Gert Smolka. A feature logic with subsorts. Technical Report 33, IWBS, IBM Deutschland, P.O. Box 80 08 80 D-7000 Stuttgart 80, Germany, 1988.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in the lexicon is that they allow for a more concise and natural represen tation. The alternative approach organizes classes in a multiple inheritance hierarchy without defaults. This means that lexical items can be described as standard feature terms organized in a type hierarchy (see, e.g. [Smolka, 1988; Carpenter et al. 1991] The advantages are clear. There is no need for an interface to the grammar and computational complexity is lower. At the moment it is an open question which of the two anppproaches is the more appropriate. In our system we decided against introducing a new formalism. ....

Gerd Smolka. A Feature Logic with Subsorts. LILOG-Report 33, IBM-Germany, Stuttgart, 1988.

....In this paper, we introduce the idea. of informa.tion based MT, which is consid era.bly more flexible tha.n interlingual MT or the conventional tra.nsfer based MT. Introduction With the intensive explora.tlon of contemporary theories on unifica.tion gramma.rs[6, 15, 13] and feature structures[7, 19] in the last deca.de, the old ima.ge of machine tra.nsla.tion (MT) as a. bru tal form of naturM language processing has given way to tha.t of a process based on a. uniform a.nd reversible a.rchitecture[16, 1, 27] The developers of MT systems based on the constra.int based formalism found a. ....

G. Smolka. "A Feature Logic with Subsorts". Technical Report LILOG-REPORT 33, IBM Deutschland GmbH, Stuttgart, West Germany, May 1988.

....88] are used as con straints to describe declaratively what proper ties should be assigned to a linguistic entity. In the lst few years, the study of the forreal semantics and formal properties of losics involving such constraints has made substan tial progress [Kasper Rounds 86, Johnson 87, Smolka 88, Smolka 89] e.g. by making precise which sublanguages of predicate logic it corre sponds to. This paves the way not only for reliable implementations of these formalisms, but also for extensions of the basic logic with a precisely defined meaning. The extension we present here, weak ....

Gert Smolka. A Feature Logic with Sub- sorts. LILOG-Report 33, IWBS, IBM Deutschland, W. Germany, May 1988. To appear in the Journal of Automated Reasoning.

....rules (see figures 3, 4 and 5 ) either eliminate variable equalities of the form x y or generate them from existing constraints. However, they do not introduce new variables. The constraint simplification rules given in figure 3 are the analog of the feature simplification rules provided in [Smolka, 1991]. The main difference being that our simplification rules have been modified to deal with relation symbols as opposed to just feature symbols. The constraint simplification rules given in figure 4 simplify constraints involving set descriptions when they interact with other constraints such as ....

....NP completeness result established earlier this translation identifies a NP complete subcls of formulae within the SchSnfinkelBernays class which is suited for NL applications. 7 Related Work Feature logics and concept languages such as KL ONE are closely related family of languages [Nebel and Smolka, 1991] The principal difference being that feature logics interpret attributive labels as functional binary relations while concept languages interpret them as just binary relations. However the integration of concept languages with feature logics has been problematic due to the fact the while path ....

[Article contains additional citation context not shown here]

Gert Smolka. A feature logic with subsorts. In Jfirgen Wedekind and C. Rohrer (eds.), editors, Unification in Grammar. MIT Press, 1991. Also appeared as LILOG Report no. 33, IWBS, IBM Deutschland.

....and uniiicai. ion operations on TFSs, respectively. This approach essentially adopts typc asscff sethantics. Snbtypc relal.ionships on type correspond to subsnmption relationships on denorations of types. Bed on this franwwork, extension to Prolog, LOGIN[2] has been developcal. Snolka[20] prol)ases a feature logic with subsorts. In this approach, negative descripLions can be dccomp ed into three kinds of primitive negations, namely, negations of sorts or complement sorts which denote the conplements of sets that positive connterparl. s denote, negations of fcatnrc existences, and ....

....forrealization eau provide efiiceut AcrEs DE COL1NG 92, NANTES, 23 28 AO 1992 3 8 5 I OC. OF COLING 92, NAI, rI S. AUO. 23 28. 1992 gorithms for generalization and unification operations as well as treat primitive negatious. The forrealization can be integrated with logic based frameworks such as [20] which can treat wider ranges of descrip tions but which do not have such efficient algorithms for these operations. Logic based frameworks can be used to obtain the data structures for this paper s forrealization. Unification algorithms for augmented terms or augmented TFSs have been developed ....

Gert Smolka. A Feature Logic with Subsorts. Tech- nical Report. LILAC Report 33, IBM Deutscfiland, 7000 Stuttgart 80, West Germauy, 1988.

....(e.g. see [11] They provide for partial descriptions of abstract objects by means of functional attributes called features. Formalizations of feature logic have been proposed in various forms (for more details see [3] in this volume) We will follow the logical approach introduced by Smolka [9, 10], where feature descriptions are standard first order formulae interpreted in first order structures. In this formalization features are considered as functional relations. Atomic formulae (which we will call atomic constraints) are of either the form A(x) or xfy, where x, y are first order vari ....

....the formulae xpiy A ylpy. The reverse case is treated in a similar fashion. If neither prefix or equality holds between the paths, there is nothing to be done. By and large, clauses where this holds for every x and every pair of differ ent constraints xpy and xp2z are the solved forms in Smolka [9], which are consistent. If we consider a clause of the form b = xLlyl A xLy, then we again have to check the relation between y and y. But now there is in general no unique relation determined by b, since this depends on which paths px and p we choose out of Lx and L2. Hence, we have to guess the ....

G. Smolka. A feature logic with subsorts. LILOG- Report 33, IBM Deutschland, Stuttgart, 1988.

....other than equality, is decidable [Mah88a] 2. The domain of rational trees has been used as a model in many computation domains and a wealth of formal and computational results are available on this domain. 3. Under certain assumptions, there is a relationship between Feature Algebra [Smo88] and the domain of rational trees, as we will see in Section 2 1.5 The First Order Theory of CLG and CLP (RT ) Although is adequate as a language to describe classes of objects, grammar rules and principles, except for the simplest cases, require some form of recursive definition. One way ....

.... of Rational Trees and the Feature Algebra The purpose of this section is to establish a relation between the logic adopted for the CLG representation theory, namely the algebra of rational trees as axiomatized by Maher [Mah88a, Mah88b] and the axiomatization of Feature Logics of Smolka [Smo88]. As already mentioned, a number of non classical logics have been proposed in order to formalize feature based grammar formalisms over the past few years. Smolka has given an axiomatization of the models of feature logics in first order predicate logic [Smo89] and he proposes to model features ....

[Article contains additional citation context not shown here]

Smolka, Gert, 1988. A Feature Logic with Subsorts, LILOG Report 33, IWBS, IBM Deutschland.

....attributes, and inheritance can also be treated within this framework. The equational theories developed herein are ordinary conditional equational theories. It is unnecessary to change the domain of discourse as for example in [39] or the semantics of equality as for example in [44]. The semantics of an order sorted logic comes for free. There is no need of a relativization and a sort theorem nor is it necessary to borrow concepts from order sorted algebra. In fact, the problem is to convince the reader that the simple equational theories developed herein are sufficient to ....

G. Smolka. A feature logic with subsorts. Technical Report 33, IBM Deutschland, LILOG, Stuttgart, 1988.

....combining methods 29 30 theoretically sound and practical natural language systems. The rest of the chapter is organized as follows. In section 3.1 we informally present the basic ideas shared by all modern constraint based grammar theories. Section 3. 2 presents the formalism of [HShfeld and Smolka, 1988] which is a gen eral characterization of such constraint based formalisms and an actual constraint language (called ) for representing linguistic structures. Although we have chosen a simple constraint language in order to highlight the new results in a clean but simple way, the generalization ....

....well formed sentences, they are perfectly well suited to a reversible system, because they are neutral with respect to interpretation and production. In the last few years constraint based formalisms have undergone a rigorous for mal investigation (consider for example [Shieber, 1989; Smolka, 1988; Smolka, 1992] This has led to a general characterization of constraint based formalisms where fea ture structures are considered to constitute a semantic domain and constraints are lIn the beginning of their formalization, unification was the predominant constraint solving mechanism; hence ....

[Article contains additional citation context not shown here]

G. Smolka. A feature logic with subsorts. Technical report, IBM Deutschland GmbH, Germany, 1988. Lilog-Report 33.

.... Lascarides Copestake 1999) which is an extension of a Kasper Rounds logic (Rounds Kasper 1986, Moshier Rounds 1987, Carpenter 1992) The ontological assumptions and formal properties of a KasperRounds logic differ in crucial respects from those of an Attribute Value logic (Johnson 1988, Smolka 1988, King 1989) and King (1994) shows that only the latter is compatible with the assumptions of HPSG as proposed in Pollard Sag (1994) Since it is unclear how defaults could be integrated into an Attribute Value logic and therefore into the setup of HPSG discussed here, a discussion of default ....

....parallel to relations like append, or more accurately a binary relation like member. If we chose a formal language for HPSG which allows us to use definite relations within the description language, such as the system defined in G otz (2000) which extends King (1989) with ideas from H ohfeld Smolka (1988) and D orre (1994) it is possible to represent a lexicon including lexical rules in the formal language without extending the signature. The figures 15 and 16 illustrate this possibility. word L 1 : L n lex rule(word) Figure 15: A lexicon with added lexical rule relations lex ....

Smolka, G., 1988. A feature logic with subsorts. LILOG-Report 33, IBM Deutschland, Stuttgart. http://www.ps.uni-sb.de/Papers/abstracts/LR-33.html.

....in a one to one relation with linguistic objects, as in HPSG II. Apart from the philosophical consequences (which will not be discussed here) this gap between HPSG II and King (1989) can 13 cf. Rounds and Kasper (1986) Moshier and Rounds (1987) and Carpenter (1992) 14 cf. Johnson (1988) Smolka (1988), and King (1989) 15 Note that the theories in an HPSG II architecture are formulated using implications on types; in fact, even stronger implicative statements with complex antecedents are used. We will see on pp. 15 of section 3.2.1 how certain stronger implicative statements can be ....

....can now go on to discuss the HPSG architecture based on this setup. An HPSG theory consists of two ingredients: the declaration of the domain of linguistic 17 For a discussion and the formal definition of a relational extension of a constraint language cf. Jaffar and Lassez (1987) and Hohfeld and Smolka (1988). 18 The different possible ways of expressing a theory are discussed in section 3.2. ON IMPLEMENTING AN HPSG THEORY 9 objects in a signature (consisting of the type hierarchy and the appropriateness conditions) and the formulation of constraints on that domain 19 . The perspective taken in ....

Smolka, G. 1988. A Feature Logic with Subsorts. LILOG technical report, number 33, IBM Deutschland GmbH.

....constraint logic programs. CLGs thus are grammars formulated by means of a suitable logical language which can be used as a constraint language in the sense of [11] 2 For example, for feature based grammars such as HPSG ( 23] a quite direct embedding of a logical language close to that of [24] into the CLP scheme of [11] is done in the formalism CUF ( 5, 4] This approach directly ooeers the operational properties of the CLP scheme by simply redening grammars as constraint logic programs, but is questionable in losing the connection to the model theoretic specications of the ....

Gert Smolka. A feature logic with subsorts. LILOG Report 33, IBM Deutschland, Stuttgart, 1988.

....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, anticipating all of these, ....

Gert Smolka. A feature logic with subsorts. LILOG Report 33, IBM Germany, Stuttgart, 1989.

....a logical language 5 We assume for the sake of clarity that this set contains exactly one element, and account for lexical ambiguity in section 5.4. 3. A TFS UNIFICATION ENGINE 59 developed in [22] extended to accommodate types, where path sharing is replaced by the notion of variables due to [41]. A TFS is described as a conjunction of specifications that might include its type, its features, along with their values, or a variable (whose name begins with a capitalized letter) that refers to it. Multiple occurrences of the same variable denote reentrancy. The syntax for specifying rules ....

Gert Smolka. A feature logic with subsorts. LILOG Report 33, IBM Deutschland, May 1988.

....feature structures as PARSING AS DYNAMIC INTERPRETATION 93 a relatively new kind of language for representating linguistic knowledge. Studies concerned with feature structures from this perspective are, for example, Johnson (1988) Carpenter (1992) Dorre Seiffert (1991) Kasper Rounds (1986) Smolka (1989), Moss (1990) These studies are primarily concerned with formal definitions of languages of feature structures and their formal properties. In the present chapter we consider feature structures also as formallanguage objects, but our interest lies mainly in considering how such objects may be ....

Smolka, G. (1989) A feature logic with subsorts. LILOG Report 33, IWBS, IBM Germany, Heidelberg.

....have been varied, in particular with respect to a formal semantics for these structures. One way has been to give an algebraic fixed point characterisation of models for grammars expressed with typed feature structures (cf. in particular Pollard, in press) The other approach (exemplified by (Smolka, 1988), King, 1989) and (Dorre and Eisele, 1991) has been to define a formal language built out of so called feature terms and standard logical connectives, and provide this formal language with a model theoretic semantics that allows typed feature structures as models. Computationally, this approach ....

....for showing satisfiability. The basic idea is that for each type hierarchy, we can give an interpretation s.t. if a feature structure is satisfiable with respect to the type hierarchy, then it has a nonempty denotation in this interpretation. Such an interpretation is canonical in the sense of (Smolka, 1988) and comparable to a Herbrand universe in first order logic. All the definitions and results of the rest of this section are taken directly from King s work, or follow from it in a straightforward way. We ll only be looking at a skeleton of the proof though to understand the major ideas, many ....

Smolka, G. (1988). A feature logic with subsorts. LILOG-Report 33, IBM Deutschland GmbH, Stuttgart.

....this extension we must first generalize the constraints of the form xfy to constraints of the form xwy, where w = f 1 : fn is a string of features (called a feature path) Such feature paths are interpreted using simple relational composition. This generalization is just syntactic sugar (see Smolka (1988)) This is no longer the case if we add functional uncertainty in the form of constraints xLy, where L is a regular expression denoting a regular language of feature paths. A constraint xLy holds if there is a word w 2 L such that xwy holds. By this existential interpretation a constraint xLy can ....

....subterm of y 1 . The reverse case is handled similarly. If neither prefix nor equality holds between the paths, there is nothing to do. By and large, clauses where the last condition holds for every x and every pair of different constraints xp 1 y 1 2 OE and xp 2 y 2 2 OE are the solved forms of Smolka (1988), which are satisfiable. If we consider a clause of the form OE = xL 1 y 1 xL 2 y 2 , then we have again to check the relation between y 1 and y 2 . But now there is in general no unique relation determined by OE, since this depends on which paths p 1 and p 2 are used out of L 1 and L 2 . Hence, ....

Smolka, G. (1988). A feature logic with subsorts. LILOG-Report 33, IWBS, IBM Deutschland, Stuttgart.

....7 7 7 7 5 LAST 1 3 7 7 7 7 7 7 7 7 7 7 7 7 7 22 4 SYNTAX OF TDL 4.6.13 Negation The sign indicates negation. Example: not mas type : GENDER mas ] The resulting feature structure is not mas type GENDER : mas Negation of types will be pushed down to atoms according the schema of [Smolka 88; Smolka 89] If list list is defined as in the tdl built ins.tdl file (page 4.2) the definition notlist : list . will result in the following (expanded) structure: 8 : cons : null ] null FIRST undef : null REST undef 9 = ....

Gert Smolka. A Feature Logic with Subsorts. LILOG Report 33, WT LILOG--IBM Germany, Stuttgart, Mai 1988.

No context found.

Gert Smolka. A feature logic with subsorts. LILOG Report 33, IWBS, IBM Germany, Stuttgart, May 1988. To appear in: J. Wedekind, C. Rohrer (eds.), Unification in Grammar. MIT Press, 1991.

....unification called unification. Mukai s [Muk87] language CIL is similar to LOGIN but has no subsorts. Smolka and Ait Kaci [SA89] show how LOGIN can be captured in order sorted logic and device a framework that combines order sorted constructor types with LOGIN s feature types. Feature Logic [Smo88a, Smo89] is a decidable logic that generalizes Ait Kaci s formalism by adding negation and quantification. Feature Logic makes explicit that Ait Kaci s terms, the feature descriptions developed by computational linguists [KB82, RK86, Joh88] and the knowledge representation language KL ONE ....

.... language LOGIN [AKN86] where relations are defined with definite clauses over a constraint language consisting of so called terms [AK86] The first step of this enterprise was to come up with a logical reformulation of Ait Kaci s term calculus and led to the development of Feature Logic [Smo88a, Smo89] a decidable logic that generalizes Ait Kaci s formalism by adding negation and quantification. Feature Logic makes explicit that Ait Kaci s terms, the feature descriptions developed by computational linguists [KB82, RK86, Joh88] and the knowledge representation language KL ONE [BS85, ....

[Article contains additional citation context not shown here]

Gert Smolka. A feature logic with subsorts. LILOG Report 33, IWBS, IBM Deutschland, Postfach 80 08 80, 7000 Stuttgart 80, Germany, May 1988.

....The features appear as edges of the graph. The terminal nodes are atoms representing primitive linguistic objects. Kasper and Rounds [10, 17] were the first to capture the relation between feature descriptions and linguistics objects in terms of a logic. Subsequently, Johnson [6] and Smolka [22, 23] realized that feature logics can be modeled straightforwardly in Predicate Logic. In this approach, which underlies the present paper, a domain of linguistic objects is called a feature algebra and is simply a structure that interprets atoms as pairwise distinct individuals and features as ....

G. Smolka. A feature logic with subsorts. LILOG Report 33, IWBS, IBM Deutschland, Postfach 80 08 80, 7000 Stuttgart 80, Germany, May 1988.

....is surprisingly natural and brings much simplicity and clarity. This approach is already suggested by Bresnan and Kaplan s pioneering paper on Lexical Functional Grammar [17] and has been worked out further in Johnson s dissertation [16] However, the present paper, which is an elaboration of [47], shows for the first time that the feature term descriptions of Kay, Ait Kaci, and Kasper and Rounds can be embedded as well into predicate logic. It turns out that feature terms are merely a syntactic extension, which can be eliminated in linear time. In Lexical Functional Grammar, feature ....

....lattice) as the intersection of the interpretations of A and B. The algorithms given in this paper for constraints without sorts can be easily extended to accommodate the sort lattice and the complexity results shown here remain unchanged. For an elaboration of Feature Logic with sort lattices see [47]. 8 Two Undecidability Results In this section we show that the set of satisfiable constraints of Feature Logic is not recursively enumerable. Moreover, we show that there are recursive sort equations such that it is undecidable whether a feature term denotes a nonempty set in at least one model ....

[Article contains additional citation context not shown here]

G. Smolka. A feature logic with subsorts. LILOG Report 33, IWBS, IBM Deutschland, Postfach 80 08 80, 7000 Stuttgart 80, Germany, May 1988.

No context found.

Gert Smolka. A feature logic with subsorts. Technical Report 33, IWBS, IBM Deutschland, P.O. Box 80 08 80 D-7000 Stuttgart 80, Germany, 1988.

No context found.

Smolka, G.: 1988, A Feature Logic with Subsorts, LILOG-REPORT 33, IBM Deutschland GmbH, Stuttgart, Germany.

No context found.

Gert Smolka. <<A Feature Logic with Subsorts>>;. LILOG Repo 33, IBM Deutschland GmbH, Stuttgart.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC