R.T. Kasper and W.C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13(1):35--58, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a form suitable for computational use. RG s multiple syntactic strata would seem to preclude its use in the kind of monotonic, unification based parsing sys tem many now consider standard ( 1] 11] However, recent work by Johnson and Moss [2] on a Kasper Rounds (KR) style logic based formalism [5] for RG, called Stratified Feature Grammar ( S F G ) has demonstrated that even RG s multiple strata are amenable to a feature structure treat ment. Based on this work, we have developed a unification based, chart parser for a lexical version of SFG suitable for building computational ....

Robert Kasper and William C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:35-58, 1990.

....such results as a sign that existing feature logics treat linguistic structure too homogeneously. What is needed are feature log ics which are more sensitive to the fine structure of linguistic theorising. The paper is relatively self contained, nonetheless the reader may find it helpful to have [Kasper and Rounds 1986, 1990] and [Blackburn and Spaan 1991, 1992] to hand. 2 Preliminaries Feature logics are abstractions from the unification based formalisms of computational linguistics. Originally feature logics embodied just one component of unification based formalisms. Early unifica tion formalisms such as GPSG ....

Kasper, R. and Rounds, W.: 1990, The Logic of Unification in Grammar, Linguistics and Philosophy 13, 33-58.

....of a grammar are the well formed phrases of the language. 38 We will illustrate the way in which Case, agreement, and unbounded dependency are handled in a feature structure grammar by using Pollard and Sag s (1994) HPSG. The HPSG 38 For the formal foundations of feature structure grammars see Kasper and Rounds (1986) and (1990), Johnson (1988) Carpenter (1992) Keller (1993) and Rounds (forthcoming) 34 attribute value graph for 2a is 31. 39 2a. John saw Mary. 31. PHON John, saw, Mary CAT HEAD 3 ( S[fin,past] SUBCAT PHON saw, Mary ....

Kasper, R and W. Rounds (1990), "The Logic of Unification in Grammar", Linguistics and Philosophy 13, pp. 35-58.

....defined within a specific formal framework. Now, properties of classes of structures that are defined in some formal way are the provenance of Model Theory. It s not surprising, then, to find treatments of the meaning of such systems of constraints couched in terms of formal logic [KR86, MR87, KR90, GPC 88, Joh88, Smo89, DVS90, Car92, Kel93] More recently, the role of logic has begun to expand beyond just providing formal semantics for the constraints to provide the entire linguistic formalism. See, for instance, Joh89, Sta92, Cor92, BGMV93, BMV94, Kel93, Rog94, Kra95] and, ....

Robert T. Kasper and William C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:35--58, 1990.

....in which case it provides values for one or more features. These values in turn are either atomic or complex feature structures. The set Feat of features and set Atom of atomic values are assumed to be finite. Feature structures can be defined in terms of labelled finite state automata following Kasper and Rounds (1986, 1990). The version of the definitions given here follows Carpenter (1993) Definition 1 (Feature Structure) A feature structure is a tuple F = #Q,q 0 , d,a# where: Q: a finite set of nodes . q 0 # Q: the root node . d : FeatQ # Q : the partial feature value function (transition ....

Kasper, R. T. and W. C. Rounds (1990) `The logic of unification in grammar', Linguistics and Philosophy, 13 (1), 35--58.

....ambiguity representation must take into account the interconnexion between the different subparts of the structure and allow a factorisation avoiding redundancy. 2. 2 Different Representations A disjunctive representation of the ambiguity remains the most natural (see [Karttunen984] Kay85] or [Kasper90] However, this approach has several drawbacks. First of all, if an ambiguity affects more than one atomic value, then a classical disjunction can only represent variation between complete structures. In other words, such a representation doesn t allow the description of the relations existing ....

Robert Kasper & William Rounds 1990. "The Logic of Unification in Grammar" in Linguistics and Philosophy, 13:1.

....which satisfies the descriptions of all words of the utterance. Model theoretic approaches may try to define new models (e.g. logically equivalent, but simpler to process) for existing theories (Stabler, 1992) or they may try to formalize models as they already exist in the linguistic literature (Kasper Rounds, 1990; Carpenter, 1992; Blackburn et al. 1993; Kracht, 1995; Rogers, 1996) Our approach falls into the last category. Following (Blackburn, 1994) we will use Kripke models to represent syntactic structures, and define a multi modal logic (Fitting, 1984) for describing them. Basing the formalization ....

Kasper, R. & W. Rounds (1990). The Logic of Unification in Grammar. Linguistics and Philosophy, 13:35--58.

....throughout the rest of this section, an untyped feature context C = F; A) is fixed. 2.1.5 Multicollection extended feature structures. Within the current literature, there are several different formalisms for recapturing feature structures. A popular one is the so called Kasper Rounds [13] representation, in which the feature structure is modelled as a finite state automaton. An extension of the Kasper Rounds formalism which integrates multicollections into the structures is employed in this work. Formally, a multicollection extended feature structure (MEFS for short) is an ....

R. T. Kasper and W. C. Rounds. The logic of unification in grammar. Linguistics and Phil., 13:35--58, 1990.

....is similar to Smolka s feature logic ( 15] from where negation has been omitted, but the disjunction operator and circular terms are still permitted. Other formalizations and implementations of feature terms, in particular those containing disjunctions, have been described e.g. by Kasper Rounds [10], Johnson [9] Maxwell Kaplan [12] Eisele Dorre [5] and Wedekind [16] The plan of this papers is as follows: In section 1.2, the syntax and the semantic of a basic feature type system is presented which corresponds essentially to a Horn system where first order terms have been replaced by ....

.... factorization rules ffl actually terminate with a factorized representation of the term t ffl do neither add nor delete any structural information (i.e. if the conclusion of a rule is satisfiable then its premise is satisfiable and vice versa) 2 Definition 10 Subsumption of feature terms (cf. [10]) A factorized set of feature terms T 2 is subsumed by a factorized set T 1 (T 2 T 1 ) iff there is a homomorphism h which maps the variables of T 1 on those of T 2 in the following manner: a) For each term x[a] 2 T 1 , there is a term x 0 [b] 2 T 2 , where h(x) x 0 and b a. b) For each ....

Robert T. Kasper and William C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:35--58, 1990.

....of a term is not fixed (open arity) 3. the term may contain disjunction operators Terms which have these properties, among others, have been called feature terms [12] The last mentioned property causes the decision problem of feature term consistency to be NP complete (Kasper [7] Kasper Rounds [8]) Due to the existence of disjunction, straightforward adaptations of first order unification algorithms are ruled out. This research was done while the author was granted a Monbusho scholarship at Kyoto University. I wish to thank the researchers in Kyoto, in particular Makoto Nagao and Yuji ....

Robert T. Kasper and William C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:35--58, 1990.

....resolution and presupposition checking can thus be stated in the same description language as the syntactic restrictions, providing the basis for highly integrated linguistic processing. CUF can be roughly characterized as a feature structure description language similar to Kasper Rounds logic [KR90] combined with the possibility of stating definite clauses over feature terms. Moreover, feature structures are typed, with the types possibly being ordered in a hierarchy. The CUF type discipline allows for an axiomatic statement of global restrictions on the structures in which the program is ....

....implemented Figure 1: Possible Parts of a CUF Program 2.1 Feature Algebras and Feature Terms In order to give an adequate formalization of CUF expressions, we need the notion of a feature algebra. This is only a slight generalization of the well known concept of a feature structure [Shi86, KR86, KR90] by dropping the restriction that it has a single root, i.e. we are talking about general directed graphs whose edges have a deterministic labelling (no two edges leaving one node are labelled the same) and some of whose terminal nodes are labelled. Edge labels and terminal node labels come ....

Robert T. Kasper and William C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13(1):35--58, 1990.

....hm n i : hm 0 1 i : hm 0 k i which equate two sequences of modalities. Such equations will hold at a node if there are transition paths from that node corresponding to both sequences, and, in addition, there is at least one node that is the joint destination of two such sequences; see Kasper and Rounds (1990) for details. We ll need the booleans, but we won t need any propositional variables; we can build all the formulas we ll need out of the path equations. zizo.tex; 17 09 1996; 18:55; no v. p.18 Zooming In, Zooming Out 19 Zi: That s basically a fragment of PDL with intersection: over this class ....

Kasper, R. and Rounds, W., 1990, "The logic of unification in grammar," Linguistics and Philosophy 13, 33--58.

.... and fragments of the language Various enrichments of the standard modal apparatus have been considered ( Blackburn, 1993 ] Blackburn and Spaan, 1993a ] Blackburn and Spaan, 1993b ] Gazdar et al. 1988 ] In addition there is the classical language of Kasper and Rounds (see [ Kasper and Rounds, 1990 ] with it s various extensions, for example [ Baader et al. 1993 ] We will discuss them in turn concentrating on the aspects of definitional strength and their decidability. Kasper and Rounds in their work advance a language L KR that has conjunction, disjunction, arc modalities h j i and ....

Robert T. Kasper and William C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:35 -- 58, 1990.

....label. This notation is intended to indicate that both agr labels share precisely the same value (token identity) as opposed to having merely type wise identical values. The feature structure description language developed in this paper extends the logic originally introduced by Rounds and Kasper [8, 9, 10, 19]. The key insight of Rounds Kasper logic is that a feature structure such as that shown in figure 1 can also be represented in linear form by a logical formula like that given below: cat : S subj : agr : number : sing person : 3) subj agr : pred agr) Each feature is represented by a ....

Kasper, R.T. and W.C. Rounds (1990) The logic of unification in grammar. Linguistics and Philosophy, 13(1), pp. 35--58.

....is inductively collected from the sentences sub strings, subsub strings and so on. We will use feature structures to represent this information. There are many ways of viewing, defining and describing feature structures, e.g. as directed acyclic graphs [18] as finite deterministic automata [13], as models for first order logic [19, 20, 9] or as Kripke frames for modal logic [2] Here we use a slightly modified version of Kasper and Rounds [13] definition of feature structures, and we will later use a subset of the equations schemata used by LFG to describe these feature structures. As ....

.... are many ways of viewing, defining and describing feature structures, e.g. as directed acyclic graphs [18] as finite deterministic automata [13] as models for first order logic [19, 20, 9] or as Kripke frames for modal logic [2] Here we use a slightly modified version of Kasper and Rounds [13] definition of feature structures, and we will later use a subset of the equations schemata used by LFG to describe these feature structures. As a basis we assume two predefined sets, one of attribute symbols and one of value symbols. In a linguistic framework these sets will typical include ....

Robert T Kasper and William T. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13(1):35--58, 1990.

....They both differ from categorial grammar in that the inputs to the derivational process have the graph structure of an f structure, rather than the linear structure of a string. Borrowing the idea that features in feature structures can be described by modal operators in a multi modal language (Kasper and Rounds, 1990; Rounds, 1997) grammatical relations in R LFG are formalized as propositional modal operators. Returning to the earlier example, the NP Sandy and the transitive verb likes would be associated with the lexical entries (1.9) and (1.10) Sandy 0 : e (1.9) y x:likes 0 (x; y) OBJ e Gammaffi ....

Kasper, Robert T. and William C. Rounds. 1990. The logic of unification in grammar. Linguistics and Philosophy, 13(1):35--58.

....descriptions in logic programming has been advocated and studied [3, 4, 5, 6, 23] Essentially, feature descriptions provide a logical version of records, a data structure found in many programming languages. Feature descriptions have been proposed in various forms with various formalizations [1, 2, 15, 20, 14, 11, 12, 22, 7, 8, 19]. We will follow the logical approach pioneered by [22] which accommodates feature descriptions as standard first order formulae interpreted in first order structures. In this approach, a semantics for feature descriptions can be given by means of a feature theory (i.e. a set of closed feature ....

....the solved form is if and only if the description is unsatisfiable. We do not know whether our simplification algorithm can be made practical, nor do we know its worst case complexity. However, the subproblem of deciding satisfiability of quantifier free formulae is known to be NP complete [14, 22]. Note that the notion of completeness considered in this paper is different from the notion of completeness considered in related work by Kasper and Rounds [14] and Moss [19] These authors study logical equivalence for rooted and quantifier free feature descriptions (called feature terms in [22, ....

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Robert T. Kasper and Rounds William C. The logic of unification in grammar. Linguistics and Philosopy, 13:35--58, 1990.

....formal framework. Now, for the most part, properties of classes of structures that are defined in a formal way like this are the provenance of Model Theory. It s not surprising, then, to find treatments of the meaning of such systems of constraints couched in terms of formal logic [KR86, MR87, KR90, GPC 88, Joh88, Smo89, DVS90, Car92, Kel93, RVSar] More recently, a number of people have noticed that, at least in some cases, extra logical mechanisms for combining constraints can be replaced by ordinary logical operations. See, for instance, Joh89, Sta92, Cor92, BGMV93, BMV94, Kel93, ....

Robert T. Kasper and William C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:35--58, 1990.

....role of union constraints, a type system, structural identity conditions (extensionality) and inequations, none of which take the system outside the realm of decidability. 1 Introduction The purpose of this paper is to present an attribute value logic, based loosely on the Rounds Kasper logic [Kasper and Rounds 1990], extended with descriptions of sets of values for features along the lines of terminological logics such as are found in kl one like languages [Nebel 1991, Brachman et al. 1991] The version of Rounds Kasper logic with variables [Smolka 1988, Carpenter 1992] is particular suited to applications ....

....1992] and to inequations as discussed by [Colmerauer 1984] and [Carpenter 1992] 2 Description Language The description language we present is motivated by three lines of research. Our first motivation is the work on attribute value logics for linguistic and logic programming applications by Kasper and Rounds [1990], Smolka [1988, Hohfeld and Smolka 1989] and Carpenter [1991, 1992] among others. Second, we were motivated by general terminological knowledge representation languages, such as those discussed by Mac Gregor [1988] Nebel [1991] and Brachman et al. 1991] among others. Finally, our approach to ....

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Kasper, R. T., and Rounds, W. C. (1990). The logic of unification in grammar. Linguistics and Philosophy, 13(1):35--58.

....one of the elements on the right, if a v f i then f(a) v f(f i ) v d 0 . Therefore if b v f(a) then b v d 0 , so the clause b d 0 can be dropped. Apply Lemma 2.1 with d = f i . Then we get OE( d 0 ; i 1) f i t f(f i ) f i 1 : 2 3. Feature logic The language KR was introduced in [10] [11] to solve the problem of expressing disjunctive information in feature structures, while at the same time capturing the constraints implicit in Shieber s PATR II [24] The language KR consists of basic and compound formulas. Assuming L and A as above, the basic formulas of KR are as follows ffl ....

R. Kasper and W. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:33--58, 1990.

....as d does. 3. Feature Logics We now introduce several logical languages which will be interpreted in variants of feature systems. All of these logics can be defined relative to the signature (L; A) Section 3 Feature Logics 9 3.1. Kasper Rounds Logic The language L(KR) was introduced in [40] [41] to solve the problem of expressing disjunctive information in feature structures, while at the same time capturing the constraints implicit in Shieber s PATR II [67] The language L(KR) consists of basic and compound formulas. Assuming L and A as above, the basic formulas of L(KR) are as ....

R. Kasper and W. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13:33--58, 1990.

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R.T. Kasper and W.C. Rounds. The logic of unification in grammar. Linguistics and Philosophy, 13(1):35--58, 1990.

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Kasper R. &; W. Rounds (1990) The Logic of Unification in Grammar, in Linguistics and Philosophy, 13:1.

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Robert Kasper & William Rounds 1990. "The Logic of Unification in Grammar" in Linguistics and Philosophy, 13:1.

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Kasper, R. T. and W. C. Rounds (1990) `The logic of unification in grammar', Linguistics and Philosophy, vol.13 (1), 35--58.

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