Multi-Criterion Search from the Semantic Point of View (Comparing TIL and Description Logic) Marie DUŽÍ, VSB-Technical University Ostrava 17.listopadu 15 708 33 Ostrava Czech Republic Marie.Duzi@vsb.cz Peter VOJTÁŠ Charles University Prague Malostranské náměstí 25 118 00 Praha 1 Czech Republic Peter.Vojtas@mff.cuni.cz Abstract In this paper we discuss two formal models apt for a search and communication in a ‘multi-agent world’, namely TIL and EL @ . Specifying their intersection, we are able to translate and switch between them. Using their union, we extend their functionalities. The main asset of using TIL is a fine-grained rigorous analysis and specification close to natural language. The additional contribution of EL @ consists in modelling multi-criterion aspects of user preferences. Using a simple example throughout the paper, we illustrate the aspects of a multi-criterion search and communication by their analysis and specification in both the systems. The paper is an introductory study aiming at a universal logical approach to the ‘multi-agent world’, which at the same time opens new research problems and trends. 1. Introduction and motivation. In this paper we discuss two formal models that are relevant in the area of search and communication in the multi-agent world, namely Transparent Intensional Logic (TIL) and a fuzzy variant EL @ of the existential description logic EL (see [2]). Since TIL has been introduced and discussed in the EJC proceedings and EL is a well-known logical system, we are not going to introduce in details the technicalities of them. Instead, we provide just a minimal necessary introduction to keep the paper self-contained and concentrate on the analytic and specification role of these systems in the area of a semantic web search that takes into account specific user fuzzy criteria. By comparing the two formalisms we aim at providing a clue to their integration. Last but not least we’d like to illustrate the assets of a rigorous logical approach to the problem. The main asset of using TIL is a fine-grained rigorous analysis and specification close to natural language. The additional contribution of EL @ consists in modelling multi-criterion aspects of user preferences. The paper is an introductory study aiming at a universal logical approach to the ‘multi-agent world’, which at the same time opens new research problems and trends. The EL @ logic is a many-valued version of the existential description logic EL (see [2]) where fuzzification concerns only concepts and the logic is enriched with aggregation (see [21]). Specifying the intersection of TIL and EL @ , viz. the TIE @ L, we are able to translate