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Register a new userA mosaic of Chu spaces and Channel Theory with applications to Object Identification and Mereological Complexity
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James F. Glazebrook PhD
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Chu Spaces and Channel Theory are well established areas of investigation in the general context of category theory. We review a range of examples and applications of these methods in logic and computer science, including Formal Concept Analysis, distributed systems and ontology development. We then employ these methods to describe human object perception, beginning with the construction of uncategorized object files and proceeding through categorization, individual object identification and the tracking of object identity through time. We investigate the relationship between abstraction and mereological categorization, particularly as these affect object identity tracking. This we accomplish in terms of information flow that is semantically structured in terms of local logics, while at the same time this framework also provides an inferential mechanism towards identification and perception. We show how a mereotopology naturally emerges from the representation of classifications by simplicial complexes, and briefly explore the emergence of geometric relations and interactions between objects.
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This thesis contributes to the formalisation of the notion of an agent within the class of finite multivariate Markov chains. Agents are seen as entities that act, perceive, and are goal-directed. We present a new measure that can be used to identify entities (called $iota$-entities), some general requirements for entities in multivariate Markov chains, as well as formal definitions of actions and perceptions suitable for such entities. The intuition behind $iota$-entities is that entities are spatiotemporal patterns for which every part makes every other part more probable. The measure, complete local integration (CLI), is formally investigated in general Bayesian networks. It is based on the specific local integration (SLI) which is measured with respect to a partition. CLI is the minimum value of SLI over all partitions. We prove that $iota$-entities are blocks in specific partitions of the global trajectory. These partitions are the finest partitions that achieve a given SLI value. We also establish the transformation behaviour of SLI under permutations of nodes in the network. We go on to present three conditions on general definitions of entities. These are not fulfilled by sets of random variables i.e. the perception-action loop, which is often used to model agents, is too restrictive. We propose that any general entity definition should in effect specify a subset (called an an entity-set) of the set of all spatiotemporal patterns of a given multivariate Markov chain. The set of $iota$-entities is such a set. Importantly the perception-action loop also induces an entity-set. We then propose formal definitions of actions and perceptions for arbitrary entity-sets. These specialise to standard notions in case of the perception-action loop entity-set. Finally we look at some very simple examples.
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices (rectangles) of the truth-table matrix defining a communication problem. The only technique that does not quite fit is information complexity, which has been investigated over the last decade. Here, we connect information complexity to one of the most powerful rectangular techniques: the recently-introduced smooth corruption (or smooth rectangle) bound. We show that the former subsumes the latter under rectangular input distributions. We conjecture that this subsumption holds more generally, under arbitrary distributions, which would resolve the long-standing direct sum question for randomized communication. As an application, we obtain an optimal $Omega(n)$ lower bound on the information complexity---under the {em uniform distribution}---of the so-called orthogonality problem (ORT), which is in turn closely related to the much-studied Gap-Hamming-Distance (GHD). The proof of this bound is along the lines of recent communication lower bounds for GHD, but we encounter a surprising amount of additional technical detail.
Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects to handle potentially conflicting information, has been discussed in literature, by some of the authors. Two applications emerged that are very relevant: energy management and business process management. We illustrate a set of guide lines to determine how to apply linear defeasible logic to those contexts.
This paper studies colimits of sequences of finite Chu spaces and their ramifications. Besides generic Chu spaces, we consider extensional and biextensional variants. In the corresponding categories we first characterize the monics and then the existence (or the lack thereof) of the desired colimits. In each case, we provide a characterization of the finite objects in terms of monomorphisms/injections. Bifinite Chu spaces are then expressed with respect to the monics of generic Chu spaces, and universal, homogeneous Chu spaces are shown to exist in this category. Unanticipated results driving this development include the fact that while for generic Chu spaces monics consist of an injective first and a surjective second component, in the extensional and biextensional cases the surjectivity requirement can be dropped. Furthermore, the desired colimits are only guaranteed to exist in the extensional case. Finally, not all finite Chu spaces (considered set-theoretically) are finite objects in their categories. This study opens up opportunities for further investigations into recursively defined Chu spaces, as well as constructive models of linear logic.
Decision makers involved in the management of civil assets and systems usually take actions under constraints imposed by societal regulations. Some of these constraints are related to epistemic quantities, as the probability of failure events and the corresponding risks. Sensors and inspectors can provide useful information supporting the control process (e.g. the maintenance process of an asset), and decisions about collecting this information should rely on an analysis of its cost and value. When societal regulations encode an economic perspective that is not aligned with that of the decision makers, the Value of Information (VoI) can be negative (i.e., information sometimes hurts), and almost irrelevant information can even have a significant value (either positive or negative), for agents acting under these epistemic constraints. We refer to these phenomena as Information Avoidance (IA) and Information OverValuation (IOV). In this paper, we illustrate how to assess VoI in sequential decision making under epistemic constraints (as those imposed by societal regulations), by modeling a Partially Observable Markov Decision Processes (POMDP) and evaluating non optimal policies via Finite State Controllers (FSCs). We focus on the value of collecting information at current time, and on that of collecting sequential information, we illustrate how these values are related and we discuss how IA and IOV can occur in those settings.
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