Hassan Ait-Kaci. A Lattice-Theoretic Approach to Computations Based on a Calculus of Partially Ordered Type Structures. PhD thesis, University of Pennsylvania, Philadelphia, PA, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that uses feature structures. Typed Feature Structure Unification in unification based grammar formalisms, unification is the meet operation on the meet semi lattice formed by partially ordering the set of feature structures by a subsumption relation [Shieber 86] Following ideas presented by [AYt Kaci 84] and introduced, for example, in the unification based formalism underlying HPSG [Pollard and Sag 87] first order unification is extended to the sorted case using an order sorted signature instead of a fiat one. In most existing implementations, descriptions of feature structure constraints are ....

Hassan Ait-Kaci. A Lattice Theo- retic Approach to Computation based on a Calculus of Partially Ordered Types Structures. Ph.D Dissertation, University of Pennsylvania, 1984.

....that uses feature structures. Typed Feature Structure Unification In unification based grammar formalisms, unification is the meet operation on the meet semi lattice formed by partially ordering the set of feature structures by a subsumption relation [Shieber 86] Following ideas presented by [Ait Kaci 84] and introduced, for example, in the unification based formalism underlying HPSG [Pollard and Sag 87] first order unification is extended to the sorted case using an order sorted signature instead of a flat one. In most existing implementations, descriptions of feature structure constraints are ....

Hassan Ait-Kaci. A Lattice Theoretic Approach to Computation based on a Calculus of Partially Ordered Types Structures. Ph.D Dissertation, University of Pennsylvania, 1984.

....Satisfiability of feature terms relative to a lexicon which is nothing else than a cycle free terminology for a feature logic [Nebel and Smolka, 1990] is also NP hard, even if satisfiability for the underlying feature logic is polynomial. For instance, adopting the terms introduced in [A it Kaci, 1984] for which satisfiability can be decided in quasi linear time, leads to an NP complete satisfiability problem if a lexicon is added. This intractability result does not seem to show up in practical applications very often, however. As a matter of fact, it is not easy to construct a terminology ....

....roles [Baader, 1991] 4 Thue Systems For feature logics, the computational complexity was analyzed quite early. The feature logic described in Sect. 2 without union t and complement : which give essentially the terms mentioned above, was shown to have a quasi linear satisfiability problem [A it Kaci, 1984] The addition of union or complement leads to NP completeness, as shown in [Kasper, 1987; Johnson, 1987; Smolka, 1988] Attributive Description Formalisms : and the Rest of the World 10 The situation in terminological logics was more problematical because of the variety of possible ....

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

....: n ) s n ) Such expressions have been used for quite some time in natural language processing [22] and more generally in knowledge representation, under the name of features. They have been used also together with subtyping mechanims in the area of programming languages to model inheritance [2]. Figure 4 describes a possible syntax for feature constraints, and suggests how the unification rules may be adapted to this case. The area of feature constraints has been very active in the last 10 years, and resulted in a complete constraint solver mechanism for the first order theory of ....

H. A it-Kaci. A Lattice-Theoretic Approach to Computation Based on a Calculus of PartiallyOrdered Type Structures. PhD thesis, University of Pennsylvania, 1984.

....constructs of these two paradigms. The LIFE language [3] subscribes to the logic programming, functional programming, and object oriented programming paradigms. The language design of LIFE is most similar to the philosophy of our approach. The central component of LIFE is a calculus of terms [1, 2], an extension of first order terms (Herbrand terms and terms) which provides structural convenience for representing record like data structures. The calculus defines a clear notion of subsumption interpretable as a subtype ordering, together with an efficient unification operation ....

....logic part of OLI for free. Third, objects are inherently typed. It is interesting to investigate if typing can be introduced into the logic part of OLI , resulting in an inheritance scheme and generic mechanism for predicates. For this, we need to generalize the notion of o terms. The calculus [1, 2] would be a good starting point. Fourth, more work is needed for an efficient implementation of the OLI language. A programming environment similar to that of SMALLTALK should also be investigated. Acknowledgement This research was supported in part by a UK HK Joint Research Scheme grant ....

H. A it-Kaci. A Lattice-Theoretic Approach to Computation Based on a Calculus of PartiallyOrdered Type Structures. PhD thesis, University fo Pennsylvania, Pennsylvania, Philadephia, PA, USA, 1984.

....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 ....

Hassan 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 the results reported in [29, 30] The LIFE language [31] subscribes to the logic programming, functional programming, and object oriented programming paradigms. The language design of LIFE is most similar to the philosophy of our approach. The central component of LIFE is a calculus of terms [32, 33], an extension of first order terms (Herbrand terms and terms) which provides structural convenience for representing record like data structures. The calculus defines a clear notion of subsumption interpretable as a subtype ordering, together with an efficient unification operation ....

....to investigate if typing can be introduced into the logic part of OLI , resulting in an inheritance scheme and generic mechanism for predicates. These issues are very useful in reusing and maintaining logical predicates. For this, we need to generalize the notion of o terms. The calculus [32, 33] would be a good starting point. Fourth, a rudimentary implementation of the OLI language has been constructed [36] but more work is needed for an efficient implementation of the OLI language. A programming environment similar to that of Smalltalk should also be investigated. Fifth, a CASE tool is ....

H. A it-Kaci. A Lattice-Theoretic Approach to Computation Based on a Calculus of PartiallyOrdered Type Structures. PhD thesis, University fo Pennsylvania, Pennsylvania, Philadephia, PA, USA, 1984.

....strings so that the join operation (which is the only lattice operation required in unification) is of constant complexity [HAKN89] In [CLR90] the disjoint forest data structure is presented. This data structure can be used to construct equivalence classes by means of a near linear process. In [AK84] and [Mos88] algorithms that compute the unifier of two feature structures of near linear complexity are given that rely on this technique. 4.3 A linear algorithm that decides Feature Structure subsumption In this section we will present an algorithm that constructs a morphism h from F = hQ; q; ....

Hassan A it-Kaci. A Lattice-Theoretic Approach to Computation based on a Calculus of Partially Ordered Type Structures. PhD thesis, Univ. of Pennsylvania, 1984.

....key of a quite unique and hitherto unheard of generative behavior of programs, which could construct missing information as needed to accommodate success. Finally, the most original part of LIFE is the structure oriented component which consists of a calculus of type structures the calculus [AK84, AK86] and rigorously accounts for some of the (multiple) inheritance convenience typically found in so called object oriented languages. An algebra of term structures adequate for the representation and formalization of frame like objects is given a clear notion of subsumption interpretable as a ....

....bounds (LUBs) are defined as well in S, so are they for terms. For example for these two terms, their LUB (most specific generalization) is person(advisor ) faculty(secretary ) employee, assistant ) person) roommate ) person) Thus, a lattice structure can be extended from S to terms [AK84, AK86]. Although it may turn out useful in other contexts, we shall ignore this generalization operation here. 4 See [AKBLN89] for a description of an efficient method for computing such GLB s. example, limiting ourselves to disjunctions of atomic terms in the context of set of sorts in Figure 3, ....

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Hassan At-Kaci. A Lattice-Theoretic Approach to Computation Based on a Calculus of Partially-Ordered Type Structures. PhD thesis, University of Pennsylvania, Philadelphia, PA, USA, 1984.

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

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Hassan AYt-Kaci. A Lattice Theoretic Approach to COmputation based on a Calculus of Partially Orde'ed Types Structures. Ph.D Disserta- tion, Universit3) of Pennsylvania.

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Hassan Al't-Kaci. A Lattice Theoretic Approach to Computation based on a Calculus of Partially Ordered Types Structures. Ph.D Dissertation, University of Pennsylvania.

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Hassan Ait-Kaci. 1984. 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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Hassan Ait-Kaci. 1984. A Lattice Theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures. Ph.D. thesis, Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA.

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