Ralf Treinen. Feature trees over arbitrary structures. In Patrick Blackburn and Maarten de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185-- 211. CSLI Publications and FoLLI, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[9] gives a terminating term rewriting system for quantifier elimination in term algebras with membership constraints, 38] gives quantifier elimination for term algebras with queues, 6] presents quantifier elimination for the first order theory of feature trees with arity predicates. [46] shows the decidability of any feature tree structure whose edge labels are elements of a decidable structure, and [48] shows the decidability of the monadic second order theory of an infinite binary tree whose edges come from a structure with a decidable monadic second order theory. Compared to ....

....of any feature tree structure whose edge labels are elements of a decidable structure, and [48] shows the decidability of the monadic second order theory of an infinite binary tree whose edges come from a structure with a decidable monadic second order theory. Compared to structures in [46], term powers allow the additional lifted relations between trees, which perform a global comparison of all leaves in a tree. It may be possible to combine our technique with [46] to obtain a family of decidable structures parameterized by both the edge label theory and the leaf theory. The main ....

[Article contains additional citation context not shown here]

R. Treinen. Feature trees over arbitrary structures. In P. Blackburn and M. de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185--211. CSLI Publications and FoLLI, 1997.

....The ae calculus over an arbitrary constraint system is an extension of the standard cc model with procedural abstraction. Symbolic constraints and combination problems A family of first order feature tree theories, indexed by the theory of the feature labels used to build the trees, is defined in [99]. A given feature label theory, which is required to carry an appropriate notion of sets, is conservatively extended to a theory of feature 17 Final CCL Report 18 trees with the predicates x[t]y (feature t leads from the root of tree x to the tree y) where we have to require t to be a ground ....

Ralf Treinen. Feature trees over arbitrary structures. In Patrick Blackburn and Maarten de Rijke, editors, Logic, Structures and Syntax, Studies in Logic, Language and Information. 1995. To appear. 40 Final CCL Report 41

....y describe the same feature trees. A record constraint Record(x) holds if and only if x is a tree. In this general form, all arguments of the constraints are variables or values from the particular domains (trees, sorts, features, or sets of features) Little is known about the general form [20, 21]. 3.2 Restricted Constraints Over Trees To make these constraints practical, we restrict them. We present three progressively more powerful restricted versions: Prolog structures, bound records, and free records. We show how to implement all three systems efficiently. The terminology bound and ....

Ralf Treinen. Feature trees over arbitrary structures. Studies in Logic, Language and Information. 1995. To appear.

....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 A METHODOLOGICAL VIEW OF CONSTRAINT SOLVING 11 constraint solver for first order features on one hand [3, 53], and in many prototype implementations of feature based languages on the other hand [2, 46] We refer to [53] for more information on feature constraints. Finally let us note that most of the efforts in symbolic constraint solving are surveyed in [28, 7] See also [29, 42] for more recent works. ....

.... constraints has been very active in the last 10 years, and resulted in a complete A METHODOLOGICAL VIEW OF CONSTRAINT SOLVING 11 constraint solver for first order features on one hand [3, 53] and in many prototype implementations of feature based languages on the other hand [2, 46] We refer to [53] for more information on feature constraints. Finally let us note that most of the efforts in symbolic constraint solving are surveyed in [28, 7] See also [29, 42] for more recent works. 3. Semantic Methods Semantic methods, as opposed to syntactic ones, do not operate directly on the constraint ....

Ralf Treinen. Feature trees over arbitrary structures. In Patrick Blackburn and Maarten de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185--211. CSLI Publications and FoLLI, 1997.

.... : f n : xf f 1 ; f n g : 9x 1 ; x n i n x[ f i ]x i 8y ( y[ f i ]x i same root label(x;y) xy) These so called arity constraints have been introduced in [28] A decidable feature logic where feature and label symbols have first class status has been investigated in [31]. The next formula is crucial for our undecidability proof. A tree t satisfies this formula iff fe;cg D t fcg and all its nodes are unlabeled: string c(x) xfcgnot root labeled(x)9y(x[c]yyx) In general, we have that Lemma 3.1 The formula 9y (x[ f ]y yx) is satisfied by t iff f 2 D t ....

R. Treinen. Feature trees over arbitrary structures. In P. Blackburn, M. de Rijke (eds.), Specifying Syntactic Structures, chap. 7, 185--211. CSLI Publications and FoLLI, 1997.

.... : f n g : 9x 1 ; x n (x[ f 1 ]x 1 : x[ f n ]x n 8y (y[ f 1 ]x 1 : y[ f n ]x n same root label(x;y) x y) These so called arity constraints have been introduced in [31] A decidable feature logic where feature symbols have first class status has been investigated in [34]. 3.4 Inductive Properties We start this section by a demonstration of the expressivity of FT and show that we can express in FT inductive properties of trees, that is properties that require an inductive construction (for instance an automaton) to define. We conclude the section by the ....

R. Treinen. Feature trees over arbitrary structures. In P. Blackburn and M. de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185--211. CSLI Publications and FoLLI, 1997.

....sentences in A is decidable. 17 2.7 Example: Feature Trees The quanti er elimination procedure for AFT has been given by [BS95] working on a language extended by so called path constraints. The weak quanti er elimination procedure presented here is derived from the more general result of [Tre97] which follows ideas of [Mal71] and [CL89] We have eight possible literals: x = y; x 6= y; Ax; Ax; xf ; xf ; x[f ]y; x[f ]y We call basic formula any formula of the form 9 x (a 1 : an ) where the a i are literals. Elimination of :xf and x[f ]y We rst show how to eliminate ....

....pre solved forms. It is possible to extend the procedure to that case of CFT with possibly in nite trees. The problem is, however, that we can not push down the inequalities to variables that are not fully constraint by a label and an arity constraint. The interested reader is referred to [Tre97] 22 Chapter 3 Semantic Methods: Automata 3.1 Word Automata and Logic The basic principle is to construct for a given formula an automaton A that recognizes the set of solutions of . In order to formulate a correspondence between logic and automata we rst need to relate their semantics. ....

Ralf Treinen. Feature trees over arbitrary structures. In Patrick Blackburn and Maarten de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185211. CSLI Publications and FoLLI, 1997.

No context found.

Ralf Treinen. Feature trees over arbitrary structures. In Patrick Blackburn and Maarten de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185-- 211. CSLI Publications and FoLLI, 1997.

No context found.

R. Treinen. Feature trees over arbitrary structures. In P. Blackburn and M. de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185--211. CSLI Publications and FoLLI, 1997.

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