Search

Knowledge Measures (KMs) aim at quantifying the amount of knowledge/information that a knowledge base carries. On the other hand, Belief Change (BC) is the process of changing beliefs (in our case, in terms of contraction, expansion and revision) taking into account a new piece of knowledge, which possibly may be in contradiction with the current belief. We propose a new quantitative BC framework that is based on KMs by defining belief change operators that try to minimise, from an information-theoretic point of view, the surprise that the changed belief carries. To this end, we introduce the principle of minimal surprise. In particular, our contributions are (i) a general information-theoretic approach to KMs for which [1] is a special case; (ii) KM-based BC operators that satisfy the so-called AGM postulates; and (iii) a characterisation of any BC operator that satisfies the AGM postulates as a KM-based BC operator, i.e., any BC operator satisfying the AGM postulates can be encoded within our quantitative BC framework. We also introduce quantitative measures that account for the information loss of contraction, information gain of expansion and information change of revision. We also give a succinct look into the problem of iterated revision, which deals with the application of a sequence of revision operations in our framework, and also illustrate how one may build from our KM-based contraction operator also one not satisfying the (in)famous recovery postulate, by focusing on the so-called severe withdrawal model as an illustrative example., Comment: 48 pages, 3 figures, preprint

OWL ontologies are a quite popular way to describe structured knowledge in terms of classes, relations among classes and class instances. In this paper, given a target class T of an OWL ontology, with a focus on ontologies with real- and boolean-valued data properties, we address the problem of learning graded fuzzy concept inclusion axioms with the aim of describing enough conditions for being an individual classified as instance of the class T. To do so, we present PN-OWL that is a two-stage learning algorithm made of a P-stage and an N-stage. Roughly, in the P-stage the algorithm tries to cover as many positive examples as possible (increase recall), without compromising too much precision, while in the N-stage, the algorithm tries to rule out as many false positives, covered by the P-stage, as possible. PN-OWL then aggregates the fuzzy inclusion axioms learnt at the P-stage and the N-stage by combining them via aggregation functions to allow for a final decision whether an individual is instance of T or not. We also illustrate its effectiveness by means of an experimentation. An interesting feature is that fuzzy datatypes are built automatically, the learnt fuzzy concept inclusions can be represented directly into Fuzzy OWL 2 and, thus, any Fuzzy OWL 2 reasoner can then be used to automatically determine/classify (and to which degree) whether an individual belongs to the target class T or not., Comment: arXiv admin note: substantial text overlap with arXiv:2008.05297

We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy closure properties associated to classical logics., Comment: 21 pages, 2 figures

The triple language RDFS is designed to represent and reason with \emph{positive} statements only (e.g."antipyretics are drugs"). In this paper we show how to extend RDFS to express and reason with various forms of negative statements under the Open World Assumption (OWA). To do so, we start from $\rho df$, a minimal, but significant RDFS fragment that covers all essential features of RDFS, and then extend it to $\rho df_\bot^\neg$, allowing express also statements such as "radio therapies are non drug treatments", "Ebola has no treatment", or "opioids and antipyretics are disjoint classes". The main and, to the best of our knowledge, unique features of our proposal are: (i) $\rho df_\bot^\neg$ remains syntactically a triple language by extending $\rho df$ with new symbols with specific semantics and there is no need to revert to the reification method to represent negative triples; (ii) the logic is defined in such a way that any RDFS reasoner/store may handle the new predicates as ordinary terms if it does not want to take account of the extra capabilities; (iii) despite negated statements, every $\rho df_\bot^\neg$ knowledge base is satisfiable; (iv) the $\rho df_\bot^\neg$ entailment decision procedure is obtained from $\rho df$ via additional inference rules favouring a potential implementation; and (v) deciding entailment in $\rho df_\bot^\neg$ ranges from P to NP.

Lehmann and Magidor's rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment for expressive DLs, such as SROIQ, providing a novel reasoning procedure that compiles a non-monotone DL knowledge base into a description logic program (dl-program).

OWL ontologies are nowadays a quite popular way to describe structured knowledge in terms of classes, relations among classes and class instances. In this paper, given a target class T of an OWL ontology, we address the problem of learning fuzzy concept inclusion axioms that describe sufficient conditions for being an individual instance of T. To do so, we present Fuzzy OWL-BOOST that relies on the Real AdaBoost boosting algorithm adapted to the (fuzzy) OWL case. We illustrate its effectiveness by means of an experimentation. An interesting feature is that the learned rules can be represented directly into Fuzzy OWL 2. As a consequence, any Fuzzy OWL 2 reasoner can then be used to automatically determine/classify (and to which degree) whether an individual belongs to the target class T.

In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the semantic web standard ontology language OWL 2, whose main ingredients are classes and roles. In this work, we show how to integrate RC within the triple language RDFS, which together with OWL2 are the two major standard semantic web ontology languages. To do so, we start from $\rho df$, which is the logic behind RDFS, and then extend it to $\rho df_\bot$, allowing to state that two entities are incompatible. Eventually, we propose defeasible $\rho df_\bot$ via a typical RC construction. The main features of our approach are: (i) unlike most other approaches that add an extra non-monotone rule layer on top of monotone RDFS, defeasible $\rho df_\bot$ remains syntactically a triple language and is a simple extension of $\rho df_\bot$ by introducing some new predicate symbols with specific semantics. In particular, any RDFS reasoner/store may handle them as ordinary terms if it does not want to take account for the extra semantics of the new predicate symbols; (ii) the defeasible $\rho df_\bot$ entailment decision procedure is build on top of the $\rho df_\bot$ entailment decision procedure, which in turn is an extension of the one for $\rho df$ via some additional inference rules favouring an potential implementation; and (iii) defeasible $\rho df_\bot$ entailment can be decided in polynomial time., Comment: 47 pages. Preprint version

The detection and representation of events is a critical element in automated surveillance systems. We present here an ontology for representing complex semantic events to assist video surveillance-based vandalism detection. The ontology contains the definition of a rich and articulated event vocabulary that is aimed at aiding forensic analysis to objectively identify and represent complex events. Our ontology has then been applied in the context of London Riots, which took place in 2011. We report also on the experiments conducted to support the classification of complex criminal events from video data.

We present the state of the art in representing and reasoning with fuzzy knowledge in Semantic Web Languages such as triple languages RDF/RDFS, conceptual languages of the OWL 2 family and rule languages. We further show how one may generalise them to so-called annotation domains, that cover also e.g. temporal and provenance extensions., Comment: This is an updated version of [291] and acts as accompanying material to my invited talk and slides at the 2018 Artificial Intelligence International Conference (A2IC-18)

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe $\mathcal{ELO}_\bot$, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe $\mathcal{ELO}_\bot$ under RC that relies entirely on a series of classical, monotonic $\mathcal{EL}_\bot$ subsumption tests. Therefore, any existing classical monotonic $\mathcal{EL}_\bot$ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.

We present a fuzzy version of description logics with concrete domains. Main features are: (i) concept constructors are based on t-norm, t-conorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are allowed; and (iv) the reasoning algorithm is based on a mixture of completion rules and bounded mixed integer programming., Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005)

Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic and, specifically, knowledge base satisfiability is an undecidable problem for Product Logic. We complete here the analysis by showing that knowledge base satisfiability is also an undecidable problem for Lukasiewicz Logic.

This volume contains the papers presented at the first edition of the Doctoral Consortium of the 5th International Symposium on Rules (RuleML 2011@IJCAI) held on July 19th, 2011 in Barcelona, as well as the poster session papers of the RuleML 2011@IJCAI main conference., Comment: HTML file with clickable links to papers

We describe a generic framework for representing and reasoning with annotated Semantic Web data, a task becoming more important with the recent increased amount of inconsistent and non-reliable meta-data on the web. We formalise the annotated language, the corresponding deductive system and address the query answering problem. Previous contributions on specific RDF annotation domains are encompassed by our unified reasoning formalism as we show by instantiating it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we provide a generic method for combining multiple annotation domains allowing to represent, e.g. temporally-annotated fuzzy RDF. Furthermore, we address the development of a query language -- AnQL -- that is inspired by SPARQL, including several features of SPARQL 1.1 (subqueries, aggregates, assignment, solution modifiers) along with the formal definitions of their semantics.

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 standard languages and tools. 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 also report on the prototypical implementations., Comment: v3: 32 pages, LaTeX; the new version includes a restriction in the syntax of weighted sum concepts, and changes the order of the paragraph "Notation". v2: 32 pages, LaTeX; the new version extends the previous one with fuzzy modified datatypes, which means changes in the syntax (Section 3.1), semantics (Section 3.2), and their representation using OWL 2 (Section 4.4)

In this paper we describe a novel a procedure to build a linear order from an arbitrary poset which (i) preserves the original ordering and (ii) allows to extend monotonic and antitonic mappings defined over the original poset to monotonic and antitonic mappings over the new linear poset.

Fuzzy Description Logics (DLs) are a family of logics which allow the representation of (and the reasoning with) structured knowledge affected by vagueness. Although most of the not very expressive crisp DLs, such as ALC, enjoy the Finite Model Property (FMP), this is not the case once we move into the fuzzy case. In this paper we show that if we allow arbitrary knowledge bases, then the fuzzy DLs ALC under Lukasiewicz and Product fuzzy logics do not verify the FMP even if we restrict to witnessed models; in other words, finite satisfiability and witnessed satisfiability are different for arbitrary knowledge bases. The aim of this paper is to point out the failure of FMP because it affects several algorithms published in the literature for reasoning under fuzzy ALC.

In fuzzy propositional logic, to a proposition a partial truth in [0,1] is assigned. It is well known that under certain circumstances, fuzzy logic collapses to classical logic. In this paper, we will show that under dual conditions, fuzzy logic collapses to four-valued (relevance) logic, where propositions have truth-value true, false, unknown, or contradiction. As a consequence, fuzzy entailment may be considered as ``in between'' four-valued (relevance) entailment and classical entailment.