Intensional logic and epistemic independency of intelligent database agents

Abstract

In the typical Web applications each intelligent database agent can be de ned as a Knowledge system (KS) with a global ontology, which integrates a number of source data distributed in Web by traditional extensional mappings, and must be robust enough in order to take in account the incomplete and locally inconsistent information of its sources. The traditional extensional semantics for mappings between the different KSs destroys the epistemic independence of KSs: the beliefs of other KSs are forced into a local knowledge of a given KS, so that its own belief depends directly and automatically from them. Actually we want to nd a kind of semantics for external mappings between KSs which is less strong w.r.t. the internal KS's (extensionally based) database mappings. These philosophical considerations motivate the need of a new, alternative semantic characterization, based not on the extension but on the meaning of concepts used in the mappings between KSs.

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The Cooperative Information Systems has no centralized schema and no central administration. Instead, each intelligent database agent (KS) is an autonomous information system, and information integration is achieved by establishing mappings among various ontologies of these independent KSs. Given the de-centralized nature of the development of the Semantic Web, there will be an explosion in the number of ontologies. Many of these ontologies (that is, KSs) will describe similar domains, but using different terminologies, and others will have overlapping domains. To integrate data from disparate ontologies, we must know the semantic correspondence between their elements. Recently are given a number of different architecture solutions [ 1,2,3,4 ]. Queries are posed to one KS, and the role of query processing is to exploit both the data that are internal to the KS, and the mappings with other KSs in the system. In this paper we investigate on the possibility of using the intensional logic for both expressing interschema (inter-ontology) knowledge, and reasoning about it. The basic idea of our approach is to propose an intensional logic-based language to express interdependencies between concepts (views de ned as conjunctive queries) belonging to different schemas (KS's ontologies). For example, one can assert in our language that the concept represented by the view GraduateStudent in the schema is the same as the concept represented by the view SeniorStudent in . Such assertion implies a sort of intensional equivalence between the two concepts, but does not imply that the extension (the set of instances) of the former is always the same as the extension of the later.

The existing research papers in the literature share our general goal of representing and using interschema knowledge (for an exhaustive consideration consider [5] ), but their approaches does not guarantee the complete epistemic independencies between different KSs.

Let and be the two KSs, denominated by 'Peter' and 'John' respectively, and x , x be the concepts of ”the Italian art in the 15'th century” with attributes in x, written in local languages of and respectively. We are able to individuate at least two extreme scenarios, developed from the initial article [6] : 1. The strongly-coupled semantics [ 3 ] for mappings between different KSs is a direct extension of extensionally based database mappings between views of KSs [5] used for a (strong) data integration systems: For any given KS its own knowledge is locally enlarged by extensional knowledge of other KSs: any dynamic change of the knowledge of other KSs is directly re ected into the local knowledge of this KS. As showed in [ 3 ], the added knowledge of other KSs is seen as some kind of local 'source' database of data-integration system of a given KS. We can paraphrase this by imperative assertion 'John must know all facts about the Italian art in the 15'th century known by Peter' (also when 'Peter' in his life cycle changes this part of its own knowledge), formally x x , where is the logic implication. 2. The weakly-coupled semantics [ 7,4 ]. At a very beginning was my intuition that the real cooperative information systems, where each KS is completely independent entity, with its own epistemic state, which has not to be directly, externally, changed by the mutable knowledge of other independent KSs, needs other meaning (approach) to the mapping between their local knowledge. First requirement is that the knowledge of other KSs can not be directly transferred into the local knowledge of a given peer. The second requirement is that, during the life time of a cooperative information system, any local change of knowledge must be independent of the beliefs that can have other KSs: thus, we have not to constrain the extension of knowledge which may have different KSs about the same type of real-world concept.

In the example above, 'John' can answer only for a part of knowledge that it really has about Italian art, and not for a knowledge that 'Peter' has. Thus, when somebody (call him 'query-agent') ask 'John' some information about Italian art in the 15'th century, 'John' is able to respond only by facts known by himself (i.e., certain answers), and eventually indicate to query-agent that for such question probably 'Peter' is able to give some answer also: so, it is the task of the query-agent to reformulate the question (w.r.t. the local language of 'Peter') to 'Peter' in order to obtain some other possible answers. We can paraphrase this by the kind of belief-sentence-mapping 'John believes that also Peter knows something about Italian art in the 15'th century', formally x x , where is the believed intensional equivalence. Such belief-sentence has referential (i.e., extensional) opacity. In this case we do not specify that the knowledge of 'John' is included in the knowledge of 'Peter' (or viceversa) for the concept 'Italian art in the 15'th century', but only that this concept, x , for 'John' implicitly corresponds to the 'equivalent' concept, x , for 'Peter'. The 'implicit correspondence between equivalent concepts' needs a formal semantic de nition for it. It was not easy task, because the mapping de ned above deals with the semantics of natural language. Motague [ 8 ] de ned the intension of a sentence as a function from possible worlds to truth values.

(Least Upper Bound) is de ned by: tion between worlds ( is a function de ned for the following two cases:

In what follows we will use one simpli ed modal logic framework (we will not consider differ from one world to the other; if

is a variable we have Carnap suggested that the intension of an expression is nothing more than all the varying extensions the expression can have. In the next we will take this de nition in order following two cases: 1. at-accumulation case: In the context of this work we will consider each temporary instance (in a some time changes of any local KS knowledge will result in one other possible world. The intensional mapping between KSs is given by couples of queries conjunctive query are intensionally equivalent, in the where for a given expression , and obtain that holds

is a logic equivalence and to the set of certain answers to the conjunctive query from KSs (we consider that each KS

is an epistemic local logic theory with the modal epistemic operator , so that the truth of a modal formula respectively (a local universe is the set of all the values that are elements of the domains need not to be satis ed. Moreover, if and are local universes for a KS and , thus, by the symmetry and the transitivity of the relation Proposition 1 Let consider the class of KSs with integrity constraints which does not equivalence is preserved by conjunction logic operation, that is, . Then, the intensional corresponds

, the then .

Thus, for any given conjunctive query (virtual concept) to some intelligent database agent, the query-agent will obtain as answer the set of certain (known) answers from this interrogated database agent, and the set of possible answers from other database agents which are able to express the intensionally equivalent virtual concepts to the original user query.

We believe that the intensional mapping semantics presented in this paper constitutes a sound basis for studying the various issues related to interschema knowledge representation and reasoning, especially for P2P database systems in Web environment, where peers can be considered as complex database agents. 4. Z. Majkic´, “Weakly-coupled ontology integration of p2p database systems,” 1st Int. Workshop 5. Tiziana Catarci and Maurizio Lenzerini, “Representing and using interschema knowledge in cooperative information systems,” J. of Intelligent and Cooperative Information Systems, vol. 2, no. 4, pp. 375–398, 1993.

References

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2. L.Sera ni, F. Giunchiglia , J. Mylopoulos , and P.A. Bernstein , “ The local relational model: Model and proof theory , ” Technical Report 0112-23 , ITC-IRST, 2001 .

3. D. Calvanese , G. De Giacomo, M. Lenzerini , and R. Rosati , “ Logical foundations of peer-to6. M.Lenzerini and Z. Majkic ´, “ General framework for query reformulation,” Semantic Webs and Agents in Integrated Economies , D3 .1, IST- 2001-34825, February,, 2003 .

7. Z. Majkic ´, “ Massive parallelism for query answering in weakly integrated p2p systems ,” Workshop GLOBE 04, August 30-September 3, Zaragoza , Spain, 2004 .

8. R. Montague , “ Formal philosophy . selected papers of richard montague,” in R.Thomason (editor), Yale University Press, New Haven, London, pp. 108 – 221 , 1974 .