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A Complete Axiomatization of a Theory with Feature and Arity Constraints
, 1994
"... CFT is a recent constraint system providing records as a logical data structure for logic programming and for natural language processing. It combines the rational tree system as defined for logic programming with the feature tree system as used in natural language processing. The formulae consi ..."
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Cited by 23 (1 self)
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CFT is a recent constraint system providing records as a logical data structure for logic programming and for natural language processing. It combines the rational tree system as defined for logic programming with the feature tree system as used in natural language processing. The formulae considered in this paper are all firstorderlogic formulae over a signature of binary and unary predicates called features and arities, respectively. We establish the theory CFT by means of seven axiom schemes and show its completeness. Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified record descriptions.
Ordering Constraints over Feature Trees
, 1999
"... Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular ..."
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Cited by 13 (5 self)
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Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular record descriptions. We introduce the constraint system FT of ordering constraints interpreted over feature trees. Under the view that feature trees represent symbolic information, the relation corresponds to the information ordering ("carries less information than"). We present two algorithms in cubic time, one for the satisfiability problem and one for the entailment problem of FT . We show that FT has the independence property. We are thus able to handle negative conjuncts via entailment and obtain a cubic algorithm that decides the satisfiability of conjunctions of positive and negated ordering constraints over feature trees. Furthermore, we reduce the satisfiability problem of Dorre's weak subsumption constraints to the satisfiability problem of FT and improve the complexity bound for solving weak subsumption constraints from O(n^5) to O(n³).
How to Win a Game with Features
 1ST INTERNATIONAL CONFERENCE ON CONSTRAINTS IN COMPUTATIONAL LOGICS, LECTURE NOTES IN COMPUTER SCIENCE
, 1994
"... We employ the modeltheoretic method of EhrenfeuchtFraisse Games to prove the completeness of the theory CFT, which has been introduced in [22] for describing rational trees in a language of selector functions. The comparison to other techniques used in this field shows that EhrenfeuchtFraisse ..."
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Cited by 8 (2 self)
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We employ the modeltheoretic method of EhrenfeuchtFraisse Games to prove the completeness of the theory CFT, which has been introduced in [22] for describing rational trees in a language of selector functions. The comparison to other techniques used in this field shows that EhrenfeuchtFraisse Games lead to simpler proofs.
Ordering Constraints over Feature Trees Expressed in Secondorder Monadic Logic
 Information and Computation
, 1998
"... The language FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. While the firstorder theory of FT is well understood, only few decidability results are known for the firstorder theory of FT . We introduc ..."
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Cited by 8 (4 self)
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The language FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. While the firstorder theory of FT is well understood, only few decidability results are known for the firstorder theory of FT . We introduce a new method for proving the decidability of fragments of the firstorder theory of FT . This method is based on reduction to second order monadic logic that is decidable according to Rabin's famous tree theorem. The method applies to any fragment of the firstorder theory of FT for which one can change the model towards sufficiently labeled feature trees  a class of trees that we introduce. As we show, the first ordertheory of ordering constraints over sufficiently labeled feature trees is equivalent to secondorder monadic logic (S2S for infinite and WS2S for finite feature trees). We apply our method for proving that entailment of FT with existential quantifiers j 1 j=9x 1 : : :9x n j 2 is decidable. Previous results were restricted to entailment without existential quantifiers which can be solved in cubic time. Meanwhile, entailment with existential quantifiers has been shown PSPACEcomplete (for finite and infinite feature trees respectively).
Type Inference for FirstClass Messages with Feature Constraints
 International Journal of Foundations of Computer Science
, 1998
"... We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for firstclass messages. OF extends traditional systems of feature constraints by a selection constraint xhyiz "by firstclass feature tree" y, in contrast to the standard sel ..."
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Cited by 5 (0 self)
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We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for firstclass messages. OF extends traditional systems of feature constraints by a selection constraint xhyiz "by firstclass feature tree" y, in contrast to the standard selection constraint x[ f ]y "by fixed feature" f . We investigate the satisfiability problem of OF and show that it can be solved in polynomial time, and even in quadratic time in an important special case. We compare OF with Treinen's constraint system EF of feature constraints with firstclass features, which has an NPcomplete satisfiability problem. This comparison yields that the satisfiability problem for OF with negation is NPhard. Based on OF we give a simple account of type inference for firstclass messages in the spirit of Nishimura's recent proposal, and we show that it has polynomial time complexity: We also highlight an immediate extension that is desirable but makes type inference NPhard.
Weak Subsumption Constraints for Type Diagnosis: An Incremental Algorithm
 In Joint COMPULOGNET /ELSNET/EAGLES Workshop on Computational Logic for Natural Language Processing
, 1995
"... We introduce constraints necessary for type checking a higherorder concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x⊆y saying that “x has at least the structure of y”, modelled by a weak instance relatio ..."
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Cited by 1 (1 self)
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We introduce constraints necessary for type checking a higherorder concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x⊆y saying that “x has at least the structure of y”, modelled by a weak instance relation between trees. This notion of instance has been carefully chosen to be weaker than the usual one which renders semiunification undecidable. Semiunification has more than once served to link unification problems arising from type inference and those considered in computational linguistics. Just as polymorphic recursion corresponds to subsumption through the semiunification problem, our type constraint problem corresponds to weak subsumption of feature graphs in linguistics. The decidability problem for weak subsumption for feature graphs has been settled by Dörre [Dör94]. In contrast to Dörre’s, our algorithm is fully incremental and does not refer to finite state automata. Our algorithm also is a lot more flexible. It allows a number of extensions (records, sorts, disjunctive types, type declarations, and others) which make it suitable for type inference of a fullfledged programming language.