Connecting Logics Research Center on Spatial Cognition (SFB/TR8) This tutorial will give a gentle introduction to the field of combining logics, with a specific focus on the technique of E-connections. E-connections is a methodology for combining logics with a rather intuitive semantics, being inspired by counterpart theory. It moreover is quite well-behaved computationally in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows for non-trivial interaction between the combined logics. We begin by briefly outlining some of the more well-known techniques for combining or extending logics, namely fusions, products, fibrings, and concrete domains. We then outline the basic ideas behind E-connections, in which a finite number of formalisms are connected by relations relating entities across different domains, intended to capture different aspects or representations of the `same object'. For instance, an `abstract' object of a description logic can be related via a relation R to its life-span in a temporal logic as well as to its spatial extension in a spatial logic. We discuss the basic differences to the other combination methodologies introduced and then proceed to present E-connections in more technical detail. In particular, we introduce the framework of 'abstract description systems', a specific 'lightweight' form of abstract logic generalising the basic syntactic and semantic features of many modal and descprition logics. This allows us to study general properties of E-connections in a logic independent way. We show how this abstract presentation of E-connections can be used to prove general decidability preservation results and finally illustrate the usefulness of the framework in several application areas, including modularising web ontologies and combining spatio-temporal with conceptual modelling and reasoning. Three Sessions I. Combining Logics: Fusions, Products, Fibrings, Concrete Domains, E-connections. II. E-connections of abstract description systems. III. Computational properties and applications of E-connections.
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Bibliography M. Bhatt, J. Hois, and O. Kutz. Ontological Modelling of Form and Function in Architectural Design. Journal of Applied Ontology, 2012. W. A. Carnielli, M. E. Coniglio, D. Gabbay, P. Gouveia, and C. Sernadas. Analysis and Synthesis of Logics - How To Cut And Paste Reasoning Systems. Springer, 2008. W. A. Carnielli and M. E. Coniglio. Combining Logics. Stanford Encyclopedia of Philosophy, 2011. http://plato.stanford.edu/entries/logic-combining/ D. Gabbay, A. Kurucz, F. Wolter, and M. Zakharyaschev. Many-Dimensional Modal Logics: Theory and Applications. Studies in Logic and the Foundations of Mathematics, Number 148, Elsevier, 2003. M. Kracht and O. Kutz. Logically Possible Worlds and Counterpart Semantics for Modal Logic. Handbook of the Philosophy of Logic, edited by Dale Jacquette, Volume 5 of the Handbook of the Philosophy of Science, edited by Dov Gabbay, Paul Thagard, and John Woods, Elsevier, 943-996, 2007. O. Kutz, T. Mossakowski, and D. Luecke Carnap, Goguen, and the Hyperontologies. Logica Universalis: 4(2), Special Issue on 'Is Logic Universal?', Volume 4, Number 2, 255-333, 2010. O.Kutz, C. Lutz, F. Wolter and M. Zakharyaschev. E-connections of abstract description systems. In Artificial Intelligence. 156(1): 1-73, 2004.
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