MultiLanguage systems (ML systems) are formal systems allowing the use of multiple distinct logical languages. In this paper we introduce a class of ML systems which use a hierarchy of first order languages, each language containing names for the language below, and propose them as an alternative to modal logics. The motivations of our proposal are technical, epistemological and implementational. From a technical point of view, we prove, among other things, that the set of theorems of the most common modal logics can be embedded (under the obvious bijective mapping between a modal and a first order language) into that of the corresponding ML systems. Moreover, we show that ML systems have properties not holding for modal logics and argue that these properties are justified by our intuitions. This claim is motivated by the study of how ML systems can be used in the representation of beliefs (more generally, propositional attitudes) and provability, two areas where modal logics have been extensively used. Finally, from an implementation point of view, we argue that ML systems resemble closely the current practice in the computer representation of propositional attitudes and metatheoretic theorem proving.

We propose a framework, called OM pairs, for the formalization of metareasoning. OM pairs allow us to generate deductively the object theory and/or the meta theory. This is done by imposing, via appropriate reflection rules, the relation we want to hold between the object theory and the meta theory. In this paper we concentrate on the proof theory of OM pairs. We study them from three different points of view: we compare the strength of the object and meta theories generated by different OM pairs; for each OM pair we study the precise form of the object theory and meta theory; and, finally, we study three important case studies.

OM pairs are our proposed framework for the formalization of metareasoning. OM pairs allow us to generate deductively the object theory and/or the meta theory. This is done by imposing, via appropriate reflection rules, the relation we want to hold between the object theory and the metatheory. In a previous paper we have studied the proof theoretic properties of OM pairs. In this paper we study their model theoretic properties, in particular the relation between the models of the meta theory and the object theory; and use these results to refine the previous analysis. Key words: Foundations of meta reasoning, reflection principles, provability and truth, model theory Submitted to The Journal of Logic and Computation 1 OM pairs A lot of work on metatheoretic reasoning can be found in the literature. As far as we know, all of this work is aimed at defining and studying the properties of specific metatheories. Nobody has ever developed a theory which would allow for a uniform study an...

Due to the increasing necessity and availability of information from different sources, information integration is becoming one of the challenging issues in artificial intelligence and computer science. A successful methodology for information integration is based on Federated Databases (FDB). However, differently form databases (DBs) a completely satisfactory formal treatment of FDB is still missing. The goal of this paper is to fill this gap. Our basic intuition is that an FDB can be formalized by considering each DB of the federation as a context. We argue that this perspective is a promising one, as some of the relevant problems in the area of information integration, such as semantic heterogeneity, can be successfully solved using contexts. In the paper we provide a formal notion of FDB schema, a semantics for such a schema, called Local Models Semantics for FDBs, and a deduction system which formalizes the logical consequence of Local Models Semantics. We show by mean...

In many applications which use a large amount of information, knowledge is partitioned and represented in a set of databases (DB) integrated in a federated database (FDB). A FDB is a collection of distributed, partial, redundant and partially autonomous DBs. Distribution, redundancy, partiality, and autonomy generate many problems such as semantic etherogenity, update propagation, inter-schema dependencies, and query distribution. A formal treatment of these problems is necessary to define FDB management systems with correct behaviour. Several approaches have been proposed in the past. However, they all fail to represent all these issues in a uniform way. This failure, from our perspective, is due to the fact that these approaches do not explicitly treat distribution, redundancy, partiality, and autonomy. The goal of this paper is to develop a formal semantics called local model semantics, for FDB, which explicitly represents distributed, redundant, partial, autonomous DBs. We substantiate the above adequancy claim by formalizing three motivating examples which involves all these aspects.