Categories of First-Order Quantifiers

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k \u3e 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility

A Response to Michelle Voss Roberts\u27 Dualities

Dualities is a serious contribution to Hindu-Christian studies, bringing fresh and challenging materials before us. It wonderfully brings together reflection on feminist concerns, attention to the metaphors by which we identify and organize natural and social realities, and critical attention to how linguistic and ontological categories, such as dualities and dualism, fluidity and fluidities, have effects of ethical and spiritual import

Mary Shelley’s Frankenstein, the Guillotine, and Modern Ontological Anxiety

Lacefield’s interdisciplinary analysis analyzes motifs of decapitation/dismemberment in Frankenstein and then moves into a discussion of the novel’s exploration of the ontological categories specified above. For example, Frankenstein’s Creature, as a kind of cyborg, exists on the contested theoretical “slice” within a number of antinomies: nature/tech, human/inhuman (alive/dead), matter/spirit, etc. These are interesting juxtapositions that point to tensions within each set of categories, and Lacefield discusses the relevance of such dichotomies for questions of modernity posed by materialist theory and technological innovation. Additionally, she incorporates a discussion of films that fuse Shelley’s themes with appeals to twentieth-century and post-millennium audiences

Defining ontological categories in an expansion of belief dynamics

There have been attempts to get some logic out of belief dynamics, i.e. attempts to define the constants of propositional logic in terms of functions from sets of beliefs to sets of beliefs. 1 It would be interesting to see whether something similar could be done for ontological categories, i.e. ontological constants. The theory presented here will be a (modest) expansion of belief dynamics: it will not only incorporate beliefs, but also parts of beliefs, so called belief fragments. On the basis of this we will give a belief-dynamical account of the ontological categories of states of affairs, individuals, properties of arbitrary adicities and properties of arbitrary orders

Recientes avances en metafísica: Categorías ontológicas y esquemas categoriales

[ES] Desde una perspectiva ontológica tradicional, y con la declarada intención de alejarse del relativismo contemporáneo, el presente escrito busca establecer algunos principios básicos para mantener la posición de la metafísica como el estudio sistemático de la realidad como un todo, y de la ontología como la ciencia del ser, sustentada en una teoría de categorías. Estas categorías están diferenciadas por las características distintivas de existencia e identidad de sus respectivos miembros, tomándose como «categorías ontológicas fundamentales» aquellas en donde sus miembros tienen condiciones para estas características de existencia e identidad que no sean especificables en una forma exhaustiva, en términos de dependencia ontológica, entre esos miembros y los miembros de otras categorías ontológicas. Este escrito hace entonces una revisión de las diferentes teorías de categorías ontológicas, y sus respectivas interpretaciones de cuántas y cuáles categorías deben ser reconocidas. [EN] From a traditional ontological perspective, and with the declared intention to move away from contemporary relativism, this paper aims to establish some basic principles to maintain the position of Metaphysics as the systematic study of reality as a whole, and Ontology as the science of being, based on a theory of categories. These categories are differentiated by the distinctive features of existence and identity of their respective members, taking as «fundamental ontological categories» those where its members have conditions for these characteristics of existence and identity that are not exhaustively specifiable, in terms of ontological dependence, between those members and members of other ontological categories. This paper then makes a revision of the different theories of ontological categories, and their respective interpretations of how many and which categories should be recognized

Enabling Representation Learning in Ontology-Driven Conceptual Modeling Using Graph Neural Networks

Conceptual Models (CMs) are essential for information systems engineering since they provide explicit and detailed representations of the subject domains at hand. Ontology-driven conceptual modeling (ODCM) languages provide primitives for articulating these domain notions based on the ontological categories put forth by upper-level (or foundational) ontologies. Many existing CMs have been created using ontologically-neutral languages (e.g., UML, ER). Connecting these models to ontological categories would provide better support for meaning negotiation, semantic interoperability, and complexity management. However, given the sheer size of this legacy base, manual stereotyping is a prohibitive task. This paper addresses this problem by proposing an approach based on Graph Neural Networks towards automating the task of stereotyping UML class diagrams with the meta-classes offered by the ODCM language OntoUML. Since these meta-classes (stereotypes) represent ontological distinctions put forth by a foundational ontology, this task is equivalent to ontological category prediction for these classes. To enable this approach, we propose a strategy for representing CM vector embeddings that preserve the model elements’ structure and ontological categorization. Finally, we present an evaluation that shows convincing learning of OntoUML model node embeddings used for OntoUML stereotype prediction.</p

Seeking evidence for the role of ontological assumptions in the thinking of managers and professionals

Shingo's (1988) seminal innovation in the theory of production management can be seen as a re-conceptualization of production as flow rather than transformation (Koskela 1992). These alternatives can in turn be regarded as reflections of opposing ontological positions which have dominated Western philosophy, holding respectively that reality is constituted of either temporal process, or atemporal substance (Roochnik 2004). Koskela & Kagioglou (2005) suggest that lean production philosophy is based in a process ontology, radically different from the atemporal metaphysics underlying conventional methods and theories. Chi (1992) has argued that the disjunction between ontological categories such as 'substance' and 'process' can constitute a particularly acute barrier to understanding. Studies such as Itza-Ortiz, Rebello & Zollman (2003) have demonstrated the possibility of specifying and classifying learners' mental models as an aid to learning. We examine procedures typically adopted in Quantity Surveying, Structural Engineering Design and Project Planning, in order to specify the mental models involved. We find evidence of an underlying substance ontology. Methods of measurement used in Quantity Surveying are designed to account for physical, rather than temporal properties. In design, the emphasis is on representing the properties of the finished structure, rather than the processes by which it is constructed. More subtly, the temporal dimensions of the construction process are represented in project planning as 'lumps' of time, thus ignoring important facets of their nature as events. We conclude that attention to the role of ontological categories in industry thinking will facilitate the teaching of process oriented approaches to construction project management

Ontology with Human Subjects Testing: An Empirical Investigation of Geographic Categories

Ontology, since Aristotle, has been conceived as a sort of highly general physics, a science of the types of entities in reality, of the objects, properties, categories and relations which make up the world. At the same time ontology has been for some two thousand years a speculative enterprise. It has rested methodologically on introspection and on the construction and analysis of elaborate world-models and of abstract formal-ontological theories. In the work of Quine and others this ontological theorizing in abstract fashion about the world was supplemented by the study, based on the use of logical methods, of the ontological commitments or presuppositions embodied in scientific theories. In recent years both types of ontological study have found application in the world of information systems, for example in the construction of frameworks for knowledge representation and in database design and translation. As ontology is in this way drawn closer to the domain of real-world applications, the question arises as to whether it is possible to use empirical methods in studying ontological theories. More specifically: can we use empirical methods to test the ontological theories embodied in human cognition? We set forth the outlines of a framework for the formulation and testing of such theories as they relate to the specific domain of geographic objects and categories

The bearable lightness of being

How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories-such as object, property, and relation-are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical form: for example, the question whether there are numbers is the question whether there are true atomic statements in which expressions function as singular terms which, if they have reference at all, stand for numbers, and the question whether there are properties of a given type is a question about whether there are meaningful predicates of an appropriate degree and level. This approach is defended against the objection that it must be wrong because makes what there depend on us or our language. Some problems confronting the Fregean approach-including Frege's notorious paradox of the concept horse-are addressed. It is argued that the approach results in a modest and sober deflationary understanding of ontological commitments

Ontological foundations for structural conceptual models

In this thesis, we aim at contributing to the theory of conceptual modeling and ontology representation. Our main objective here is to provide ontological foundations for the most fundamental concepts in conceptual modeling. These foundations comprise a number of ontological theories, which are built on established work on philosophical ontology, cognitive psychology, philosophy of language and linguistics. Together these theories amount to a system of categories and formal relations known as a foundational ontolog