The ontology of biological sequences.

BACKGROUND: Biological sequences play a major role in molecular and computational biology. They are studied as information-bearing entities that make up DNA, RNA or proteins. The Sequence Ontology, which is part of the OBO Foundry, contains descriptions and definitions of sequences and their properties. Yet the most basic question about sequences remains unanswered: what kind of entity is a biological sequence? An answer to this question benefits formal ontologies that use the notion of biological sequences and analyses in computational biology alike. RESULTS: We provide both an ontological analysis of biological sequences and a formal representation that can be used in knowledge-based applications and other ontologies. We distinguish three distinct kinds of entities that can be referred to as "biological sequence": chains of molecules, syntactic representations such as those in biological databases, and the abstract information-bearing entities. For use in knowledge-based applications and inclusion in biomedical ontologies, we implemented the developed axiom system for use in automated theorem proving. CONCLUSION: Axioms are necessary to achieve the main goal of ontologies: to formally specify the meaning of terms used within a domain. The axiom system for the ontology of biological sequences is the first elaborate axiom system for an OBO Foundry ontology and can serve as starting point for the development of more formal ontologies and ultimately of knowledge-based applications

Formal Qualitative Spatial Augmentation of the Simple Feature Access Model

The need to share and integrate heterogeneous geospatial data has resulted in the development of geospatial data standards such as the OGC/ISO standard Simple Feature Access (SFA), that standardize operations and simple topological and mereotopological relations over various geometric features such as points, line segments, polylines, polygons, and polyhedral surfaces. While SFA\u27s supplied relations enable qualitative querying over the geometric features, the relations\u27 semantics are not formalized. This lack of formalization prevents further automated reasoning - apart from simple querying - with the geometric data, either in isolation or in conjunction with external purely qualitative information as one might extract from textual sources, such as social media. To enable joint qualitative reasoning over geometric and qualitative spatial information, this work formalizes the semantics of SFA\u27s geometric features and mereotopological relations by defining or restricting them in terms of the spatial entity types and relations provided by CODIB, a first-order logical theory from an existing logical formalization of multidimensional qualitative space

Analysing top-level and domain ontology alignments from matching systems

Top-level ontologies play an important role in the construction and integration of domain ontologies, providing a well-founded reference model that can be shared across knowledge domains. While most efforts in ontology matching have been particularly dedicated to domain ontologies, the problem of matching domain and top-level ontologies has been addressed to a lesser extent. This is a challenging task, specially due to the different levels of abstraction of these ontologies. In this paper, we present a comprehensive analysis of the alignments between one domain ontology from the OAEI Conference track and three well known top-level ontologies (DOLCE, GFO and SUMO), as generated by a set of matching tools. A discussion of the problem is presented on the basis of the alignments generated by the tools, compared to the analysis of three evaluators. This study provides insights for improving matching tools to better deal with this particular task

Improving Model Finding for Integrated Quantitative-qualitative Spatial Reasoning With First-order Logic Ontologies

Many spatial standards are developed to harmonize the semantics and specifications of GIS data and for sophisticated reasoning. All these standards include some types of simple and complex geometric features, and some of them incorporate simple mereotopological relations. But the relations as used in these standards, only allow the extraction of qualitative information from geometric data and lack formal semantics that link geometric representations with mereotopological or other qualitative relations. This impedes integrated reasoning over qualitative data obtained from geometric sources and “native” topological information – for example as provided from textual sources where precise locations or spatial extents are unknown or unknowable. To address this issue, the first contribution in this dissertation is a first-order logical ontology that treats geometric features (e.g. polylines, polygons) and relations between them as specializations of more general types of features (e.g. any kind of 2D or 1D features) and mereotopological relations between them. Key to this endeavor is the use of a multidimensional theory of space wherein, unlike traditional logical theories of mereotopology (like RCC), spatial entities of different dimensions can co-exist and be related. However terminating or tractable reasoning with such an expressive ontology and potentially large amounts of data is a challenging AI problem. Model finding tools used to verify FOL ontologies with data usually employ a SAT solver to determine the satisfiability of the propositional instantiations (SAT problems) of the ontology. These solvers often experience scalability issues with increasing number of objects and size and complexity of the ontology, limiting its use to ontologies with small signatures and building small models with less than 20 objects. To investigate how an ontology influences the size of its SAT translation and consequently the model finder’s performance, we develop a formalization of FOL ontologies with data. We theoretically identify parameters of an ontology that significantly contribute to the dramatic growth in size of the SAT problem. The search space of the SAT problem is exponential in the signature of the ontology (the number of predicates in the axiomatization and any additional predicates from skolemization) and the number of distinct objects in the model. Axiomatizations that contain many definitions lead to large number of SAT propositional clauses. This is from the conversion of biconditionals to clausal form. We therefore postulate that optional definitions are ideal sentences that can be eliminated from an ontology to boost model finder’s performance. We then formalize optional definition elimination (ODE) as an FOL ontology preprocessing step and test the simplification on a set of spatial benchmark problems to generate smaller SAT problems (with fewer clauses and variables) without changing the satisfiability and semantic meaning of the problem. We experimentally demonstrate that the reduction in SAT problem size also leads to improved model finding with state-of-the-art model finders, with speedups of 10-99%. Altogether, this dissertation improves spatial reasoning capabilities using FOL ontologies – in terms of a formal framework for integrated qualitative-geometric reasoning, and specific ontology preprocessing steps that can be built into automated reasoners to achieve better speedups in model finding times, and scalability with moderately-sized datasets

Robustly Efficient Equilibria in Non-Convex Economies

An economy has a robustly efficient marginal cost pricing equilibrium (mcpe) if it has an mcpe that is Pareto efficient and if this property is preserved under small variations in preferences endowments and technologies. We consider economies in which there is a finite number of equilibria, each of which varies continuously with preferences and endowments. We prove that there exist no robustly efficient marginal cost pricing equilibria

Robustly Efficient Equilibria in Non-Convex Economies

An economy has a robustly efficient marginal cost pricing equilibrium (mcpe) if it has an mcpe that is Pareto efficient and if this property is preserved under small variations in preferences endowments and technologies. We consider economies in which there is a finite number of equilibria, each of which varies continuously with preferences and endowments. We prove that there exist no robustly efficient marginal cost pricing equilibria

Ontology patterns for the representation of quality changes of cells in time

Background: Cell tracking experiments, based on time-lapse microscopy, have become an important tool in biomedical research. The goal is the reconstruction of cell migration patterns, shape and state changes, and, comprehensive genealogical information from these data. This information can be used to develop process models of cellular dynamics. However, so far there has been no structured, standardized way of annotating and storing the tracking results, which is critical for comparative analysis and data integration. The key requirement to be satisfied by an ontology is the representation of a cell’s change over time. Unfortunately, popular ontology languages, such as Web Ontology Language (OWL), have limitations for the representation of temporal information. The current paper addresses the fundamental problem of modeling changes of qualities over time in biomedical ontologies specified in OWL. Results: The presented analysis is a result of the lessons learned during the development of an ontology, intended for the annotation of cell tracking experiments. We present, discuss and evaluate various representation patterns for specifying cell changes in time. In particular, we discuss two patterns of temporally changing information: n-ary relation reification and 4d fluents.These representation schemes are formalized within the ontology language OWL and are aimed at the support for annotation of cell tracking experiments. We analyze the performance of each pattern with respect to standard criteria used in software engineering and data modeling, i.e. simplicity, scalability, extensibility and adequacy. We further discuss benefits, drawbacks, and the underlying design choices of each approach. Conclusions: We demonstrate that patterns perform differently depending on the temporal distribution of modeled information. The optimal model can be constructed by combining two competitive approaches. Thus, we demonstrate that both reification and 4d fluents patterns can work hand in hand in a single ontology. Additionally, we have found that 4d fluents can be reconstructed by two patterns well known in the computer science community, i.e. state modeling and actor-role pattern