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.

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.

Conditionals are generally considered the backbone of human (and AI) reasoning: the "if-then" connection between two propositions is the stepping stone of arguments and a lot of the research effort in formal logic has focused on this kind of connection. A conditional connection satisfies different properties according to the kind of arguments it is used for. The classical material implication is appropriate for modelling the "ifthen" connection as it is used in Mathematics, but the equivalence between the material implication A B and A B is not appropriate for many other contexts.

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.

In the context of vandalism and terrorist activities, video surveillance forms an integral part of any incident investigation and, thus, there is a critical need for developing an "automated video surveillance system" with the capability of detecting complex events to aid the forensic investigators in solving the criminal cases. As an example, in the aftermath of the London riots in August 2011 police had to scour through more than 200,000 hours of CCTV videos to identify suspects. Around 5,000 offenders were found by trawling through the footage, after a process that took more than five months. With the aim to develop an open and expandable video analysis framework equipped with tools for analysing, recognising, extracting and classifying events in video, which can be used for searching during investigations with unpredictable characteristics, or exploring normative (or abnormal) behaviours, several efforts for standardising event representation from surveillance footage have been made [9, 10, 11, 22, 23, 28, 30, 37]. While various approaches have relied on offering foundational support for the domain ontology extension, to the best of our knowledge, a systematic ontology for standardising the event vocabulary for forensic analysis and an application of it has not been presented in the literature so far. In this paper, we present an OWL 2 [25] ontology for the semantic retrieval of complex events to aid video surveillance-based vandalism detection.

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.

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.

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.