Ait-Kaci, Hassan. 1984. A lattice theoretic approach to computation based on a calculus of partially ordered type structures. Doctoral dissertation, University of Pennsylvania.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....will not terminate. However, one could substitute the equivalent b h f b i to obtain a well formed theory. xii The importance of being lazy xiii b f b f a ## FIGURE 14 A theory that is not well formed A more realistic example is the junk slot encoding of the append relation (Ait Kaci 1984). We here assume an appropriate extension of the wellformedness condition to disjunctive theories. append 2 4 arg1 hi arg2 L arg3 L 3 5 2 6 6 6 6 6 6 6 6 6 4 arg1 H j T1 arg2 L arg3 H j T2 junk 2 6 6 4 append arg1 T1 arg2 L arg3 T2 3 7 7 5 3 7 7 7 7 7 7 7 7 7 5 FIGURE 15 ....

Ait-Kaci, Hassan. 1984. A lattice theoretic approach to computation based on a calculus of partially ordered type structures. Doctoral dissertation, University of Pennsylvania.

....issue by basing the formalization of DLRs in section 5 on the modular encoding with the lex rule type. Note that the use of STORE and the lex rule type in the modular encoding is quite traditional in that it is an instance of the so called junk slot encoding of relations as introduced by A t Kaci (1984) and employed by King (1992) and Carpenter (1992) The key motivation for formalizing lexical rules in HPSG as DLRs develops from the already mentioned fact that in the formal language for HPSG of King (1989, 1994) the notion of an HPSG grammar has been simplified to a point where, from a formal ....

....from the original specification. Since we based our lexical rule specification language on SRL, which does not provide such relations as first class citizens, we would need to introduce these relations into our ontology and refer to them using a socalled junk slot encoding of relations (A t Kaci 1984, King 1992, Carpenter 1992) Alternatively, one could redefine the lexical rule specification language and its interpretation to be based on an extension of SRL with relations as provided by the Relational Speciate Re entrant Language (RSRL) Richter et al. 1999, Richter 1999) Since the ....

A t-Kaci, H., 1984. A Lattice Theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA.

....the form a 1 = b 1 u a 2 = b 2 u : u a n = b n u a 1 = a 2 u a 2 = a 3 u : u a n Gamma1 = a n then the original graph will have 2n 1 nodes, but 2n of these are collapsed by normalization step 8. To discover this efficiently, we use a version of A Kaci s algorithm for unifying Psi terms (Ait Kaci, 1984; Ait Kaci Nasr, 1986) the algorithm relies on the UNION FIND technique to identify nodes to be merged, and runs in time just slightly more than linear in the number of nodes in N . Therefore the cost of the non recursive portion of graph normalization is roughly linear in the number of nodes ....

Ait-Kaci, H. (1984). A Lattice Theoretic Approach to Computation Based on a Calculus of Partially-Ordered Type Structures. Ph.D. thesis, University of Pennsylvania.

.... as a type hierarchy of word classes, with each type inheriting information from its supertypes and possibly adding other information (Flickinger, Pollard, and Wasow, 1987; Pollard and Sag, 1987) The information pertaining to each type is represented by means of a typed feature structure (A t Kaci, 1984; Carpenter, 1992; Keller 1993) typically depicted as a set of attributes and values (which can themselves be feature structures with their own attributes and values) Here we are concerned primarily with information about the semantic content and subcategorization of a word class (i.e. of the ....

At-Kaci, H. (1984). A lattice-theoretic approach to computation based on a calculus of partially oredered types. Unpublished doctoral dissertation, University of Pennsylvania.

.... been shown to provide adequate foundations for set theory and arithmetic (Tarski and Givant, 1987) and has been used to model description logics (Brink and Schmidt, 1992) A number of precise characterizations of algebraizable logics have been developed (Blok and Pigozzi, 1989) In the mid 1980s At Kaci (1984, 1986) gave a lattice theoretic model of knowledge base languages with operational semantics through term rewriting that resolved many of the issues of complexity and deduction algorithms for term subsumption knowledge representation systems. This y calculus is particularly interesting because it ....

At-Kaci, H. (1984). A lattice-theoretic approach to computation based on a calculus of partiallyordered types. PhD. University of Pennsylvania, Philadelphia.

....not every record has a field f . Next we note that the familiar term notation can still be used in CFT if a little syntactic sugar is provided. For instance, the equational constraint X = point(Y; Z) employing the binary constructor point translates into the conjunction X: point Xf1; 2g X[1]Y X[2]Z: Note that constructors and features are dual in the sense that features are argument selectors for constructors. CFT can also express constructors that identify their arguments by keywords rather than by position. For instance, the equation P = point(xval: X; yval: Y; color: Z) can ....

....= f(y; z) Feature descriptions have a long and winded history. One root are the unification grammar formalisms FUG [14] and LFG [13] developed for applications in computational linguistics (see [8] for a more recent paper in this area) Another, independent root is Ait Kaci s term calculus [1, 2], which is the basis of several constraint programming languages [3, 4, 5] Smolka [20] gives a unified logical view of most earlier feature formalisms and studies an expressive feature constraint logic. Feature trees appeared only recently with the work on FT [7, 6] To our knowledge the notion ....

H. Ait-Kaci. A Lattice-Theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvenia, Philadelphia, PA, 1984.

....presented in [5] They have been implemented and tested on several applications. We first introduce the notion of typed features. It allows the definition of a structure over the primitive symbols used in the grammar. The unifier can take advantage of this structure in a manner similar to [1]. We then introduce the notion of typed constituents and the FSET construct. It allows the declaration of explicit constraints on the set of admissible paths in functional descriptions. Typing the primitive elements of the formalism and the constituents allows a more concise expression of grammars ....

....concise expression of grammars and better checking of the input descriptions. It also provides more readable and better documented grammars. Most work in computational linguistics using a unification based formalism (e.g. 24, 27, 12, 14, Kaplan Bresnan] does not make use of explicit typing. In [1], Ait Kaci introduced Y terms, which are very similar to feature structures, and introduced the use of type inheritance in unification. Y terms were intended to be general purpose programming constructs. We base our extension for typed features on this work but we also add the notion of typed ....

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Ait-Kaci, H. A Lattice-theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvania, 1984. UMI #8505030.

.... type system to recover an expanded rule effectively equivalent to that in Figure 1 (though the entire values of SYN and SEM would be carried over) In Meurers formulation the coindexation generated is interpreted as genuine reentrancy since the lexicon is defined utilizing junk slot encoding (Ait Kaci, 1984) of the set of possible words, as shown below: word (L 1 : Ln 1 STORE h lex rule OUT 1 i This constraint states that a word must be subsumed by one of the basic descriptions or by a description derived via one or more lexical rule applications (i.e. any description tagged 1 ) ....

Ait-Kaci, Hassan. (1984). A lattice-theoretic approach to computation based on a calculus of partially ordered type structures. University of Pennsylvania, Doctoral Dissertation.

....and provide some polynomial cases. For instance, when the labelling function is locally injective (i.e. injective on the neighborhood of each vertex (or if edges are labelled, on the set of edges incident to each vertex) then morphism is polynomial, whatever the structure of G and H may be (see [Kac84] for feature structures and [LB94] for conceptual graphs) But when labels are partially ordered then the condition for matching vertices (or edges) can be for any vertex c, the label of the image must be less or equal to the label of c . Then, morphism becomes a projection, which can make the ....

H. Ait Kaci. A lattice-Theoretic Approach to Computation Based on A Calculus of Partially Ordered Type Structures. PhD Thesis, University of Pennsylvania, 1984.

....reported here has been done while the author was with IBM Deutschland. The author s article [23] is a more recent work on feature logics. 1 1 Introduction This paper presents a set description logic that generalizes and integrates formalisms that have been developed for knowledge representation [1, 2] and computational linguistics [13, 21, 11, 9] The logic comes with an open world model theoretic semantics, where admissible worlds can be required to satisfy a classification scheme postulated by means of a sort lattice. The logic supports the typically partial description of objects using ....

....present a quantifier elimination algorithm that computes for every feature term an equivalent quantifier free feature term, thus showing that even with quantification no more sets can be described and consistency and subsumption remain decidable. Our feature logic generalizes Ait Kaci s formalism [1, 2], from which it inherits the use of subsorts. Ait Kaci s formalism was developed independently of the linguistically motivated approaches with knowledge representation as application in mind. From today s perspective, Ait Kaci s formalism suffers 6 from the fact that it is nonlogical, that is, ....

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H. Ait-Kaci. A Lattice-Theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvenia, Philadelphia, PA, 1984.

....of types T into three subsets: constrained, hiding and simple types. The motivation for the distinctions is computational and in some sense already an optimisation. In short, it obviates the need for some rather complex partial evaluation later on and reduces the number of choice points. 6 See [1]. Here s the intuitive meaning of the three sets: constrained types are exactly those types that unify with some antecedent of the grammar, and whose structure is thus constrained by the conditions stated in the grammar. hiding types are types that are not constrained themselves but ....

Ait-Kaci, H. (1984). A lattice theoretic approach to computation based on a calculus of partially ordered type structures. PhD thesis, University of Pennsylvania.

....are highly desired[15] There are several approaches which introduce other aspects, in addition to IS A relation, in order to enhance expressiveness. Among them are inheritance systems[21, 22] taxonomy systems such as KL ONE[2] feature structures[4] and deductive and object oriented approaches[1, 14, 16, 26, 27]. Some of them introduce the concept of role. A role is usually defined as a relation between objects, This research was supported in part by the Science Research Grant in Aid from Ministry of Education, Science, Sports and Culture of Japan. and is sometimes called an attribute or a property ....

....can be considered as a restricted usage of has connection and is connection of LAURA[3] which was created for scheme design of relational databases. Here an IS NOT A relation is also used for specifying and checking inconsistency. In this way, DOT can be used in scheme design of databases. 9 term[1], O logic[16] F logic[14] and Quixote[26] provide advanced knowledge representation frameworks by extending the first order logic. ITL[9] is a knowledge representation language whose syntax is based on natural language. Since these approaches provide rich expressive capabilities which are ....

Ait-Kaci, H., "A Lattice Theoretic Approach to Computation Based on Calculus on Partially Ordered Type Structures", Ph.D. Thesis, Univ. of Pennsylvania, 1984.

....models of our theories, however, these substitutes will not provide us with the usual set theoretic interpretation of negation that matches its intended use in linguistic principles. Junk slots, the encoding of relations as components of an object by means of extra attributes and extra sorts (Ait Kaci, 1984; Carpenter, 1992) cannot also encode relational negation, and require the signature to contain uninteresting and unmotivated sorts. 3 It has been suggested (Kasper et al. 1995) that one might be able to restrict the use of negated relations to an inventory of decidable ones that can be ....

Ait-Kaci, H. 1984. A Lattice Theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures . Ph.D. thesis, University of Pennsylvania.

....the two tasks. This stance is in contrast to the position advocated in [McDonald et al. 87] that separate tasks should be implemented using distinct specialized formalisms. Usability and formal soundness: Formal analyses of feature structure systems similar to FUF have been established in [Ait Kaci 84] Kasper 87] and [Kasper Rounds 86] The work presented in this thesis is informed by this formal analysis and I have ensured that most extensions added to the base FUG formalism were compatible with these formal results. In particular, FUF is monotonic and bidirectional. I have, however, ....

....between different types of constraints is determined dynamically: How different constraints interact can be determined at run time depending on the current context of generation. This means the grammar can be modularized by constraints with specific interaction left unspecified. 15 cf. Ait Kaci 84] for the description of a programming language based on Y terms, a variation of functional descriptions and [Johnson 88, pp.88 93] for a description of the encoding of arbitrary Turing machines into functional descriptions 16 In this input, the transfer of possession is described as a ....

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Ait-Kaci, H. A Lattice-theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvania, 1984. UMI #8505030.

.... will ensure that unification is welldefined and produces a unique result, which is crucial for efficient and natural unification based processing (Pereira 1987) 3 Feature Structures We will begin by introducing an untyped collection of feature structures which are similar to the terms of Ait Kaci (1984) and the sorted feature structures of Smolka (1988) and Pollard and Moshier (1990) Definition 2 (Feature Structure) A feature structure is a tuple F = hQ; q; ffi i where ffl q : the root node in Q ffl Q : a finite set of nodes rooted at q so that Q = fffi( q) j 2 Pathg (see ....

....unifiers exist for pairs of consistent feature structures, up to alphabetic variance. Proof: The usual unification algorithm for feature 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 Ait Kaci (1984) or Pollard and Moshier (1990) 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 ....

[Article contains additional citation context not shown here]

Ait-Kaci, H. (1984). A Lattice-Theoretic Approach to Computation Based on a Calculus of Partially Ordered Types. PhD thesis, University of Pennsylvania.

....Moreover, the theory can not be brought into well formed format through partial evaluation: the process will not terminate. However, one could substitute the equivalent b Theta f b to obtain a well formed theory. A more realistic example is the junk slot encoding of the append relation (Ait Kaci 1984). We here assume an appropriate extension of the well formedness condition to disjunctive theories. The theory append 2 4 arg1 hi arg2 L arg3 L 3 5 2 6 6 6 6 6 6 6 6 4 arg1 H j T1 arg2 L arg3 H j T2 junk 2 6 6 4 append arg1 T1 arg2 L arg3 T2 3 7 7 5 3 7 7 7 7 7 7 7 7 5 ....

Ait-Kaci, H. (1984). A lattice theoretic approach to computation based on a calculus of partially ordered type structures. Ph. D. thesis, University of Pennsylvania.

....account recently achieved theoretical results concerning expressivity and tractability of terminological representation formalisms. In particular, the terminological logic used incorporates co reference constraints a quite powerful construction also used in similar formalisms such as terms [2] and feature logic [35] This system is also aimed more at database applications because it supports updates of instances and means of applying (forward chaining) rules to database entities. These rules do not act only as integrity constraints but they are also used to conclude additional ....

H. Ait-Kaci. A Lattice-Theoretic Approach to Computations Based on a Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvenia, Philadelphia, Pa., 1984.

.... junk slot ) needs to be introduced on objects of type word to house the lexical rule, or (in the alternative encoding described below) the second word related to. This junk slot technique for encoding (possibly recursive) relations on the level of the description language was first used by Ait Kaci (1984). To formulate a word principle encoding a lexicon including lexical rules, the junk slot technique has for example been used in several implementations of hpsg grammars (Keller (1993) Kuhn (1993) Meurers (1993) Figure 2 shows a type definition for word, which defines an extended lexicon ....

Ait-Kaci, Hassan. 1984. A lattice theoretic approach to computation based on a calculus of partially ordered type structures. Ph.D. thesis, University of Pennsylvania.

....number of qq. The difficulty is essentially the same as for regular expressions: there is no canonical form for regular expressions, though their identity (or containment for that matter) can be deduced from a finite automaton representation. An efficient implementation of same as reasoning ([1]) which is part of the Classic system, works on exactly this principle: a data structure, called a description graph in [6] represents the coreference relationships in a concept, and to see whether that concept is subsumed by a term like (same as (pp) rr) one needs to trace the paths pp and ....

Ait-Kaci, A Lattice Theoretic Approach to Computation Based on a Calculus of Partially-Ordered Type Structures. Ph.D. thesis, University of Pennsylvania, 1984.

....= hVAR; T ; F ; appropi is a signature, R is finite and R ft ) OE j t 2 T and OE is a term g 3.4 Example This simple grammar shows a junk slot encoding of the append relation 2 . The type hierarchy with the appropriateness conditions is depicted as a graph in the usual manner. 2 See (Ait Kaci 1984) list const 2 4 person gender gen father person 3 5 2 6 6 6 6 4 append arg1 list arg2 list arg3 list junk list 3 7 7 7 7 5 e list 2 4 ne list hd tl list 3 5 a b c gen fem masc append ) arg1: e list arg2: L arg3: L junk: e list arg1: hd: H tl: T 1 ) arg2: L arg3: ....

....M = u 2 fv j hvi 2 [ gram] M g 2 5 Conclusion and outlook We have presented a compilation scheme that translates HPSG constraint grammars into efficient logic programs by using a classification of types. The compilation is sound and semi finitely complete. It should be pointed out that (Ait Kaci 1984) and particularly (Ait Kaci et al. 1993) address a problem very similar to the one presented here. They provide a proof system which has the very nice property of lazy sort unfolding, i.e. applying constraints only when necessary. However, for this to work, the theory has to obey certain ....

Ait-Kaci, H. (1984). A lattice theoretic approach to computation based on a calculus of partially ordered type structures. Ph. D. thesis, University of Pennsylvania.

....[3, 4] is that the components of tuples are not restricted to taking only atomic values, but may be other tuples or even sets of tuples. A second property of complex objects and related information structures is that there is a natural ordering on the domain of values with an associated algebra [5, 6, 7]. For example, in Bancilhon and Khoshafian s ordering on tuples [1] Name) 0 J.Doe 0 ] v [Name) 0 J.Doe 0 ;Age)21] This research was supported in part by NSF IRI86 10617, NSF MCS 8219196 CER, ARO DAA6 29 84 k 0061, DAA29 849 0027, and a grant from AT T s Telecommunications Program at ....

H. Ait-Kaci, A Lattice Theoretic Approach to Computation based on Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvania, 1985.

....than one superclass) such as ZetaLisp [20] or Smalltalk [12] use an ad hoc solution for combining class properties which depend on the temporal total order in which the classes are defined or appear in an expression. This is clearly semantically unclean and pragmatically hazardous. Other proposals [3, 19, 14] have formalized the concept of class inheritance in lattice theoretic terms. This captures the essential properties useful in practice for object oriented languages, and allows a better handling of class expressions for efficient implementation. e.g. given a taxonomy of objects a subsumption ....

....3: A poset which is not a semi lattice fw 1 ; w k g. This is precisely the effect that the following construction achieves. To our knowledge, this construction is not conventional. It is related to what is known as completion by ideals [8] and detailed in the particular following form in [3] and [4] In what follows, we make the assumption that the poset is finite. 1 First, we need some definitions. The restricted powerset of a poset S; is the set 2 (S) of non empty finite subsets of pairwise incomparable elements of S. Such subsets are called cochains or, more figuratively, ....

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Ait-Kaci, H. A Lattice-Theoretic Approach to Computation Based on a Calculus of Partially-Ordered Type Structures. PhD thesis, Computer and Information Science, University of Pennsylvania, Philadelphia, PA (1984). Implementation of Lattice Operations 29

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Ait-Kaci, Hassan (1983), A Lattice Theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures. Ph.D Thesis, University of Pennsylvania.

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Ait-Kaci, H., "Lattice Theoretic Approach to Computation Based on A Calculus of Partially Ordered Type Structures," Ph.D. Thesis, University of Pennsyvania, 1984.

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H. Ait-Kaci, A lattice theoretic approach to computation based on a calculus of partially ordered type structures., PhD Thesis, University of Pennsylvania, 1984.

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