We investigate principles of rationality based on symmetry in Polyadic Pure Inductive Logic. The aim of Pure Inductive Logic (PIL) is to determine how to assign probabilities to sentences of a language being true in some structure on the basis of rational considerations. This thesis centres on principles arising from instances of symmetry for sentences of first-order polyadic languages. We begin with the recently introduced Permutation Invariance Principle (PIP), and find that it is determined by a finite number of permutations on a finite set of formulae. We test the consistency of PIP with established principles of the subject and show, in particular, that it is consistent with Super Regularity. We then investigate the relationship between PIP and the two main polyadic principles thus far, Spectrum Exchangeability and Language Invariance, and discover there are close connections. In addition, we define the key notion of polyadic atoms as the building blocks of polyadic languages. We explore polyadic generalisations of the unary principle of Atom Exchangeability and prove that PIP is a natural extension of Atom Exchangeability to polyadic languages. In the second half of the thesis we investigate polyadic approaches to the unary version of Constant Exchangeability as invariance under signatures. We first provide a theory built on polyadic atoms (for binary and then general languages). We introduce the notion of a signature for non-unary languages, and principles of invariance under signatures, independence, and instantial relevance for this context, as well as a binary representation theorem. We then develop a second approach to these concepts using elements as alternative building blocks for polyadic languages. Finally, we introduce the concepts of homomorphisms and degenerate probability functions in Pure Inductive Logic. We examine which of the established principles of PIL are preserved by these notions, and present a method for reducing probability functions on general polyadic languages to functions on binary languages.

This dissertation proposes a suite of novel approaches for solving multiagent decision and optimization problems based on the Collaborative Design Network (CDN), a framework for multiagent decision making. The framework itself is distributed, decision-theoretic and was originally proposed for multiagent component-centred design. This application is a novel use of the CDN, and demonstrate the generality of the CDN framework for general decision-theoretic planning. First, the framework is applied towards tackling a multiagent decision problem outside of collaborative design called multiagent expedition (MAE), a testbed problem which abstracts many of the features of real-world multiagent decision-making problems. We formally introduce MAE, and show it to be a subclass of a decentralized partially observable Markov Decision process (Dec-POMDP). We apply the CDN to the online MAE planning problem. We demonstrate that the CDN can plan in MAE with conditional optimality given a set of basic assumptions on the structure and organization of the agent team. We introduce a set of knowledge representational aspects to achieve conditionally optimal planning. We experimentally verify our approach on a series of benchmark problems created for this dissertation to test the various aspects of our CDN solution. We also investigate further methods for scalability and speedup in MAE. The concept of \emph{partial evaluation} (PE) is introduced, based on the assumption that an agent has an intended effect given an agent's action and considers all other effects unintended. This assumption is used to derive a bound for planning that partitions the set of joint plans into a set of fully evaluated and a set of partial evaluated plans. Plans which are partially evaluated can significantly speed up planning in the centralized case. PE is also applied to the CDN, to both public decisions between agents and private decisions local to an agent. We demonstrate that applying PE to public decisions in the CDN results in either intractable communication or suboptimal planning. When applied to private decisions, we show PE can still be very effective in decreasing planning runtime.

We investigate the Principle of Predicate Exchangeability in the framework of Pure Inductive Logic. While this principle was known to Rudolf Carnap, who started research in Inductive Logic, the principle has been somewhat neglected in the past. After providing the framework of Pure Inductive Logic, we will show Representation Theorems for probability functions satisfying Predicate Exchangeability, filling the gap in the list of Representation Theorems for functions satisfying certain rational principles. We then introduce a new principle, called the Principle of Strong Predicate Exchangeability, which is weaker than the well-known Principle of Atom Exchangeability, but stronger than Predicate Exchangeability and give examples of functions that satisfy this principle. Finally, we extend the framework of Inductive Logic to Second Order languages, which allows for increasing a rational agent’s expressive strength. We introduce Wilmers’ Principle, a rational principle that rational agents might want to adopt in this extended framework, and give a representation theorem for this principle.

We propose and investigate several new principles of rational reasoning within the framework of Pure Inductive Logic, PIL, where probability functions defined on the sentences of a first-order language are used to model an agent's beliefs. The Elephant Principle is concerned with how learning, modelled by conditioning, may be uniquely `remembered'. The Perspective Principle requires that, from a given prior, conditioning on statistically similar experiences should result in similar assignments, and is found to be a necessary condition for Reichenbach's Axiom to hold. The Abductive Inference Principle and some variations are proposed as possible formulations of a restriction of C.S. Peirce's notion of hypothesis in the context of PIL, though characterization results obtained for these principles suggest that they may be too strong. The Finite Values Property holds when a probability function takes only finitely many values when restricted to sentences containing only constant symbols from some fixed finite set. This is shown to entail a certain systematic method of assigning probabilities in terms of possible worlds, and it is considered in this light as a possible principle of inductive reasoning. Classification results are given, stating which members of certain established families of probability functions satisfy each of these new principles. Additionally, we define the theory of a principle P of PIL to be the set of those sentences which are assigned probability 1 by every probability function which satisfies P. We investigate the theory of the established principle of Spectrum Exchangeability by finding separately the theories of heterogeneous and homogeneous functions. The theory of Spectrum Exchangeability is found to be equal to the theory of finite structures. The theory of Johnson's Sufficientness Postulate is also found. Consequently, we find that Spectrum Exchangeability, Johnson's Sufficientness Postulate and the Finite Values Property are all inconsistent with the principle of Super-Regularity: that any consistent sentence should be assigned non-zero probability.

<p>This thesis presents the implementation of a knowledge base system for rough sets [Paw92]within the logic programming framework. The combination of rough set theory with logic programming is a novel approach. The presented implementation serves as a prototype system for the ideas presented in [VDM03a, VDM03b]. The system is available at "http://www.ida.liu.se/rkbs". </p><p>The presented language for describing knowledge in the rough knowledge base caters for implicit definition of rough sets by combining different regions (e.g. upper approximation, lower approximation, boundary) of other defined rough sets. The rough knowledge base system also provides methods for querying the knowledge base and methods for computing quantitative measures. </p><p>We test the implemented system on a medium sized application example to illustrate the usefulness of the system and the incorporated language. We also provide performance measurements of the system.</p>

This thesis presents the implementation of a knowledge base system for rough sets [Paw92]within the logic programming framework. The combination of rough set theory with logic programming is a novel approach. The presented implementation serves as a prototype system for the ideas presented in [VDM03a, VDM03b]. The system is available at "http://www.ida.liu.se/rkbs". The presented language for describing knowledge in the rough knowledge base caters for implicit definition of rough sets by combining different regions (e.g. upper approximation, lower approximation, boundary) of other defined rough sets. The rough knowledge base system also provides methods for querying the knowledge base and methods for computing quantitative measures. We test the implemented system on a medium sized application example to illustrate the usefulness of the system and the incorporated language. We also provide performance measurements of the system.

This paper concerns about key business process in the production companies, namely, the new product development. The object of this thesis has been to create a tool to estimate the risk of the new product development. To reach this goal, current tools used to deciding the risk must have been explored. As the best tool, appropriate for assessing the risk of new product development has proved the Bayesian Network. This paper explains the construction of the Bayesian network and shows the way how to generate the probabilities in the network to be accurate for the risk estimation. Based on this theoretical knowledge has been built an information system, which estimates the risk of the new products and administer the risks.

Numerous studies on Queueing systems, such as Internet traffic flows, have shown to be bursty, self-similar and/or long-range dependent, because of the heavy (long) tails for the various distributions of interest, including intermittent intervals and queue lengths. Other studies have addressed vacation in no-customers’ queueing system or when the server fails. These patterns are important for capacity planning, performance prediction, and optimization of networks and have a negative impact on their effective functioning. Heavy-tailed distributions have been commonly used by telecommunication engineers to create workloads for simulation studies, which, regrettably, may show peculiar queueing characteristics. To cost-effectively examine the impacts of different network patterns on heavy- tailed queues, new and reliable analytical approaches need to be developed. It is decided to establish a brand-new analytical framework based on optimizing entropy functionals, such as those of Shannon, Rényi, Tsallis, and others that have been suggested within statistical physics and information theory, subject to suitable linear and non-linear system constraints. In both discrete and continuous time domains, new heavy tail analytic performance distributions will be developed, with a focus on those exhibiting the power law behaviour seen in many Internet scenarios. The exposition of two major revolutionary approaches, namely the unification of information geometry and classical queueing systems and unifying information length theory with transient queueing systems. After conclusions, open problems arising from this thesis and limitations are introduced as future work.