Gert Smolka and Hassan Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has been recognized as a powerful description language for feature trees. For the first area, this is immediate by the role of constraints in constraint logic programming [19] and in concurrent constrained based languages [26] while in the second area different approaches have been proposed. [24, 27, 20, 25] have advocated the use of predicate logic as feature description languages. 6] argues that predicate logic is the right language to express phenomena in both fields, and that feature trees constitute the canonical semantical model. Feature trees [4] are possibly infinite, finitely branching ....

Gert Smolka and Hassan Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....called assortment. The resulting terms are called filters, and unification adapted by means of a so called filtration function, which may be compared to a constraint resolution mechanism. Other approaches have been proposed in order to deal with constrained symbolic types, e.g. SCH 88, 89] SMO 89] generally based on equational unification [JOU 90] KIR 88] In this paper, we address the problem of the compatibility of our assorted signatures with the extension of the initial poset of classes into a lattice. After recalling At Kaci restricted power set construction , we present our ....

G. Smolka & H. At-Kaci, "Inheritance Hierarchies: Semantics and Unification", in Journal of Symbolic Computation, Special Issue on Unification, C. Kirchner, Ed., March 1989.

....combinations are used in record structures. At Kaci was the first to study such structures mathematically, calling them # terms [2] The resulting term calculus is the formal foundation of the programming languages LOGIN [3] and LIFE [4] which are similar to PROLOG, but use feature unification [51] instead of syntactic unification. In contrast to several description logics, attributes in terms are functional : they can have only one value. This is convenient, since objects can be identified by some unique attribute value. # terms have been successfully applied in the context of SCM, ....

Smolka, G., and At-Kaci, H. Inheritance hierarchies: Semantics and unification. In Unification,C.Kirchner,Ed. Academic Press, London, 1990, pp. 489--516.

....An earlier section discussed the application of our framework to logic programming with inheritance [1, 2] There, it was assumed that the subtype relation over the set of type constructors is a (finite) semilattice. The theory of terms [1, 2] can be formulated in terms of order sorted logic [36]. It turns out that order sorted unification, i.e. unification when some types may be subtypes of other types, admits unique most general unifiers when the sort structure is a finite semilattice and there is no overloading of constructors [46] In the presence of overloading or polymorphism, ....

G. Smolka and H. Ait-Kaci, "Inheritance Hierarchies: Semantics and Unification", in Unification, ed. C. Kirchner, Academic Press, 1990, pp. 489-516.

....are used in record structures. A t Kaci was the first to study such structures mathematically, calling them # terms [2] The resulting # term calculus is the formal foundation of the programming languages LOGIN [3] and LIFE [4] which are similar to PROLOG, but use feature unification [51] instead of syntactic unification. In contrast to several description logics, attributes in # terms are functional : they can have only one value. This is convenient, since objects can be identified by some unique attribute value. # terms have been successfully applied in the context of SCM, ....

Smolka, G., and Aït-Kaci, H. Inheritance hierarchies: Semantics and unification. In Unification, C. Kirchner, Ed. Academic Press, London, 1990, pp. 489--516.

....particular, recursive queries with logical variables in the Datalog style can be handled within the same formal framework. Note also that, given MaudeLog s type structure, the unification performed on logical variables is order sorted [30] For objects this yields a variant of feature unification [32, 23, 13], the details of which we are currently investigating. An important topic that we hope to address in future work is the tradeoff between message passing and instantiation of logical variables as computational mechanisms for query processing. This is because in MaudeLog messages can not only be ....

G. Smolka and H. Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....Feature Logic We begin with a short overview of feature logic. Feature terms and feature logic have originally been developed for semantic analysis of natural language [16, 31] Later, they were used as a general mechanism for knowledge representation [3, 26] and as a basis for logic programming [15, 33]. Throughout this paper, we will concentrate on an intuitive understanding, based on the formal semantics described by Smolka [32] In feature logic, feature terms denote sets of objects characterized by certain features. In their simplest form, feature terms consist of a conjunction of ....

Smolka, G., and At-Kaci, H. Inheritance hierarchies: Semantics and unification. In Unification, C. Kirchner, Ed. Academic Press, London, 1990, pp. 489--516.

....with a short overview of feature logic. Feature terms and feature logic have originally been developed for semantic analysis of natural language [SUP 83, Kay84] Later, they were used as a general mechanism for knowledge representation [BL84, NS89] and as a basis for logic programming [KR86, SA90] Throughout this paper, we will concentrate on an intuitive understanding, based on the formal semantics described by Smolka [Smo92] In feature logic, feature terms denote sets of objects characterized by certain features. In their simplest form, feature terms consist of a conjunction of ....

Gerd Smolka and Hassan A t-Kaci. Inheritance hierarchies: Semantics and unification. In Claude Kirchner, editor, Unification, pages 489--516. Academic Press, London, 1990.

....description language for feature trees. For the first area, this is clear from the role constraints play in constraint logic programming (Jaffar and Lassez 1987) and in concurrent constrained based languages (Smolka 1995) and, although in the second area various approaches have been proposed, Smolka and Ait Kaci 1989, Johnson 1988 and Smolka 1992 have all advocated the use of predicate logic as feature description languages. Moreover, Backofen 1994a argues that predicate logic is the right language to express phenomena in both fields, and that feature trees constitute the canonical semantical model. Feature ....

Smolka, Gert, and Hassan Ait-Kaci. 1989. Inheritance Hierarchies: Semantics and Unification. Journal of Symbolic Computation 7:343--370.

....in so called unification grammars [12, 11] developed for natural language processing, and also the formalisms of Mukai [16, 17] These early feature structure formalism were presented in a nonlogical form. Major steps in the process of their understanding and logical reformulation are the articles [19, 22, 10, 21]. The paper is organized as follows. Section 2 defines the basic notions and shows that the feature tree structure T is a model of FT. Moreover, Section 2 discusses the differences in expressivity between Herbrand and FT. Section 3 gives a basic simplification system that decides satisfiability of ....

G. Smolka and H. At-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....a short overview of feature logic. Feature terms and feature unification have originally been developed for semantic analysis of natural language [SUP 83, Kay84] Later, they were used as a general mechanism for knowledge representation [BL84, NS90] and as a basis for logic programming [KR86, SAK90] In our presentation, we will concentrate on an intuitive understanding, more formal descriptions including semantic aspects can be found elsewhere [Smo92] Note that we use full feature logic including besides the basic intersection unions as well as complements. By use of Skolem ....

Gerd Smolka and Hassan At-Kaci. Inheritance hierarchies: Semantics and unification. In Claude Kirchner, editor, Unification, pages 489--516. Academic Press, London, 1990.

....with a short overview of feature logic. Feature terms and feature logic have originally been developed for semantic analysis of natural language [SUP 83, Kay84] Later, they were used as a general mechanism for knowledge representation [BL84, NS89] and as a basis for logic programming [KR86, SA90] In our presentation, we will concentrate on an intuitive understanding, based on the formal semantics described by Smolka in [Smo92] A feature is a (name: value) pair used to represent a description or attribute of an object. Feature terms denote sets of objects characterized by certain ....

Gerd Smolka and Hassan A t-Kaci. Inheritance hierarchies: Semantics and unification. In Claude Kirchner, editor, Unification, pages 489--516. Academic Press, London, 1990.

....used in STFS is that of shapes . A shape defines the structure of a lexical entry, allowing for the definition of both typed and untyped structures. STFS also permits the definition of hierarchies of shapes organized as a partial order, including the standard mechanisms of multiple inheritance [15]. Following we show the syntax of the definition of shapes for a verbal entry in the lexicon. DefShapes Lex (LU) Auxiliary Shapes AGR (agr: gen,num,per) English verbs Everb (CAT:v,LU,MOR,pred,ggf,vtype,aktion,tense, asp: fut,cond,part,prog,nec) num,form, subj: role,form,semfeat, AGR) ....

Smolka, G., and Ait--Kaci, H. 1990. Inheritance Hierarchies: Semantics and Unification. In Kirchner, C. ed. Unification. San Diego, California: Academic Press Inc.

....term rewriting techniques may be used to compute other relations than congruences. Particularly interesting are non symmetric relations like pre orders. For instance, logics of inequalities [7] rewriting logic [21] ordered algebras [8] subset logic [12, 24] unified algebras [2, 22] taxonomies [1, 23, 26], subtypes [5] refinement calculus [20] all them use some kind of pre order on expressions. In this paper we will show the applicability of rewriting techniques to monotonic pre order relations on first order terms (inequality logics) that is the deduction of inequalities here we call them ....

G. Smolka and H. Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....will allow us to construct the fs for sleep. As unification is an associative operation, partial orders Hasse diagrams can be interpreted algebraically or logically and no extralogical ordering or procedurality is being smuggled into the theory (e.g. Carpenter, 1992; de Paiva, 1993; Smolka and Ait Kaci, 1988; Zajac, 1993) Classes can be seen as simply being part of the lexical description language, however, in what follows we assume a typed feature structure framework where the classes are types (or sorts in the terminology of Pollard and Sag (1987) which label fs nodes. Therefore, types are an ....

Smolka, G. and H. Ait-Kaci (1988) `Inheritance hierarchies: Semantics and unification', Journal of Symbolic Computation, vol.7, 343--370.

....of the semantic approach was initiated by Ait Kaci and Nasr s [AKN86] language LOGIN, which replaces ordinary first order terms with record structures and employs a typed 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 ....

Gert Smolka and Hassan Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....the term s denotation in the feature graph algebra F . Their work was inspired by fug, which contributed the notion of a feature term, and Shieber s work on patr ii [46, 44] which contributed the notions of feature graph and agreement (often called path equations) In 1987, Ait Kaci and Smolka [48] showed how feature based inheritance hierarchies can be captured as algebraic specifications using order sorted equational logic. They realized that memberships can be equivalently expressed without feature terms by equational constraints and that unification of feature terms corresponds to ....

G. Smolka and H. Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....in so called unification grammars [13, 12] developed for natural language processing, and also the formalisms of Mukai [17, 18] These early feature structure formalism were presented in a nonlogical form. Major steps in the process of their understanding and logical reformulation are the articles [20, 23, 11, 22]. Feature trees, the feature tree structure T , and the axiomatization of T were first given in [6] The paper is organized as follows. Section 2 defines the basic notions and discusses the differences in expressivity between Herbrand and FT. Section 3 gives a basic simplification system that ....

....constraints; for instance, the constructor constraint x : A(y; z) can be expressed equivalently as Ax xf1; 2g x1y x2z, if we assume that A is a sort and the numbers 1; 2 are features. Second, it seems attractive to extend FT such that it can accommodate a sort lattice as used in [1, 3, 4, 5, 23]. One possibility to do this is to assume a partial order on sorts and replace sort constraints Ax with quasi sort constraints [A]x whose declarative semantics is given as [A]x j BA Bx: Given the assumption that the sort ordering has greatest lower bounds if lower bounds exist, it seems that ....

G. Smolka and H. Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....formalization of what feature unification is supposed to do. AitKaci [1, 2] also outlines a model theoretic semantics for his formalism that is equivalent to the semantics presented in this paper, but he doesn t exploit this idea any further (for instance, for the definition of subsumption) In [24] we give an initial algebra semantics (closed world) for feature descriptions drawn over inheritance hierarchies using order sorted equational logic [25] This approach accommodates data types whose elements are described by features as well as data types whose elements are described by ....

....terms are built up by selection (the inverse of unary function application) intersection, union and complement. Thus ordinary terms and feature terms are orthogonal concepts that can coexist profitably in a knowledge representation or logic programming language. For instance, Smolka and Ait Kaci [24] investigate inheritance hierarchies accommodating both kinds of terms and present a unification algorithm combining order sorted unification with feature unification. In Section 3 we have sketched how feature logic can be reduced to predicate logic. Technically, this means that feature logic is ....

G. Smolka and H. Ait-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....attributes in addition to being partially ordered. Inheritance of attributes of all supertypes to a type is done in accordance to term subsumption and unification. Unification in the context of such an inheritance hierarchy amounts to solving equations in an order sorted algebra as explained in [SAK89], to which the reader is referred for a full formal account. For example, given a simple signature for the specification of linear lists S = flist; cons; nilg 5 with nil list and cons list, it is yet possible to specify that cons 5 We shall always leave and implicit. has an ....

Gert Smolka and Hassan At-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....language processing, and also the formalisms of Mukai [19, 20] for a thorough survey of precursors in this field, cf. 8] These early feature structure formalisms were presented in a non logical form. Major steps in the process of their understanding and logical reformulation are the articles [22, 25, 13, 24]. Feature trees, the feature tree structure T , and the axiomatization of T were first given in [7] The technique of relative simplification of constraints was first introduced and used in [6] to explain the behavior of functions as passive constraints in LIFE. The paper is organized as follows. ....

....constraints; for instance, the constructor constraint x : A(y; z) can be expressed equivalently as Ax xf1; 2g x1y x2z, if we assume that A is a sort and the numbers 1; 2 are features. Second, it seems attractive to extend FT such that it can accommodate a sort lattice as used in [1, 3, 4, 5, 25]. One possibility to do this is to assume a partial order on sorts and replace sort constraints Ax with quasi sort constraints [A]x whose declarative semantics is given as: A]x j BA Bx: Given the assumption that the sort ordering has greatest lower bounds if lower bounds exist, it seems ....

G. Smolka and H. At-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....language processing, and also the formalisms of Mukai [19, 20] for a thorough survey of precursors in this field, cf. 8] These early feature structure formalisms were presented in a non logical form. Major steps in the process of their understanding and logical reformulation are the articles [22, 25, 13, 24]. Feature trees, the feature tree structure T , and the axiomatization of T were first given in [7] The technique of relative simplification of constraints was first introduced and used in [6] to explain the behavior of functions as passive 1 Le Fun [4] is an extension of Prolog seen as a ....

....constraints; for instance, the constructor constraint x : A(y; z) can be expressed equivalently as Ax xf1; 2g x1y x2z, if we assume that A is a sort and the numbers 1; 2 are features. Second, it seems attractive to extend FT such that it can accommodate a sort lattice as used in [1, 3, 4, 5, 25]. One possibility to do this is to assume a partial order on sorts and replace sort constraints Ax with quasi sort constraints [A]x whose declarative semantics is given as: A]x j BA Bx: Given the assumption that the sort ordering has greatest lower bounds if lower bounds exist, it seems ....

G. Smolka and H. At-Kaci. Inheritance hierarchies: Semantics and unification. Journal of Symbolic Computation, 7:343--370, 1989.

....attributes in addition to being partially ordered. Inheritance of attributes of all supertypes to a type is done in accordance to term subsumption and unification. Unification in the context of such an inheritance hierarchy amounts to solving equations in an order sorted algebra as explained in [22], to which the reader is referred for a full formal account. For example, given a signature for the specification of linear lists = flist; cons; nilg 4 with nil list and cons list, it is yet possible to specify that cons has an attribute tail ) list. We shall specify this as: list : fnil; ....

Smolka, G., and At-Kaci, H., "Inheritance Hierarchies: Semantics and Unification." Journal of Symbolic Computation 7, pp. 343--370. 1989.

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Gert Smolka and Hassan AYt- Kaci. <<Inheritance Hierarchies: Semantics and Unification>>;. J. Symbolic Computation 7, 343- 370.

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Smolka G, Ait-Kaci H. Inheritance hierarchies: semantics and unification. Journal of Symbolic Computation 1989;7:343--370

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