Propositional Typicality Logic (PTL) extends propositional logic with a connective • expressing the most typical (alias normal or conventional) situations in which a given sentence holds. As such, it generalises e.g.~preferential logics that formalise reasoning with conditionals such as ``birds typically fly''. In this paper, we study revision of sets of PTL-sentences. We first show why it is necessary to extend the PTL-language with a possibility operator, and then define the revision of PTL-sentences syntactically and characterise it semantically. We show that this allows us to represent a wide variety of existing revision methods, such as propositional revision and revision of epistemic states. Furthermore, we provide several examples showing why our approach is innovative. In more detail, we study revision of a set of conditionals under preferential closure, and the addition and contraction of possible worlds from an epistemic state.

In this work we address the following question: can we measure how much knowledge a knowledge base represents? We answer to this question (i) by describing properties (axioms) that a knowledge measure we believe should have in measuring the amount of knowledge of a knowledge base (kb); and (ii) provide a concrete example of such a measure, based on the notion of entropy. We also introduce related kb notions such as (i) accuracy; (ii) conciseness; and (iii) Pareto optimality. Informally, they address the following questions: (i) how precise is a kb in describing the actual world? (ii) how succinct is a kb w.r.t. the knowledge it represents? and (iii) can we increase accuracy without decreasing conciseness, or vice-versa?

Serializable and incremental semantic reasoners make it easier to reason on a mobile device with limited resources, as they allow the reuse of previous inferences computed by another device without starting from scratch. This paper describes an extension of the fuzzy ontology reasoner fuzzyDL to make it the first serializable and incremental semantic reasoner. We empirically show that the size of the serialized files is smaller than in another serializable semantic reasoner (JFact), and that there is a significant decrease in the reasoning time.

Fuzzy Description Logics (DLs) are a formalism for the representation of structured knowledge affected by imprecision or vagueness. A key factor in the practical success of fuzzy DLs is the availability of highly implemented reasoners. This paper studies two optimisation techniques (ABox partitioning based on individual groups and optimisation problem partitioning) in the setting of the fuzzy ontology reasoner fuzzy DL. We study the applicability of these techniques in expressive fuzzy DL languages, proposing a new strategy, and perform an empirical evaluation proving that they are not helpful in practice so far.

Description Logics (DLs) are a family of logic-based Knowledge Representation (KR) formalisms, which are particularly suitable for representing incomplete yet precise structured knowledge. Several fuzzy extensions of DLs have been proposed in the KR field in order to handle imprecise knowledge whic h is particularly pervading in those domains where entities could be better described in natural language. Among the many approaches to fuzzification in DLs, a simple yet interesting one involves the use of fuzzy concrete domains. In this paper, we present a method for learning within the KR framework of fuzzy DLs. The method induces fuzzy DL inclusion axioms from any crisp DL knowledge base. Notably, the induced axioms may contain fuzzy concepts automatically generated from numerical concrete domains during the learning process. We discuss the results obtained on a popular learning problem in comparison with state-of-the-art DL learning algorithms, and on a test bed in order to evaluate the classification performance.

Fuzzy Description Logics (DLs) are logics that allow to deal with structured vague knowledge. Although a relatively important amount of work has been carried out in the last years concerning the use of fuzzy DLs as ontology languages, the problem of automatically managing the evolution of fuzzy ontologies has received very little attention so far. We describe here a logic-based computational method for the automated induction of fuzzy ontology axioms which follows the machine learning approach of Inductive Logic Programming. The potential usefulness of the method is illustrated by means of an example taken from the tourism application domain.

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

Ontologies have succeeded as a knowledge representation formalism in many domains of application. Nevertheless, they are not suitable to represent vague or imprecise information. To overcome this limitation, several extensions to classical ontologies based on fuzzy logic have been proposed. Even though different fuzzy logics lead to fuzzy ontologies with very different logical properties, the combined use of different fuzzy logics has received little attention to date. This paper proposes a fuzzy extension of the Description Logic [Formula: see text] — the logic behind the ontology language OWL 2 — that joins Gödel and Zadeh fuzzy logics. We analyze the properties of the new fuzzy Description Logic in order to provide guidelines to ontology developers to exploit the best features of each fuzzy logic. The proposal also considers degrees of truth belonging to a finite set of linguistic terms rather than numerical values, thus being closer to real experts' reasonings. We prove the decidability of the combined logic by presenting a reasoning preserving procedure to obtain a crisp representation for it. This result is generalized to offer a similar reduction that can be applied when any other finite t -norms, t -conorms, negations or implications are considered in the logic.

Fuzzy Description Logics (Fuzzy DLs) are logics that allow to deal with structured knowledge affected by fuzziness. Fuzzy DLs are at the heart of Fuzzy OWL 2, a fuzzy version of the standard ontology language OWL 2. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in other fields. In particular, the integration of aggregation operators (AOs) in fuzzy DLs has received little attention so far. In this work, we show how to support aggregation operators in fuzzy DLs. We provide syntax and semantics of a fuzzy DL extended with AOs, and provide a calculus for a family of AOs (weighted sum, OWA and quantifier-guided OWA). We also show how to encode them into our proposal for Fuzzy OWL 2.

Defeasible inheritance networks are a non-monotonic framework dealing with hierarchical knowledge. On the other hand, rational closure, a main representative of the preferential approach, is acknowledged as a landmark. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics, a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is build on top of the classical entailment relation.

Fuzzy ontologies extend classical ontologies to allow the representation of imprecise and vague knowledge. Although a relatively important amount of work has been carried out in the last years and they have been successfully used in several applications, several notions from fuzzy logic, such as fuzzy integrals, have not been considered yet in fuzzy ontologies. In this work, we show how to support fuzzy integrals in fuzzy ontologies. As a theoretical formalism, we provide the syntax and semantics of a fuzzy Description Logic with fuzzy integrals. We also provide a reasoning algorithm for a family of fuzzy integrals and show how to encode them into the language Fuzzy OWL 2.

We describe a generic framework for representing and reasoning with annotated Semantic Web data, formalise the annotated language, the corresponding deductive system, and address the query answering problem. We extend previous contributions on RDF annotations by providing a unified reasoning formalism and allowing the seamless combination of different annotation domains. We demonstrate the feasibility of our method by instantiating it on (i) temporal RDF; (ii) fuzzy RDF; (iii) and their combination. A prototype shows that implementing and combining new domains is easy and that RDF stores can easily be extended to our framework.

The need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing a procedure to represent such information within current Semantic Web languages. In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to represent fuzzy ontologies using OWL 2 annotation properties.

We outline SoftFacts, an ontology mediated top-k information retrieval system over relational databases. An ontology layer is used to define (in terms of a OWL-QL like Semantic Web language) the relevant abstract concepts and relations of the application domain, while graded facts are stored into a relational database. Queries are conjunctive queries with ranking aggregates and scoring functions and the results of a query may be ranked according to user defined scoring functions. We will illustrate SoftFacts' architecture, the representation and the query language, sketch the reasoning algorithms of the SoftFacts system and its Protégé plug-in.

Fuzzy Description Logics are logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in the fuzzy logic literature. In this work, we extend fuzzy DLs towards supporting fuzzy spatial reasoning and, thus, offer a framework for modeling spatial relations such as "region a is part of region b, which is connected to region c, a is close to c and b is right over c".

Fuzzy Description Logics (DLs) are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, little attention has been given to the role of datatypes in fuzzy DLs. This paper presents a fuzzy DL with three kinds of extended datatype restrictions, together with the necessary rules to reason with them.

Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. First, we overview and investigate the existence and computation of minimal fixed-points of multivalued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice. We show that a multivalued operator can be defined whose fixed-points are in one-to-one correspondence with the models of the logic program.

In this paper we present fuzzyDL, an expressive fuzzy description logic reasoner.We present its salient features, including some novel concept constructs and queries, and examples of use cases: matchmaking and fuzzy control.

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.

Fuzzy Description Logics (fuzzy DLs)have been proposed as a language to describe structured knowledge with vague concepts. It is well known that the choice of the fuzzy operators may determine some logical properties. However, up to date the study of fuzzy DLs has been restricted to the Łukasiewicz logic and the "Zadeh semantics". In this work, we propose a novel semantics combining the common product t-norm with the standard negation. We show some interesting properties of the logic and propose a reasoning algorithm based on a mixture of tableaux rules and the reduction to mixed Integer Quadratically Constrained Programming.

In this paper we address a novel issue for deductive databases with huge data repositories, namely the problem of evaluating ranked top-k queries. The problem occurs whenever we allow queries such as "find cheap hotels close to the conference location" in which fuzzy predicates like cheap and close occur. We show how to compute efficiently the top-k answers of conjunctive queries with fuzzy predicates.

It is generally accepted that knowledge based systems would be smarter if they could manage uncertainty and/or imprecision. In this paper we extend Description Logics, well-known logics for managing structured knowledge, allowing to express that a sentence is not just true or false, but true to some degree, which is taken from a certainty lattice.

Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis in the so-called Gelfond–Lifschitz transformation. The primary goal of this work is to present an alternative and epistemic-based characterization of stable model semantics, to the Gelfond-Lifschitz transformation. In particular, we show that stable model semantics can be defined entirely as an extension of the Kripke-Kleene semantics. Indeed, we show that the closed world assumption can be seen as an additional source of ‘falsehood’ to be added cumulatively to the Kripke-Kleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.

Schema matching is the problem of finding correspondences (mapping rules, e.g. logical formulae) between heterogeneous schemas. This paper presents a probabilistic framework, called sPLMap, for automatically learning schema mapping rules. Similar to LSD, different techniques, mostly from the IR field, are combined.Our approach, however, is also able to give a probabilistic interpretation of the prediction weights of the candidates, and to select the rule set with highest matching probability.

Research on multimedia information retrieval (MIR) has recently witnessed a booming interest. A prominent feature of this research trend is its simultaneous but independent materialization within several fields of computer science. The resulting richness of paradigms, methods and systems may, on the long run, result in a fragmentation of efforts and slow down progress. The primary goal of this study is to promote an integration of methods and techniques for MIR by contributing a conceptual model that encompasses in a unified and coherent perspective the many efforts that are being produced under the label of MIR. The model offers a retrieval capability that spans two media, text and images, but also several dimensions: form, content and structure. In this way, it reconciles similarity-based methods with semantics-based ones, providing the guidelines for the design of systems that are able to provide a generalized multimedia retrieval service, in which the existing forms of retrieval not only coexist, but can be combined in any desired manner. The model is formulated in terms of a fuzzy description logic, which plays a twofold role: (1) it directly models semantics-based retrieval, and (2) it offers an ideal framework for the integration of the multimedia and multidimensional aspects of retrieval mentioned above. The model also accounts for relevance feedback in both text and image retrieval, integrating known techniques for taking into account user judgments. The implementation of the model is addressed by presenting a decomposition technique that reduces query evaluation to the processing of simpler requests, each of which can be solved by means of widely known methods for text and image retrieval, and semantic processing. A prototype for multidimensional image retrieval is presented that shows this decomposition technique at work in a significant case.

Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e., set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval. In this paper we will present a fuzzy extension of ALC, combining Zadeh's fuzzy logic with a classical DL. In particular, concepts becomes fuzzy and, thus, reasoning about imprecise concepts is supported. We will define its syntax, its semantics, describe its properties and present a constraint propagation calculus for reasoning in it.

A Terminological Logic is presented as an information retrieval model, with a four-valued semantics that gives to its inference relation the avour of relevance, that is a strict connection in meaning between the premises and the conclusion of the arguments licensed by the logic. The logic also permits the expression of meta-knowledge enforcing a closed-world reading of the knowledge concerning specified individuals and primitive concepts. A Gentzen-style, sound and complete calculus for reasoning in the logic is given, thus establishing the basis for an information retrieval engine.

According to recent research, the task of Information Retrieval (IR) can successfully be described as the extraction, from a given document base, of those documents d that, given a query q, make the formula d -> q valid, where d and q are formulae of the chosen logic and ``->'' denotes the brand of logical implication formalized by the logic in question. In this paper, although essentially subscribing to this view, we propose that the logic to be chosen for this endeavour be a Terminological Logic (TL): according to this view the IR task becomes that of singling out those documents d such that q subs d, where d and q are terms} of the chosen TL and ``subs'' denotes subsumption between terms. We argue that TLs are particularly suitable for modelling IR; we do this by showing that they can successfully be employed in representing documents under a variety of aspects (e.g. structural, layout, content), in representing queries and in representing domain and lexical knowledge. The fact that a single logical language can be used for all these representational endeavours ensures that all these sources of knowledge will participate in the retrieval process in a principled way. In this paper we introduce MIRTL, a TL for modelling IR according to the above guidelines; its syntax, formal semantics and inferential algorithm are described.