This paper investigates that interaction. In particular it studies constraint implication problems, which are important both in understanding the semantics of type/constraint systems and in query optimization. It shows that path constraints interact with types in a highly intricate way. For that purpose a number of results on path constraint implication are established in the presence and absence of type systems. These results demonstrate that adding a type system may in some cases simplify reasoning about path constraints and in other cases make it harder. For example, it is shown that there is a path constraint implication problem that is decidable in PTIME in the untyped context, but that becomes undecidable when a type system is added. On the other hand, there is an implication problem that is undecidable in the untyped context, but becomes not only decidable in cubic time but also finitely axiomatizable when a type system is imposed

We analyze several classes of path constraints for semistructured data and prove a umber of decidability and complexity results for such constraints. While some of our decidability results were known before, we believe that our improved complexity bounds are new. Our proofs are based on techniques from modal logic and automata theory. We believe that our modal logic perspective sheds additional light on the reasons for previously known decidability and complexity results.

The system FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. We investigate the first-order theory of FT and its fragments, both over finite trees and over possibly infinite trees. We prove that the first-order theory of FT is undecidable, in contrast to the first-order theory of FT which is well-known to be decidable. We determine the complexity of the entailment problem of FT with existential quantification to be PSPACE-complete, by proving its equivalence to the inclusion problem of non-deterministic finite automata. Our reduction from the entailment problem to the inclusion problem is based on a new alogrithm that, given an existential formula of FT , computes a finite automaton which accepts all its logic consequences.

. Path constraints have been studied for semistructured data modeled as a rooted edge-labeled directed graph [4, 11--13]. In this model, the implication problems associated with many natural path constraints are undecidable [11, 13]. A variant of the graph model, called the deterministic data model , was recently proposed in [10]. In this model, data is represented as a graph with deterministic edge relations, i.e., the edges emanating from any node in the graph have distinct labels. This model is more appropriate for representing, e.g., ACeDB [27] databases and Web sites. This paper investigates path constraints for the deterministic data model. It demonstrates the application of path constraints to, among others, query optimization. Three classes of path constraints are considered: the language Pc introduced in [11], an extension of Pc , denoted by P w c , by including wildcards in path expressions, and a generalization of P w c , denoted by P c , by representing pa...

Abstract not found

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).

Although negation-free languages are widely used in logic and computer science, relatively little is known about their expressive power. To address this issue we consider kinds of non-symmetric bisimulations called directed simulations, and use these to analyse the expressive power and model theory of negation-free modal and temporal languages. We first use them to obtain preservation, safety and definability results for a simple negation-free modal language. We then obtain analogous results for stronger negation-free languages. Finally, we extend our methods to deal with languages with non-Boolean negation. Keywords: Expressive power, modal logic, negation-free languages. 1

We analyze several classes of path constraints for semistructured data in a uni- ed framework and prove some decidability and complexity results for these constraints by embedding them in Propositional Dynamic Logic. While some of our decidability results were known before, we believe that our improved complexity bounds are new. Our proofs, based on techniques from modal logic, shed additional light on the reasons for previously known decidability and complexity results.

This paper describes a new formalization of Lexical-Functional Grammar called R-LFG (where the "R" stands for "Resource-based"). The formal details of R-LFG are presented in Johnson (1997); the present work concentrates on motivating R-LFG and explaining to linguists how it differs from the "classical" LFG framework presented in Kaplan and Bresnan (1982). This work is largely a reaction to the linear logic semantics for LFG developed by Dalrymple and colleagues (Dalrymple et al., 1995; Dalrymple et al., 1996a; Dalrymple et al., 1996b; Dalrymple et al., 1996c). As they note, LFG's f-structure completeness and coherence constraints fall out as a by-product of the linear logic machinery they propose for semantic interpretation, thus making those f-structure mechanisms redundant. Given that linear logic machinery or something like it is independently needed for semantic interpretation, it seems reasonable to explore the extent to which it is capable of handling feature structure constraints as well. R-LFG represents the extreme position that all linguistically required feature structure dependencies can be captured by the resource-accounting machinery of a linear or similiar logic independently needed for semantic interpretation. The goal is to show that LFG linguistic analyses can be expressed as clearly and perspicuously using the smaller set of mechanisms of R-LFG as they can using the much larger set of mechanisms in LFG: if this is the case then we will have shown that positing these extra f-structure mechanisms are not linguistically warranted. One way to show this would be to present a translation procedure which reduces LFGs to equivalent R-LFGs, but currently no such procedure is known. Thus we proceed on a case by case basis, demonstrating that particular LFG anal...

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 first-order theory of FT is well understood, only few decidability results are known for the first-order theory of FT . We introduce a new method for proving the decidability of fragments of the first-order 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 first-order 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 order-theory of ordering constraints over sufficiently labeled feature trees is equivalent to second-order 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 PSPACE-complete (for finite and infinite feature trees respectively).