Basic conceptual structures theory

Although the theory of Conceptual Structures is over 10 years old, basic notions (like canonical graphs) are far from settled and are subject to constant extensions and reformulations. However, most of these are done in an informal way, which doesn't help in clarifying the issues involved. It is our hope that this paper will provide a first step towards the complete and rigorous account of Conceptual Structures (CS) Theory, which is needed for ongoing standardization and implementation efforts. Towards that goal, we present formal definitions of some of the central notions of CS theory (type, referent, concept, relation, conceptual graph, canonical formation rules, canon, and canonical graph) in its simplest form, i.e. no contexts nor coreference links are allowed and referents must be individuals. We thereby introduce higher-order types in order to enable the use of conceptual graphs at the metalevel, the restriction operation of the canonical formation rules is extended to make use of the relation hierarchy, we show the relationship between denotation and conformity relation, and we give a rigorous meaning to the canonical basis, among other things

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

Quantum Particles as Conceptual Entities: A Possible Explanatory Framework for Quantum Theory

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses, ..., in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of 'the one and the many' in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrodinger's Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter.Comment: 45 pages, 10 figure

Vox et Silentium Dei: A Socio-Cognitive Linguistic Theory of Religious Violence

Contemporary research in the study of language and cognition frequently characterizes religious metaphors as either monoliths of experience or stable synchronic structures, if not both. In addition, by virtue of how the foundational theory of this paper, Conceptual Metaphor Theory, has been situated in the literature, pre-modern theist writing on figurative language has been largely ignored. This has resulted in a general application of Conceptual Metaphor Theory to religious language which characterizes religious experience as phenomenologically invalid with the contingent effect of contradicting the basic experiential nature of metaphor. Here, I account for these principal theoretical discrepancies through an exploration of the qualities and varieties of religious metaphor, culminating in a proposed amendment to Conceptual Metaphor Theory. In the latter portion of my thesis, I apply the amended theory to the journal of the American missionary John Allen Chau to demonstrate its theoretical efficacy in relation to an analysis of sovereignty metaphors within Chau’s evangelical ideology

Cross-cultural evidence of value structures and priorities in childhood

We broaden the developmental focus of the theory of universals in basic human values (Schwartz, 1992) by presenting supportive evidence on children’s values from six countries: Germany, Italy, Poland, Bulgaria, the USA, and New Zealand. 3,088 7-11-year-old children completed the Picture-Based Value Survey for Children (PBVS-C, Döring et al., 2010). Grade 5 children also completed the Portrait Values Questionnaire (PVQ, Schwartz, 2003). Findings reveal that the broad value structures, sex-differences in value priorities, and pan-cultural value hierarchies typical of adults have already taken form at this early age. We discuss the conceptual implications of these findings for the new field of children’s basic values by embedding them in the recent developmental literature

The Computability-Theoretic Content of Emergence

In dealing with emergent phenomena, a common task is to identify useful descriptions of them in terms of the underlying atomic processes, and to extract enough computational content from these descriptions to enable predictions to be made. Generally, the underlying atomic processes are quite well understood, and (with important exceptions) captured by mathematics from which it is relatively easy to extract algorithmic con- tent. A widespread view is that the difficulty in describing transitions from algorithmic activity to the emergence associated with chaotic situations is a simple case of complexity outstripping computational resources and human ingenuity. Or, on the other hand, that phenomena transcending the standard Turing model of computation, if they exist, must necessarily lie outside the domain of classical computability theory. In this article we suggest that much of the current confusion arises from conceptual gaps and the lack of a suitably fundamental model within which to situate emergence. We examine the potential for placing emer- gent relations in a familiar context based on Turing's 1939 model for interactive computation over structures described in terms of reals. The explanatory power of this model is explored, formalising informal descrip- tions in terms of mathematical definability and invariance, and relating a range of basic scientific puzzles to results and intractable problems in computability theory