Cognitive context and arguments from ontologies for learning

The deployment of learning resources on the web by different experts has resulted in the accessibility of multiple viewpoints about the same topics. In this work we assume that learning resources are underpinned by ontologies. Different formalizations of domains may result from different contexts, different use of terminology, incomplete knowledge or conflicting knowledge. We define the notion of cognitive learning context which describes the cognitive context of an agent who refers to multiple and possibly inconsistent ontologies to determine the truth of a proposition. In particular we describe the cognitive states of ambiguity and inconsistency resulting from incomplete and conflicting ontologies respectively. Conflicts between ontologies can be identified through the derivation of conflicting arguments about a particular point of view. Arguments can be used to detect inconsistencies between ontologies. They can also be used in a dialogue between a human learner and a software tutor in order to enable the learner to justify her views and detect inconsistencies between her beliefs and the tutor’s own. Two types of arguments are discussed, namely: arguments inferred directly from taxonomic relations between concepts, and arguments about the necessary an

Towards ontology interoperability through conceptual groundings

Abstract. The widespread use of ontologies raises the need to resolve heterogeneities between distinct conceptualisations in order to support interoperability. The aim of ontology mapping is, to establish formal relations between a set of knowledge entities which represent the same or a similar meaning in distinct ontologies. Whereas the symbolic approach of established SW representation standards – based on first-order logic and syllogistic reasoning – does not implicitly represent similarity relationships, the ontology mapping task strongly relies on identifying semantic similarities. However, while concept representations across distinct ontologies hardly equal another, manually or even semi-automatically identifying similarity relationships is costly. Conceptual Spaces (CS) enable the representation of concepts as vector spaces which implicitly carry similarity information. But CS provide neither an implicit representational mechanism nor a means to represent arbitrary relations between concepts or instances. In order to overcome these issues, we propose a hybrid knowledge representation approach which extends first-order logic ontologies with a conceptual grounding through a set of CS-based representations. Consequently, semantic similarity between instances – represented as members in CS – is indicated by means of distance metrics. Hence, automatic similarity-detection between instances across distinct ontologies is supported in order to facilitate ontology mapping

Institutionalising Ontology-Based Semantic Integration

We address what is still a scarcity of general mathematical foundations for ontology-based semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the first-order ontology-based approach to semantic integration and a formalisation of ontological commitment, we propose a general theory that uses a syntax-and interpretation-independent formulation of language, ontology, and ontological commitment in terms of institutions. We claim that our formalisation generalises the intuitive notion of ontology-based semantic integration while retaining its basic insight, and we apply it for eliciting and hence comparing various increasingly complex notions of semantic integration and ontological commitment based on differing understandings of semantics

A Pragmatic Interpretation of Quantum Logic

Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be interpreted as a pragmatic language of assertive formulas which formalize statements about physical systems that are empirically justified or unjustified in the framework of quantum mechanics. According to this interpretation, QL formalizes properties of the metalinguistic notion of empirical justification within quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic. By the way, some elucidations of the standard notion of quantum truth are also obtained. Key words: pragmatics, quantum logic, quantum mechanics, justifiability, global pluralism.Comment: Third version: 20 pages. Sects. 1, 2, and 4 rewritten and improved. Explanations adde

Counting Incompossibles

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all

Expressing the tacit knowledge of a digital library system as linked data

Library organizations have enthusiastically undertaken semantic web initiatives and in particular the data publishing as linked data. Nevertheless, different surveys report the experimental nature of initiatives and the consumer difficulty in re-using data. These barriers are a hindrance for using linked datasets, as an infrastructure that enhances the library and related information services. This paper presents an approach for encoding, as a Linked Vocabulary, the "tacit" knowledge of the information system that manages the data source. The objective is the improvement of the interpretation process of the linked data meaning of published datasets. We analyzed a digital library system, as a case study, for prototyping the "semantic data management" method, where data and its knowledge are natively managed, taking into account the linked data pillars. The ultimate objective of the semantic data management is to curate the correct consumers' interpretation of data, and to facilitate the proper re-use. The prototype defines the ontological entities representing the knowledge, of the digital library system, that is not stored in the data source, nor in the existing ontologies related to the system's semantics. Thus we present the local ontology and its matching with existing ontologies, Preservation Metadata Implementation Strategies (PREMIS) and Metadata Objects Description Schema (MODS), and we discuss linked data triples prototyped from the legacy relational database, by using the local ontology. We show how the semantic data management, can deal with the inconsistency of system data, and we conclude that a specific change in the system developer mindset, it is necessary for extracting and "codifying" the tacit knowledge, which is necessary to improve the data interpretation process

Exploiting conceptual spaces for ontology integration

The widespread use of ontologies raises the need to integrate distinct conceptualisations. Whereas the symbolic approach of established representation standards – based on first-order logic (FOL) and syllogistic reasoning – does not implicitly represent semantic similarities, ontology mapping addresses this problem by aiming at establishing formal relations between a set of knowledge entities which represent the same or a similar meaning in distinct ontologies. However, manually or semi-automatically identifying similarity relationships is costly. Hence, we argue, that representational facilities are required which enable to implicitly represent similarities. Whereas Conceptual Spaces (CS) address similarity computation through the representation of concepts as vector spaces, CS rovide neither an implicit representational mechanism nor a means to represent arbitrary relations between concepts or instances. In order to overcome these issues, we propose a hybrid knowledge representation approach which extends FOL-based ontologies with a conceptual grounding through a set of CS-based representations. Consequently, semantic similarity between instances – represented as members in CS – is indicated by means of distance metrics. Hence, automatic similarity detection across distinct ontologies is supported in order to facilitate ontology integration

OntoMathPROOntoMath^{PRO} Ontology: A Linked Data Hub for Mathematics

In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.Comment: 15 pages, 6 images, 1 table, Knowledge Engineering and the Semantic Web - 5th International Conferenc