987 ).", | |
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| "start": 815, | |
| "end": 837, | |
| "text": "(Meseguer et al. 1987)", | |
| "ref_id": "BIBREF23" | |
| }, | |
| { | |
| "start": 1076, | |
| "end": 1089, | |
| "text": "(Pereira 1987", | |
| "ref_id": "BIBREF28" | |
| } | |
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| "section": "Inheritance and Appropriat eness", | |
| "sec_num": "2" | |
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| "text": "We will begin by introducing an untyped collection of fea ture structures which are similar to the ?p-terms of AYt-Kaci ( \u2022 0 : Q -+ Ty pe : a total node type assignment", | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| "text": "\u2022 6 : Feat x Q -+ Q : a partial fe ature value function Thus a feature structure is a rooted, connected, directed graph with vertices labeled by types and edges labeled by features. We will write q : a L q' : a' if c(f, q) = q' and 0(q) = a and 0(q') = a'. We think of each node as representing a partial frame or record with values for its slots given by its outgoing arcs. We let Path = Fe at* be the set of paths, which consist of finite sequences of features. We let \u00a3 denote the empty path and extend c to paths by setting 6(\u00a3, q) = q and 6(f7r,q) = c(1r, c(f, q)).", | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| "text": "Our definition requires that every node be reachable from the root node ij, where c( 1r, ij) is the node that can be reached from ij along the path 1r.", | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| "text": "Note that we have not disallowed cyclic feature structures, in which there is some non-empty path 1r and node q such that 6(1r,q) = q.", | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| { | |
| "text": "We extend our ordering on types to an ordering of the feature structures in the usual way (see Pollard and Moshier 1990) .", | |
| "cite_spans": [ | |
| { | |
| "start": 95, | |
| "end": 120, | |
| "text": "Pollard and Moshier 1990)", | |
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| "section": "Feature Structures", | |
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| "text": "Definition 3 (Subsumption) F = (Q,ij,0, c) subsumes F' = (Q', ii.', 0',c'), F h F', iff there is a \u2022 total h : Q -+ Q' such that \u2022 h ( ij) = ii' \u2022 0(q) k 0'(h(q)) fo r every q E Q - \u2022 h(c(f, q)) = c'(f, h(q)) fo r every q E Q and fea ture f such that c(f, q) is defined", | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| "text": "The last two conditions on h can be stated graphically as requiring that if q : a L q' : a' in F-then h( q) : r L h ( q') : r' in F' and furthermore, a k T and a' h r'. Such a mapping takes each node of the more general structure \u2022 onto a node of the more specific structure in a way that preserves structure sharing and does not lose any type information.", | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| "text": "Subsumption is only a pre-ordering, so we write F rv F' if F !;;; F' and F' !;;; F and say that F and F' are alphabetic variants. We could work in the collection of feature structures modulo al phabetic variance, which is guaranteed to be a partial order, but this becomes tedious (for an elegant approach to representing these equivalence classes, see Moshier (1988) ). In our situation, with only a pre-order, we define a unifier of a pair of feature structures F and F' to be any feature structure F\" such that F h G and F' k G if and only if F\" h G. The primary result concerning subsumption is stated as follows:", | |
| "cite_spans": [ | |
| { | |
| "start": 353, | |
| "end": 367, | |
| "text": "Moshier (1988)", | |
| "ref_id": "BIBREF24" | |
| } | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| "text": "Theorem 4 (Unification) Unique unifiers exist fo r pairs of consistent feature structures, up to alphabetic variance.", | |
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| "section": "Feature Structures", | |
| "sec_num": "3" | |
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| "text": "Proof: The usual unification algorithm for fe ature structure works with the addition of a step that unifies the types of the inputs to produce the type of the result and fails if the types are not consistent. See Ai\"t-Kaci (1984) or Pollard and. Moshier (1990) .", | |
| "cite_spans": [ | |
| { | |
| "start": 247, | |
| "end": 261, | |
| "text": "Moshier (1990)", | |
| "ref_id": "BIBREF32" | |
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| "sec_num": "3" | |
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| "text": "In theory, the asymptotic behavior of the unification algorithm is not affected; type unification can be carried out by table look-up. In practice, the negligible constant overhead of type unification at every step of the process will actually save time in that inconsistencies can be detected before any recursive structures need to be inspected.", | |
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| "text": "We now define a notion of typing which singles out some of the fe ature structures as be ing well-typed. Intuitively, a feature structure is well-typed if every feature that appears is appropriate and takes an appropriate value.", | |
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| "text": "Definition 5 (Well-Typing) A fe ature structure F = (Q,q,0,6) is well-typed if q : a \ufffd q' : a' in F implies Approp(f, a) \ufffd a'.", | |
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| "text": "If Fis a feature structure and F' a well-typed feature structure such that F \ufffd F' then we say that F' is a well-typed extension of F and that F is typable .", | |
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| "text": "Fortunately, the user does not need to specify all of the values for appropriate features about which nothing is known; a type inference procedure can be defined that determines the minimum possible types that will extend a feature structure so that it is well-typed. Proof: A constructive type inference procedure can proceed by successively increasing the types on those nodes which do not yet meet the appropriateness conditions. All that is required is the iteration of the following steps untH a closure is reached:", | |
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| "section": "\u25a1", | |
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| "text": "\u2022 if a feature is defined at a node, the type of the node should be unified with the minimal type appropriate for the feature.", | |
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| "section": "\u25a1", | |
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| "text": "\u2022 if a feature is defined and its value is not of great enough type, unify in the type for the minimal value.", | |
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| "text": "Thus every typable feature structure has a minimal well-typed extension which is unique up to alphabetic variance. This process is not sensitive to the order in which nodes and features are chosen. It is also guaranteed to terminate as there are only a finite number of types and nodes to start with. To see that the result is minimal, simply notice that each operation in the iteration was required so that the result is well-typed.", | |
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| "text": "The function T yplnf displays a host of interesting properties. For instance, it can be factored into two separate operations corresponding to the two steps in Typlnf. It is not hard to see that that F \ufffd Typlnf(F), Typlnf(F) = Typlnf(Typlnf(F)), and F \ufffd F' implies that Typlnf(F) \ufffd Typlnf(F'). More significantly, we have:", | |
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| { | |
| "text": "(", | |
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| "text": "1) T yplnf(Typlnf( Fi ) LJ \u2022 \u2022 \u2022 LJ T yplnf(F n )) = Typlnf(F 1 LJ \u2022 \u2022 \u2022 LJ F n )", | |
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| "text": "whenever the latter exists. This means that we can be as lazy as we like about type inference at run time without fe ar of information loss. It also follows that the type inference procedure can be composed with a unification procedure for feature structures to provide a unification procedure for well-typed fe ature structures. The significance of this theorem is that it will be possible to compute the least specific well-typed fe ature structure that extends a consistent pair of well-typed feature structures. This notion of well-typing is not the only one possible. It is a lso sensible to consider a stronger notion of typing whereby every fe ature that is appropriate must be defined. This notion, called total well-typing, corresponds to the composition of Typlnf with a second closure operator that adds in features that have not been defined in Typlnf(F) and gives them their minim a l values. As Franz (1990) points out, the appropriateness conditions must meet a certain acyclicity condition to ensure the termination of type inference for this stronger notion of typing. These more strongly typed systems allow better management of memory since feature structures of a given type are of a known size and can have their feature values indexed positionally rather than by feature/value pairs. On the other hand, the notion of well-typing that we consider here is simpler and is also better suited to applications in which the number of features containing information is sparse relative to the number of possible features that can be defined for any given feature structure. For instance, in the application to HPSG we provide below, feature structures occurring early in the search space . will be quite sparse compared to their later instantiations.", | |
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| "text": "vVe can describe our feature structures with a variant of the feature logic introduced by Rounds and Kasper (1986) . We present a simultaneous definition of both the well-formed fo rmulas or descriptions and of satisfa ction of a formula by a fe ature structure, which we write F F <f>:", | |
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| { | |
| "start": 90, | |
| "end": 114, | |
| "text": "Rounds and Kasper (1986)", | |
| "ref_id": "BIBREF34" | |
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| "section": "Feat ure Logic", | |
| "sec_num": "4" | |
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| "text": "F F a the root node of F is assigned a type at least as specific as a F F 7r : </> the value of F at 1r is defined and satisfies </> F F 7r ::E:: 1r' the paths 1r and 1r' lead to the same node in F F F </> I\\ 'ljJ F F </> and F F 1/;.", | |
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| "section": "Definition 8 (Formulas and Satisfaction) FORM ULA SATISFACTION CONDITION", | |
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| "text": "F F </> V 1/; F F </> or F F 'l/J.", | |
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| "section": "Definition 8 (Formulas and Satisfaction) FORM ULA SATISFACTION CONDITION", | |
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| "text": "The bchavior of this logic on the typed feature structures we present here can be given a complete equational axiomatization along the lines of Rounds and Kasper (1986) Proof: The proof of Rounds and Kasper (1986) can be easily adapted by applying the type inference procedure. The key result is that the set of minimal satisfiers of a conjunction is derived by the pairwise unification of the minimal satisfiers of the conjuncts.", | |
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| "end": 168, | |
| "text": "Rounds and Kasper (1986)", | |
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| "text": "Rounds and Kasper (1986)", | |
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| "section": "Definition 8 (Formulas and Satisfaction) FORM ULA SATISFACTION CONDITION", | |
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| "text": "Departing from Pollard and Sag (1987) and following Pollard and Moshier (1990), we attach constraints to types rather than allowing general implicative and negative constraints. The constraints attached to types will be much more expressive than the easily decidable conditions arising from the inheritance and appropriateness conditions in the type scheme which are only intended to specify the class of well-typed fe ature structures over which the constraints range.", | |
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| "section": "\u25a1 5 Constraint Systems and Solutions", | |
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| "text": "Definition 10 ( Constraint S ystem) A constraint system \ufffd associates each type r with a fe ature logic fo rmula", | |
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| "section": "\u25a1 5 Constraint Systems and Solutions", | |
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| { | |
| "text": "\ufffd 7\" \u2022", | |
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| "section": "\u25a1 5 Constraint Systems and Solutions", | |
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| "text": "We provide for the multiple inheritance of constraints, letting ! \ufffd 7\" be the conjunction of the constraints associated with T and all of its supertypes; formally ! \ufffd 7\" = /\\ (j c 7\" \ufffd (j ; Since the feature structures in \ufffd (j may contain arbitrary types, the system \ufffd may be recursive. Pollard and Sag (1987) show how systems of constraints of this general form can \u2022 be used to model not only language-specific grammars, but also entire linguistic theories ( universal grammars) . In general, we will be interested in solving queries with respect to systems of constraints, where a query simply consists of an feature logic description. In applications to parsing, a query would represent the value of the phonology fe ature and a constraint on the syntactic category of the result; for generation, a query might represent instantiated semantic and pragmatic features. A solution is then a well-typed fe ature structure which satisfies both the query and all of the constraints expressed by the grammar.", | |
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| "start": 459, | |
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| "text": "( universal grammars)", | |
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| "section": "\u25a1 5 Constraint Systems and Solutions", | |
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| "text": "A fea ture structure F is a solution to a query 1/; with respect to a system \ufffd of cons!raints just \u2022 in case F F 1/; and the maximal substructure F q _ roqted at each node q of F satisfies the inherited constraint on its type B", | |
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| "text": "(q), so that F q I= !\ufffd o( q ) \u2022", | |
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| "text": "We will provide a complete method for generating the solutions to queries with respect to constraint systems that is defined in terms of non-deterministic feature structure rewriting. Our method is inspired by the rewriting operation employed by Art-Kaci (1984) , which, to the best of our knowledge, was the first programming system based upon recursively defined constraints on feature structures; but our method is cleaner in that it provides a strong distinction between the logical language and its feature structure models and also more general in that it applies to cyclic feature structures. More importantly, our system is provably complete.", | |
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| "text": "Art-Kaci (1984)", | |
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| "text": "The basic operation of rewriting is to non-deterministically choose a node in the feature structure and then non-deterministically choose a minimal satisfier for the inherited constraint associated with the type attached to that node to be unified into the feature structure. This is analogous to SLD-resolution as applied to definite clauses, in which a subgoal is replaced by the body of a clause after unifying the head of the clause with the subgoal.", | |
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| "text": "Let 7r \u2022 F be the fe ature structure consisting of the path 1r with F attached to its terminal node.", | |
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| "text": "Definition 12 (Rewriting) If F is a well-typed fe ature structure where the node at path 1r is assigned type u and if G is a minimal satisfier of the inherited constraint ! \ufffd (j on u then rewriting is defined so that F \u21d2 Typlnf(F LI 1r \u2022 G) .", | |
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| "text": "Of course, as we mentioned earlier, type inference can be interleaved arbitrarily with this rewriting operation. We can also interleave rewriting along arbitrary paths, using the notation F ==> F' if F \u21d2 F' for some path 1r.", | |
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| "text": "Our next theorem shows that minimal solutions can be effectively generated by rewriting. In effect, it is the completeness theorem for our operational interpretation; it tells us that every solution can be found by rewriting. In particular, a breadth-first enumeration of the search space determined by the rewriting system will eventually uncover every solution. is a solution to the query 1/; with respect to the constraint system \ufffd if and only if F \ufffd F fo r every path 1r fo r which F is defined. F is a minimal solution if and only if there is a derivation of F by rewriting fro m a minimal satisfier of 'lj; . Proof: {Sketch) The conditions on a solution are just that every node satisfy the constraint on its type. This happens if and only if the unifying in of a minimal satisfier to the constraint does not add any new information .", | |
| "cite_spans": [], | |
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| { | |
| "start": 364, | |
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| "text": "is a solution to the query 1/; with respect to the constraint system \ufffd if and only if F \ufffd F fo r every path 1r fo r which F is defined. F is a minimal solution if and only if there is a derivation of F by rewriting fro m a minimal satisfier of 'lj;", | |
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| "sec_num": null | |
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| "text": "The usual fixed-point style induction suffices to establish minimality. Suppose we fix a solution to the query 1/;. In the base case, this solution must be more specific than a minimal satisfier of the query 1/;. The inductive hypothesis is that at every stage during rewriting we are dealing with a fe ature structure which subsumes the solution.", | |
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| "section": "Theorem 13 (Solution) F", | |
| "sec_num": null | |
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| "text": "During rewriting, we unify in constraints associated with more general types than in the solution since we have a fe ature structure which subsumes the solution. Since we inherit con straints, rewriting can be done so that it unifies in a minimal satisfier to a constraint which subsumes the minimal satisfier associated with the corresponding node in the solution . The rewriting process will eventually reach a solution aft er a finite number of steps or continue on indefinitely, because there are only a finite number of steps that can be taken without adding in more nodes due to the finite number . of nodes in a feature structure and finite number of types in the inheritance hierarchy.", | |
| "cite_spans": [], | |
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| "section": "Theorem 13 (Solution) F", | |
| "sec_num": null | |
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| "text": "If rewriting reaches a solution, then by the inductive hypothesis, that solution must be at least as general as the given solution. Finite satisfiers which are not generated by rewriting from a minimal satisfier of the query can thus not be minimal. append( 1r1 , 1r2 , 1r3) , where 1r1 , 1r2, and 1r3 are paths; this means that the value of the path 1r3 must be the concatenation of the values of 1r1 and 1r2\u2022 Such relations can be given definite-clause-style recursive definitions, as in:", | |
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| { | |
| "start": 250, | |
| "end": 274, | |
| "text": "append( 1r1 , 1r2 , 1r3)", | |
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| "sec_num": null | |
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| "text": "(2) append ( 1r1 , 1r2, 1r3 ) Adding definitions of this kind to our feature logic is somewhat analogous to augmenting an un derlying constraint language with definite relations as proposed by Hohfeld and Smolka (1988) . However, it should be borne in mind that the 7ri in our definition schemata are path parameters, not genuine logical variables. Ai't-Kaci (1984) showed how relations could be encoded as types with arguments specified by fe atures and arbitrary constraints for definitions; each use of such a relation then requires a node in a feature structure at which to be anchored (usually as the value of a so-called garbage fea ture). Franz (1990) implemented relations directly, requiring their arguments to be typed; in the case of append, all of the arguments would be of type list, which has two subtypes: nil (empty list), which is not appropriate for any fe atures, and ne-list (nonempty list), which is appropriate for the fe atures FIRST with value restriction .l and REST with value restriction list.", | |
| "cite_spans": [ | |
| { | |
| "start": 193, | |
| "end": 218, | |
| "text": "Hohfeld and Smolka (1988)", | |
| "ref_id": "BIBREF13" | |
| }, | |
| { | |
| "start": 646, | |
| "end": 658, | |
| "text": "Franz (1990)", | |
| "ref_id": "BIBREF11" | |
| } | |
| ], | |
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| "start": 11, | |
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| "text": "( 1r1 , 1r2, 1r3 )", | |
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| ], | |
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| "section": "\u25a1 For the sake of brevity we have not discussed constraints which express n-ary relational dependencies between path values. An example of a relational dependency expression would be", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The typed system described here has been implemented in both Lisp (Franz 1990 ) and Pro log. Emele and Zajac (personal communication) report that Fr anz's (1990) grammar has been ported, with a 100-fold speedup, to their TFS system (1990) which was originally based on Alt-Kaci (1984 . We anticipate that a number of the optimizations employed in TFS will carry over to the system described here. In Franz 's system, compilation is first carried out on the type scheme and constraints to detect errors and compute minimal satisfiers. A serious processing bottleneck can be traced to the search incurred by disjunctive constraint solving. This naturally leads to the issue of which search strategy should be employed. The conclusion of Franz ( 1990) was that specialized search strategies would be needed for linguistic applications. Ideally, a general mechanism for specifying search preference would be provided. The complexity of the basic operations of this system is very low. Subsumption can be computed in linear time by explicit construction of the mapping function . Similarly, efficient near-linear unification algorithms can be used (Jaffar 1984) . On the other hand, disjunctive representations are very compact in that the number of minimal satisfiers for a formula is exponential in the size of the formula in the worst case and satisfiability of a formula is NP complete (Kasper and Rounds 1986) . Relatively efficient practical algorithms for dealing with disjunctions have been developed by Kasper (1987) and Eisele and Dorre (1988) . Another option that is being explored is the utilization of total typing as discussed above, for managing memory allocation and improving the speed of both unification and the unwinding of information upon backtracking. The features values themselves could then be retrieved automatically without searching through a collection of feature-value pairs. Hopefully, compilation and run-time optimization techniques employed for logic programs can also be directly incorporated, such as type indexing for rules and deterministic tree pruning.", | |
| "cite_spans": [ | |
| { | |
| "start": 66, | |
| "end": 77, | |
| "text": "(Franz 1990", | |
| "ref_id": "BIBREF11" | |
| }, | |
| { | |
| "start": 269, | |
| "end": 283, | |
| "text": "Alt-Kaci (1984", | |
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| { | |
| "start": 735, | |
| "end": 748, | |
| "text": "Franz ( 1990)", | |
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| }, | |
| { | |
| "start": 1143, | |
| "end": 1156, | |
| "text": "(Jaffar 1984)", | |
| "ref_id": "BIBREF14" | |
| }, | |
| { | |
| "start": 1385, | |
| "end": 1409, | |
| "text": "(Kasper and Rounds 1986)", | |
| "ref_id": "BIBREF18" | |
| }, | |
| { | |
| "start": 1507, | |
| "end": 1520, | |
| "text": "Kasper (1987)", | |
| "ref_id": "BIBREF16" | |
| }, | |
| { | |
| "start": 1525, | |
| "end": 1548, | |
| "text": "Eisele and Dorre (1988)", | |
| "ref_id": "BIBREF8" | |
| } | |
| ], | |
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| "section": "Implementation", | |
| "sec_num": "6" | |
| }, | |
| { | |
| "text": "Furthermore, the connections between constraint-based grammars and terminological knowl edge representations based on inheritance networks such as KL-ONE (Brachman and Schmolze 1985) and especially its descendant LOOM (Mac Gregor 1988) has only begun to be explored (Kasper 1989, Nebel and Smolka 1989) ; there is a great deal of promise that insights from these systems can be employed to produce more powerful and efficient type inference and search tech niques. Kasper and Pollard are currently exploring the possibility of a chart-parser analog for HPSG-style grammars that exploits the possible-worlds mechanism of LOOM for conceptually clean and space-efficient structure sharing within the chart.", | |
| "cite_spans": [ | |
| { | |
| "start": 266, | |
| "end": 289, | |
| "text": "(Kasper 1989, Nebel and", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 290, | |
| "end": 302, | |
| "text": "Smolka 1989)", | |
| "ref_id": "BIBREF27" | |
| } | |
| ], | |
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| }, | |
| { | |
| "text": "There are many possible extensions that could be added to our constraint systems. In particular, Pollard and Moshier (1990) have provided a compatible account of set valued fe ature structures, Carpenter (1990) has added a notion of inequation analagous to the inequations of Prolog II (Colmerauer 1984) , and a general notion of feature structure extensionality is discussed in Pollard and Carpenter (to appear).", | |
| "cite_spans": [ | |
| { | |
| "start": 97, | |
| "end": 123, | |
| "text": "Pollard and Moshier (1990)", | |
| "ref_id": "BIBREF32" | |
| }, | |
| { | |
| "start": 286, | |
| "end": 303, | |
| "text": "(Colmerauer 1984)", | |
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| } | |
| ], | |
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| }, | |
| { | |
| "text": "One thing that this system shares with PATR-II and other general unification-based systems is that while the solutions to queries can be recursively enumerated, it is undecidable whether a query has a solution. While we do not present a proof here, the result follows from the fact that logic programs an d queries can be reduced to the solution of a system of constraints (the trick is to include proof trees as a type and encode the notion of an acceptable proof tree with respect to a program as a constraint on its type). Of course, this does not render our system unusable any more than Prolog or PATR-II are rendered useless by their undecidability; it just means that the user must exercise due caution in constructing linguistically reasonable grammars, in order to ensure that all-paths parsing always terminates. In generation, of course, nontermination is to be expected; but in this case, fortunately, a single solution will suffice.", | |
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| "FIGREF0": { | |
| "uris": null, | |
| "text": "ure Structure) A fe ature structure is a tuple F = (Q, q, 8, c5) where \u2022 q : the root node in Q \u2022 Q : a finite set of nodes roo ted at ij so that Q = { c5( 1r, q) I 1r E Path} (s ec below fo r definition of c5( 1r, q) and Path) t A subset X of a partial ordering (S, \ufffd) is said to be consistent if it has an upper bound. A partial order is consistently complete if every (possibly empty) consistent set X has a least upper bound, which we write LJ X, or xUy when X = {x, y}.", | |
| "num": null, | |
| "type_str": "figure" | |
| }, | |
| "FIGREF1": { | |
| "uris": null, | |
| "text": "Type Inference) There is an effectively computable partial fu nction Typlnf fro m the feature structures onto the well-typed fea ture structures such that Typlnf(F) is defined if and only if Fi s typable. In that case F \ufffd F' fo r a well-typed F' if and only if Typlnf(F) \ufffd F' .", | |
| "num": null, | |
| "type_str": "figure" | |
| }, | |
| "FIGREF2": { | |
| "uris": null, | |
| "text": "by adding in additional axioms for type unification (Pollard in press) and appropriateness (Pollard and Carpenter to appear). The primary result of Rounds and Kasper carries over to the present situation: Theorem 9 (Minimal Satisfiers) Fo r every fo rmula </> there is a finite set {Fo, ... , F n -i} of pairwise incomparable fe ature structures, unique up to alphabetic invariance, such that F F </> if and only if Fi \ufffd F fo r some i < n.", | |
| "num": null, | |
| "type_str": "figure" | |
| }, | |
| "FIGREF3": { | |
| "uris": null, | |
| "text": "f-( 1r1 : nil /\\ 1r2 == 1r3) V ( 7rt \u2022 FIRST \ufffd 7r3 \u2022 FIRST /\\ append( 7rt \u2022 REST, 7r2 , 7r3 \u2022 REST))", | |
| "num": null, | |
| "type_str": "figure" | |
| }, | |
| "TABREF0": { | |
| "html": null, | |
| "type_str": "table", | |
| "text": "", | |
| "num": null, | |
| "content": "<table><tr><td>a finite consistently complete t partial order of the types by subsumption, called the inheritance hierarchy</td></tr><tr><td>\u2022 Feat is a finite set of features</td></tr><tr><td>\u2022 Approp : Fe at x Ty pe -+ Ty pe is a partial fu nction such that:</td></tr><tr><td>-(Minimal Introduction)</td></tr><tr><td>fo r every f there is a least type a \u2022 such that Approp(f, a) is defined</td></tr><tr><td>(Upward Closure and Monotonicity)</td></tr><tr><td>if a \ufffd T and App. rop(f, a) is defined then Approp(f, r) is defined and</td></tr><tr><td>Approp(f, a) \ufffd Approp(f, r)</td></tr></table>" | |
| } | |
| } | |
| } | |
| } |