Abstract. We present a novel combination of disjunctive logic programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a well-balanced interface between disjunctive logic programs and description logics, which guarantees the decidability of the resulting formalism without assuming syntactic restrictions. We show that the new formalism has very nice semantic properties. In particular, it faithfully extends both disjunctive programs and description logics. Furthermore, we describe algorithms for reasoning in the new formalism, and we give a precise picture of its computational complexity. We also provide a special case with polynomial data complexity. 1

Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DL-Lite family of tractable description logics (DLs) [11, 19]. An important result of these works is that the main

Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination).

Abstract. We present a novel approach to fuzzy dl-programs under the answer set semantics, which is a tight integration of fuzzy disjunctive programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly integrated disjunctive dl-programs by fuzzy vagueness in both the description logic and the logic program component. We show that the new formalism faithfully extends both fuzzy disjunctive programs and fuzzy description logics, and that under suitable assumptions, reasoning in the new formalism is decidable. Furthermore, we present a polynomial reduction of certain fuzzy dl-programs to tightly integrated disjunctive dl-programs. We also provide a special case of fuzzy dl-programs for which deciding consistency and query processing have both a polynomial data complexity. 1

Abstract. This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web. More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified nonmonotonic negation), and probabilistic uncertainty in a uniform framework for the Semantic Web. We define important concepts dealing with both probabilistic uncertainty and fuzzy vagueness, such as the expected truth value of a crisp sentence and the probability of a vague sentence. Furthermore, we describe a shopping agent example, which gives evidence of the usefulness of probabilistic fuzzy description logic programs in realistic web applications. In the extended report, we also provide algorithms for query processing in probabilistic fuzzy description logic programs, and we delineate a special case where query processing can be done in polynomial time in the data complexity. 1

This paper describes fuzzy CARIN, a knowledge representation language combining fuzzy description logics with Horn Rules. Fuzzy CARIN integrates the management of fuzzy logic into the non recursive CARIN system. It provides a sound and complete algorithm for representing and reasoning about fuzzy ALCN R extended with non recursive Horn Rules. Such an extension is most useful in realistic applications dealing with uncertainty and imprecision, such as multimedia processing and medical applications. Additionally, it provides the ability of answering to union of conjunctive queries, which is a novelty not previously addressed by fuzzy DL systems. 1.

We present a novel approach to fuzzy description logic programs (or simply fuzzy dl-programs) under the answer set semantics, which is a tight integration of fuzzy disjunctive logic programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly coupled disjunctive dl-programs by fuzzy vagueness in both the description logic and the logic program component. We show that the new formalism faithfully extends both fuzzy disjunctive logic programs and fuzzy description logics, and that under suitable assumptions, reasoning in the new formalism is decidable. We present a polynomial reduction of certain fuzzy dl-programs to tightly coupled disjunctive dl-programs, and we analyze the complexity of consistency checking and query processing for certain fuzzy dl-programs. Furthermore, we provide a special case of fuzzy dl-programs for which deciding consistency and query processing can both be done in polynomial time in the data complexity. Key words: tightly coupled fuzzy description logic programs, answer set semantics, Semantic Web, fuzzy disjunctive logic programs, fuzzy description logics, tightly coupled description logic programs, fuzzy vagueness, tractability.

Abstract. We show how a fuzzy answer set program can be compiled to an equivalent fuzzy propositional theory whose models correspond to the answer sets of the program. This creates a basis for constructing fuzzy answer set solvers, such as solvers based on fuzzy SAT-solvers or on linear programming. Keywords: answer set programming, fuzzy logic, Clark’s completion, fuzzy ASSAT. 1

While applications in different areas have shown the necessity of dealing with uncertain knowledge, Semantic Web techniques based on standard Description Logics do not have such a capability. Motivated by this discrepancy, we introduce an expressive fuzzy description logic, fZSI, which extends the classic Description Logic SI to deal with uncertain knowledge about concepts and roles as well as instances of concepts and roles. In the family of Fuzzy Logics it is semantically based on Zadeh Logic, which naturally interprets uncertain knowledge about concepts and roles as fuzzy sets and fuzzy relations, and interprets uncertain knowledge about instances as elements with degrees of membership. The paper focuses on several reasoning methods for the main reasoning problems in fZSI, including consistency checking, instance range entailment, and f-retrieval problems.