Quantum Gravity as Topological Quantum Field Theory

The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.Comment: 23 pages, amstex, JMP special issue (deadline permitting). (Text not changed

Qualitative modelling and analysis of regulations in multi-cellular systems using Petri nets and topological collections

In this paper, we aim at modelling and analyzing the regulation processes in multi-cellular biological systems, in particular tissues. The modelling framework is based on interconnected logical regulatory networks a la Rene Thomas equipped with information about their spatial relationships. The semantics of such models is expressed through colored Petri nets to implement regulation rules, combined with topological collections to implement the spatial information. Some constraints are put on the the representation of spatial information in order to preserve the possibility of an enumerative and exhaustive state space exploration. This paper presents the modelling framework, its semantics, as well as a prototype implementation that allowed preliminary experimentation on some applications.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Loops and Knots as Topoi of Substance. Spinoza Revisited

The relationship between modern philosophy and physics is discussed. It is shown that the latter develops some need for a modernized metaphysics which shows up as an ultima philosophia of considerable heuristic value, rather than as the prima philosophia in the Aristotelian sense as it had been intended, in the first place. It is shown then, that it is the philosophy of Spinoza in fact, that can still serve as a paradigm for such an approach. In particular, Spinoza's concept of infinite substance is compared with the philosophical implications of the foundational aspects of modern physical theory. Various connotations of sub-stance are discussed within pre-geometric theories, especially with a view to the role of spin networks within quantum gravity. It is found to be useful to intro-duce a separation into physics then, so as to differ between foundational and empirical theories, respectively. This leads to a straightforward connection bet-ween foundational theories and speculative philosophy on the one hand, and between empirical theories and sceptical philosophy on the other. This might help in the end, to clarify some recent problems, such as the absence of time and causality at a fundamental level. It is implied that recent results relating to topos theory might open the way towards eventually deriving logic from physics, and also towards a possible transition from logic to hermeneutic.Comment: 42 page

Self-Reference, Biologic and the Structure of Reproduction

This paper concentrates on relationships of formal systems with biology. The paper is based on previous papers by the author. We have freely used texts of those papers where the formulations are of use, and we have extended the concepts and discussions herein considerably beyond the earlier work. We concentrate on formal systems not only for the sake of showing how there is a fundamental mathematical structure to biology, but also to consider and reconsider philosophical and phenomenological points of view in relation to natural science and mathematics. The relationship with phenomenology comes about in the questions that arise about the nature of the observer in relation to the observed that arise in philosophy, but also in science in the very act of determining the context and models upon which it shall be based.We examine the schema behind the reproduction of DNA. The DNA molecule consists of two interwound strands, the Watson Strand (W) and the Crick Strand (C). The two strands are bonded to each other via a backbone of base-pairings and these bonds can be broken by certain enzymes present in the cell. In reproduction of DNA the bonds between the two strands are broken and the two strands then acquire the needed complementary base molecules from the cellular environment to reconstitute each a separate copy of the DNA. At this level the situation can be described by a symbolism like this. DNA = -------> --------> = = DNA DNA. Here E stands for the environment of the cell. The first arrow denotes the separation of the DNA into the two strands. The second arrow denotes the action between the bare strands and the environment that leads to the production of the two DNA molecules. The paper considers and compares many formalisms for self-replication, including aspects of quantum formalism and the Temperley-Lieb algebra.Comment: LaTeX document, 71 pages, 33 figures. arXiv admin note: substantial text overlap with arXiv:quant-ph/020400

Ontology mapping: the state of the art

Ontology mapping is seen as a solution provider in today's landscape of ontology research. As the number of ontologies that are made publicly available and accessible on the Web increases steadily, so does the need for applications to use them. A single ontology is no longer enough to support the tasks envisaged by a distributed environment like the Semantic Web. Multiple ontologies need to be accessed from several applications. Mapping could provide a common layer from which several ontologies could be accessed and hence could exchange information in semantically sound manners. Developing such mapping has beeb the focus of a variety of works originating from diverse communities over a number of years. In this article we comprehensively review and present these works. We also provide insights on the pragmatics of ontology mapping and elaborate on a theoretical approach for defining ontology mapping

Semantics of nouns and nominal number

In the present paper, I will discuss the semantic structure of nouns and nominal number markers. In particular, I will discuss the question if it is possible to account for the syntactic and semantic formation of nominals in a parallel way, that is I will try to give a compositional account of nominal semantics. The framework that I will use is "twolevel semantics". The semantic representations and their type-theoretical basis will account for general cross-linguistic characteristics of nouns and nominal number and will show interdependencies between noun classes, number marking and cardinal constructions. While the analysis will give a unified account of bare nouns (like dog / water), it will distinguish between the different kinds of nominal terms (like a dog / dogs / water). Following the proposal, the semantic operations underlying the formation of the SR are basically the same for DPs as for CPs. Hence, from such an analysis, independent semantic arguments can be derived for a structural parallelism of nominals and sentences - that is, for the "sentential aspect" of noun phrases. I will first give a sketch of the theoretical background. I will then discuss the cross-linguistic combinatorial potential of nominal constructions, that is, the potential of nouns and number markers to combine with other elements and form complex expressions. This will lead to a general type-theoretical classification for the elements in question. In the next step, I will model the referential potential of nominal constructions. Together with the combinatorial potential, this will give us semantic representations for the basic elements involved in nominal constructions. In an overview, I will summarize our modeling of nouns and nominal number. I will then discuss in an outlook the "sentential aspect" of noun phrases