k --Universal Finite Graphs

This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not definable by an infinite disjunction of first-order existential sentences with a finite number of variables and that there exist k-universal graphs with no k-extendible induced subgraphs

Constraints for Semistructured Data and XML

Integrity constraints play a fundamental role in database design. We review initial work on the expression of integrity constraints for semistructured data and XML

Relevant Consequence and Empirical Inquiry

A criterion of adequacy is proposed for theories of relevant consequence. According to the criterion, scientists whose deductive reasoning is limited to some proposed subset of the standard consequence relation must not thereby suffer a reduction in scientific competence. A simple theory of relevant consequence is introduced and shown to satisfy the criterion with respect to a formally defined paradigm of empirical inquiry

Notes on Hierarchies and Inductive Inference

The following notes rework a discussion due to Kevin Kelly on the application of topological notions in the context of learning (see Kelly (1990)). All the results except for (2), (4) and (9) are due to Kelly, but are proved differently

Providing a Unified Account of Definite Noun Phrases in Discourse

Linguistic theories typically assign various linguistic phenomena to one of the categories, syntactic, semantic, or pragmatic, as if the phenomena in each category were relatively independent of those in the others. However, various phenomena in discourse do not seem to yield comfortably to any account that is strictly a syntactic or semantic or pragmatic one. This paper focuses on particular phenomena of this sort-the use of various referring expressions such as definite noun phrases and pronouns-and examines their interaction with mechanisms used to maintain discourse coherence.Engineering and Applied Science

The Decidability of Some Restricted Implication Problems for Path Constraints

In [10], we introduced a path constraint language and established the undecidability of its associated implication problems. In this paper, we identify several fragments of the language, and establish the decidability of the implication and finite implication problems for each of these fragments in the context of semistructured databases. In addition, we demonstrate that these fragments suffice to express important semantic information such as extent constraint, inverse relationships and local database constraints commonly found in object-oriented databases. We also show that these fragments are useful for, among other things, query optimization

Infinitary Logic and Inductive Definability Over Finite Structures

The extensions of first-order logic with a least fixed point operators (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [AV91b] investigated the relation of these two logics in the absence of an ordering, using a mchine model of generic computation. In particular, they showed that the two languages have equivalent expressive power if and only if P = PSPACE. These languages can also be seen as fragments of an infinitary logic where each formula has a bounded number of variables, Lω∞ω (see, for instance, [KV90]). We present a treatment of the results in [AV91b] from this point of view. In particular, we show that we can write a formula of FO + LFP and P from ordered structures to classes of structures where every element is definable. We also settle a conjecture mentioned in [AV91b] by showing that FO + LFP in properly contained in the polynomial time computable fragment of Lω∞ω, raising the question of whether the latter fragment is a recursively enumerable class