Who Cares about Axiomatization? Representation, Invariance, and Formal Ontologies

The philosophy of science of Patrick Suppes is centered on two important notions that are part of the title of his recent book (Suppes 2002): Representation and Invariance. Representation is important because when we embrace a theory we implicitly choose a way to represent the phenomenon we are studying. Invariance is important because, since invariants are the only things that are constant in a theory, in a way they give the “objective” meaning of that theory. Every scientific theory gives a representation of a class of structures and studies the invariant properties holding in that class of structures. In Suppes’ view, the best way to define this class of structures is via axiomatization. This is because a class of structures is given by a definition, and this same definition establishes which are the properties that a single structure must possess in order to belong to the class. These properties correspond to the axioms of a logical theory. In Suppes’ view, the best way to characterize a scientific structure is by giving a representation theorem for its models and singling out the invariants in the structure. Thus, we can say that the philosophy of science of Patrick Suppes consists in the application of the axiomatic method to scientific disciplines. What I want to argue in this paper is that this application of the axiomatic method is also at the basis of a new approach that is being increasingly applied to the study of computer science and information systems, namely the approach of formal ontologies. The main task of an ontology is that of making explicit the conceptual structure underlying a certain domain. By “making explicit the conceptual structure” we mean singling out the most basic entities populating the domain and writing axioms expressing the main properties of these primitives and the relations holding among them. So, in both cases, the axiomatization is the main tool used to characterize the object of inquiry, being this object scientific theories (in Suppes’ approach), or information systems (for formal ontologies). In the following section I will present the view of Patrick Suppes on the philosophy of science and the axiomatic method, in section 3 I will survey the theoretical issues underlying the work that is being done in formal ontologies and in section 4 I will draw a comparison of these two approaches and explore similarities and differences between them

Editorial: Formal Ontologies meet Industry

The Formal Ontologies meet Industry (FOMI) workshop series is a scientific initiative supported by the International Association for Ontology and its Applications (IAOA) aimed at bringing together academics and practitioners interested in ontologies for industry. FOMI addresses research and application topics concerning, e.g., the design of domain-specific ontologies, the development of ontology-based information systems, or the investigation of the theoretical underpinnings of formal ontology when tuned to engineering applications

Using cross-lingual information to cope with underspecification in formal ontologies

Description logics and other formal devices are frequently used as means for preventing or detecting mistakes in ontologies. Some of these devices are also capable of inferring the existence of inter-concept relationships that have not been explicitly entered into an ontology. A prerequisite, however, is that this information can be derived from those formal definitions of concepts and relationships which are included within the ontology. In this paper, we present a novel algorithm that is able to suggest relationships among existing concepts in a formal ontology that are not derivable from such formal definitions. The algorithm exploits cross-lingual information that is implicitly present in the collection of terms used in various languages to denote the concepts and relationships at issue. By using a specific experimental design, we are able to quantify the impact of cross-lingual information in coping with underspecification in formal ontologies

Probabilistic latent semantic analysis as a potential method for integrating spatial data concepts

In this paper we explore the use of Probabilistic Latent Semantic Analysis (PLSA) as a method for quantifying semantic differences between land cover classes. The results are promising, revealing ‘hidden’ or not easily discernible data concepts. PLSA provides a ‘bottom up’ approach to interoperability problems for users in the face of ‘top down’ solutions provided by formal ontologies. We note the potential for a meta-problem of how to interpret the concepts and the need for further research to reconcile the top-down and bottom-up approaches

Lexically-based Ontologies and Ontologically Based Lexicons

This paper deals with the relations between ontologies and lexicons. We study the role of these two components and their evolution during the last years in the field of Computational Linguistics. Subsequently, we survey the current lines of research at ILC-CNR which tackle this topic. They involve (I) the reuse of already existing Lexical Resources to derive formal ontologies, (II) the conversion and combination of terminologies into rich and formal Lexical Resources and (III) the use of formal ontologies as the backbone of multilingual Lexical Resources

Ontologies, Mental Disorders and Prototypes

As it emerged from philosophical analyses and cognitive research, most concepts exhibit typicality effects, and resist to the efforts of defining them in terms of necessary and sufficient conditions. This holds also in the case of many medical concepts. This is a problem for the design of computer science ontologies, since knowledge representation formalisms commonly adopted in this field do not allow for the representation of concepts in terms of typical traits. However, the need of representing concepts in terms of typical traits concerns almost every domain of real world knowledge, including medical domains. In particular, in this article we take into account the domain of mental disorders, starting from the DSM-5 descriptions of some specific mental disorders. On this respect, we favor a hybrid approach to the representation of psychiatric concepts, in which ontology oriented formalisms are combined to a geometric representation of knowledge based on conceptual spaces

Non classical concept representation and reasoning in formal ontologies

Formal ontologies are nowadays widely considered a standard tool for knowledge representation and reasoning in the Semantic Web. In this context, they are expected to play an important role in helping automated processes to access information. Namely: they are expected to provide a formal structure able to explicate the relationships between different concepts/terms, thus allowing intelligent agents to interpret, correctly, the semantics of the web resources improving the performances of the search technologies. Here we take into account a problem regarding Knowledge Representation in general, and ontology based representations in particular; namely: the fact that knowledge modeling seems to be constrained between conflicting requirements, such as compositionality, on the one hand and the need to represent prototypical information on the other. In particular, most common sense concepts seem not to be captured by the stringent semantics expressed by such formalisms as, for example, Description Logics (which are the formalisms on which the ontology languages have been built). The aim of this work is to analyse this problem, suggesting a possible solution suitable for formal ontologies and semantic web representations. The questions guiding this research, in fact, have been: is it possible to provide a formal representational framework which, for the same concept, combines both the classical modelling view (accounting for compositional information) and defeasible, prototypical knowledge ? Is it possible to propose a modelling architecture able to provide different type of reasoning (e.g. classical deductive reasoning for the compositional component and a non monotonic reasoning for the prototypical one)? We suggest a possible answer to these questions proposing a modelling framework able to represent, within the semantic web languages, a multilevel representation of conceptual information, integrating both classical and non classical (typicality based) information. Within this framework we hypothesise, at least in principle, the coexistence of multiple reasoning processes involving the different levels of representation

Extending the Foundational Model of Anatomy with Automatically Acquired Spatial Relations

Formal ontologies have made significant impact in bioscience over the last ten years. Among them, the Foundational Model of Anatomy Ontology (FMA) is the most comprehensive model for the spatio-structural representation of human anatomy. In the research project MEDICO we use the FMA as our main source of background knowledge about human anatomy. Our ultimate goals are to use spatial knowledge from the FMA (1) to improve automatic parsing algorithms for 3D volume data sets generated by Computed Tomography and Magnetic Resonance Imaging and (2) to generate semantic annotations using the concepts from the FMA to allow semantic search on medical image repositories. We argue that in this context more spatial relation instances are needed than those currently available in the FMA. In this publication we present a technique for the automatic inductive acquisition of spatial relation instances by generalizing from expert-annotated volume datasets

Strengths and Limitations of Formal Ontologies in the Biomedical Domain

We propose a typology of representational artifacts for health care and life sciences domains and associate this typology with different kinds of formal ontology and logic, drawing conclusions as to the strengths and limitations for ontology in a description logics framework. The four types of domain representation we consider are: (i) lexico-semantic representation, (ii) representation of types of entities, (iii) representations of background knowledge, and (iv) representation of individuals. We advocate a clear distinction of the four kinds of representation in order to provide a more rational basis for using ontologies and related artifacts to advance integration of data and enhance interoperability of associated reasoning systems. We highlight the fact that only a minor portion of scientifically relevant facts in a domain such as biomedicine can be adequately represented by formal ontologies as long as the latter are conceived as representations of entity types. In particular, the attempt to encode default or probabilistic knowledge using ontologies so conceived is prone to produce unintended, erroneous models