Ontologies are shared models of a domain that encode a view which is common to a set of different parties. Contexts are local models that encode a party's subjective view of a domain. In this paper we show how ontologies can be contextualized, thus acquiring certain useful properties that a pure shared approach cannot provide. We say that an ontology is contextualized or, also, that it is a contextual ontology, when its contents are kept local, and therefore not shared with other ontologies, and mapped with the contents of other ontologies via explicit (context) mappings. The result is Context OWL (C-OWL), a language whose syntax and semantics have been obtained by extending the OWL syntax and semantics to allow for the representation of contextual ontologies.

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.

It is widely agreed on that most cognitive processes are contextual in the sense that they depend on the environment, or context, inside which they are carried on. Even concentrating on the issue of contextuality in reasoning, many different notions of context can be found in the Artificial Intelligence literature. Our intuition is that reasoning is usually performed on a subset of the global knowledge base. The notion of context is used as a means of formalizing this idea of localization. Roughly speaking, we take a context to be the set of facts used locally to prove a given goal plus the inference routines used to reason about them (which in general are different for different sets of facts). Our perspective is similar to that proposed in [McC87, McC91]. The goal of this paper is to propose an epistemologically adequate theory of reasoning with contexts. The emphasis is on motivations and intuitions, rather than on technicalities. The two basic definitions are reported i...

I wish honorable gentlemen would have the fairness to give the entire context of what I did say, and not pick out detached words. (Cobden, Speeches 46, 1849, quoted intheOED) The importance of contextual reasoning is emphasized by various researchers in AI.

As discussed in previous papers, belief contexts are a powerful and appropriate formalism for the representation and implementation of propositional attitudes in a multiagent environment. In this paper we show that a formalization using belief contexts is also elaboration tolerant. That is, it is able to cope with minor changes to input problems without major revisions. Elaboration tolerance is a vital property for building situated agents: it allows for adapting and re-using a previous problem representation in different (but related) situations, rather than building a new representation from scratch. We substantiate our claims by discussing a number of variations to a paradigmatic case study, the Three Wise Men problem. Introduction Belief contexts (Giunchiglia 1993; Giunchiglia & Serafini 1994; Giunchiglia et al. 1993) are a formalism for the representation of propositional attitudes. Their basic feature is modularity: knowledge can be distributed into different and separated mod...

In this paper we investigate the simple logical properties of contexts. We describe both the syntax and semantics of a general propositional language of context, and we give a Hilbert style proof system for this language. A propositional logic of context extends classical propositional logic in two ways. Firstly, a new modality, ist(; OE), is introduced. It is used to express that the sentence, OE, holds in the context, . Secondly, each context has its own vocabulary, i.e. a set of propositional atoms which are defined or meaningful in that context. The main results of this paper are the soundness and completeness of this Hilbert style proof system. We also provide soundness and completeness results (i.e., correspondence theory) for various extensions of the general system. Finally, we prove that our logic is decidable, and give a brief comparison of our semantics to Kripke semantics. 1 Introduction In this paper we investigate the simple logical properties of contexts. Contexts were...

In this paper we present a new notion of formal system, so called multilanguage system (ML-system) which allows the use of multiple distinct languages, each language being associated with its theory. ML-systems allow the use of inference rules, called bridge rules, whose premises and consequences need not belong to the same language. Bridge rules allow the propagation of results among theories, thus making them "partially" dependent on one another. Some examples of ML-systems are proposed and argued to formalize naturally and elegantly propositional attitudes and, in particular, belief.

The goal of this paper is to provide a possible foundation for meta-reasoning in the fields of artificial intelligence and computer science. We first investigate the relationship that we want to hold between meta-theory and object-theory. We then outline a methodology in which reflection rules serve to deductively generate a meta-theory from its object theory. Finally, we apply this methodology and define a hierarchical meta-logic, namely a formal system generating an entire meta-hierarchy, which is sound and complete with respect to a semantics formalising the desired meta/object relationship.

This paper presents an overview of the REFLECT project. It defines the notion of knowledge level reflection that has been central to the project, it compares this notion with existing approaches to reflection in related fields, and investigates some of the consequences of the concept of knowledge level reflection: what is a general architecture for knowledge level reflection, how to model the object component in such an architecture, what is the nature of reflective theories, how can we design such architectures, and what are the results of our actual experiments with such systems?

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 metatheories, each with a first order language containing names for the language below, and propose them as an alternative to modal logics. The motivations of our proposal are technical and epistemological. From a technical point of view, we prove, among other things, that modal logics can be embedded in 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. We motivate our claim by studying how they can be used in the representation of beliefs (more generally, propositional attitudes) and provability, two areas where modal logics have been extensively used. 1