To deal with autonomous agents' knowledge and subjective beliefs in the open, heterogeneous and inherently distributed settings concerned by Agreement Technologies, we need special formalisms that combine knowledge, taking also into account disagreements and heterogeneity from multiple interconnected contexts. For agents to reason jointly, they need to combine knowledge by means of correspondences and links between context elements. Each context contains a chunk of knowledge de ning a logical theory, that we call ontology or ontology unit. While standard logics may be used, to deal with the issues of subjectiveness and heterogeneity in the semantic web, special knowledge representation formalisms based on web standards have been proposed, sometimes called contextual logics or modular ontology languages (e.g. [1] [2]). Among others, assumptions about the domains covered by the distinct ontology units a ect the expressivity of the languages used for de ning correspondences. Nevertheless, in distributed and open settings we may expect that di erent units should be combined in many di erent, subtle ways. Towards this goal, we have been motivated to propose the representation framework EHDQD+L SHIQ (or simply E SHIQ). The proposed framework alleviates the assumptions for overlapping or disjoint domains posed by DDL and E -connections, respectively. The E-SHIQ framework. Given a nite index set of units' identi ers I, each unit Mi consists of a TBox Ti, RBox Ri, and ABox Ai in the SHIQ fragment of Description Logics (DL)[3]. SHIQ provides role transitivity and hierarchy, quali ed cardinality restrictions and inverse roles. For each unit i 2 I, let NCi , NRi and NOi be the sets of concept, role and individual names respectively. Each term C 2 NCi is interpreted by an interpretation function Ii = h iIi ; Ii i to a set of elements in the domain iIi modelled in the unit. Each term R 2 NRi is interpreted as a relation of elements RIi iIi iIi , and each x 2 NOi as a single element xIi 2 iIi . It holds that for each C v D 2 Ti, CIi DIi , where C; D are possibly complex concepts, and for each R v S 2 Ri, RIi SIi , where fR; Sg NRi . Each Ai contains concept and role assertions i.e. C(x), R(x; y), that are interpreted to membership xIi 2 CIi and relation hxIi ; yIi i 2 RIi of elements in the domain. An element, axiom or assertion c in unit Mi is denoted by i : c. Towards combining knowledge of di erent units, the proposed framework allows: (a) concept-to-concept subjective correspondences [4], [1], speci ed by onto-bridge rules i : C !w j : D, or into-bridge rules i : C !v j : D, where i 6= j 2 I, C 2 NCi ; D 2 NCj ; (b) Individual subjective correspondences i : a 7 != j : b,
where a 2 NOi and b 2 NOj , from the point of view of Mj ; (c) Link-properties
[
The implemented distributed tableau algorithm extends the Pellet reasoner
with new expansion rules for distributed reasoning, allowing local reasoning
chunks to be combined. These rules allow nodes in the completion graph of
a reasoning chunk for unit i labelled with concepts of a unit j, s.t. i 6= j 2 I, to
be projected to corresponding nodes in j. These nodes are locally exploited by j.
When the knowledge of multiple units is being combined, an inconsistency may
be detected in any of the local reasoning chunks. This reasoning chunk cannot
further participate in the collaborative reasoning process, since any projection
in it will lead to a clash. For the de nition of the framework and the instance
retrieval algorithm we refer the reader to previous work [
Acknowledgement:This research project is being supported by the project "IRAKLITOS II" of the O.P.E.L.L. 2007 - 2013 of the NSRF (2007 - 2013), co-funded by the European Union and National Resources of Greece. 3 As in standard DL, a simple ij-property is neither transitive, nor has a transitive sub-property.