On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Proofs, Paradoxes, and Probabilities : The Logical Turn of Philosophy in Finland

This monograph describes the emergence of independent research on logic in Finland. The emphasis is placed on three well-known students of Eino Kaila: Georg Henrik von Wright (1916-2003), Erik Stenius (1911-1990), and Oiva Ketonen (1913-2000), and their research between the early 1930s and the early 1950s. The early academic work of these scholars laid the foundations for today's strong tradition in logic in Finland and also became internationally recognized. However, due attention has not been given to these works later, nor have they been comprehensively presented together. Each chapter of the book focuses on the life and work of one of Kaila's aforementioned students, with a fourth chapter discussing works on logic by authors who would later become known within other disciplines. Through an extensive use of correspondence and other archived material, some insight has been gained into the persons behind the academic personae. Unique and unpublished biographical material has been available for this task. The chapter on Oiva Ketonen focuses primarily on his work on what is today known as proof theory, especially on his proof theoretical system with invertible rules that permits a terminating root-first proof search. The independency of the parallel postulate is proved as an example of the strength of root-first proof search. Ketonen was to our knowledge Gerhard Gentzen's (the 'father' of proof theory) only student. Correspondence and a hitherto unavailable autobiographic manuscript, in addition to an unpublished article on the relationship between logic and epistemology, is presented. The chapter on Erik Stenius discusses his work on paradoxes and set theory, more specifically on how a rigid theory of definitions is employed to avoid these paradoxes. A presentation by Paul Bernays on Stenius' attempt at a proof of the consistency of arithmetic is reconstructed based on Bernays' lecture notes. Stenius correspondence with Paul Bernays, Evert Beth, and Georg Kreisel is discussed. The chapter on Georg Henrik von Wright presents his early work on probability and epistemology, along with his later work on modal logic that made him internationally famous. Correspondence from various archives (especially with Kaila and Charlie Dunbar Broad) further discusses his academic achievements and his experiences during the challenging circumstances of the 1940s.

Group Beliefs : Studies on the Nature and Logic of Collective Doxastic Attitudes

This thesis studies the nature and logic of collective doxastic attitudes, or what is referred to in ordinary language as "group beliefs". Beliefs and other intentional attitudes are attributed to groups and collections of people, and such attributions are used to explain and predict the actions of groups. The thesis develops an understanding of group beliefs as voluntarily adopted views or acceptances rather than as ordinary beliefs. Such an understanding can provide new answers to questions concerning collective knowledge and justification of group beliefs, and it allows developing modal logics with collective doxastic and epistemic notions. The thesis consists of six articles. The first three articles are philosophical studies concerned with the nature of group beliefs. The last three articles are logical studies that aim at developing proof-theoretical calculi for reasoning about collective doxastic attitudes.

Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

Constructive Perspectives on Inductive Logic

Constructive (intuitionist, anti-realist) semantics has thus far been lacking an adequate concept of truth in infinity concerning factual (i.e., empirical, non-mathematical) sentences. One consequence of this problem is the difficulty of incorporating inductive reasoning in constructive semantics. It is not possible to formulate a notion for probable truth in infinity if there is no adequate notion of what truth in infinity is. One needs a notion of a constructive possible world based on sensory experience. Moreover, a constructive probability measure must be defined over these constructively possible empirical worlds. This study defines a particular kind of approach to the concept of truth in infinity for Rudolf Carnap's inductive logic. The new approach is based on truth in the consecutive finite domains of individuals. This concept will be given a constructive interpretation. What can be verifiably said about an empirical statement with respect to this concept of truth, will be explained, for which purpose a constructive notion of epistemic probability will be introduced. The aim of this study is also to improve Carnap's inductive logic. The study addresses the problem of justifying the use of an "inductivist" method in Carnap's lambda-continuum. A correction rule for adjusting the inductive method itself in the course of obtaining evidence will be introduced. Together with the constructive interpretation of probability, the correction rule yields positive prior probabilities for universal generalizations in infinite domains.

Dependence Logic: Investigations into Higher-Order Semantics Defined on Teams

This thesis is a study of a rather new logic called dependence logic and its closure under classical negation, team logic. In this thesis, dependence logic is investigated from several aspects. Some rules are presented for quantifier swapping in dependence logic and team logic. Such rules are among the basic tools one must be familiar with in order to gain the required intuition for using the logic for practical purposes. The thesis compares Ehrenfeucht-Fraïssé (EF) games of first order logic and dependence logic and defines a third EF game that characterises a mixed case where first order formulas are measured in the formula rank of dependence logic. The thesis contains detailed proofs of several translations between dependence logic, team logic, second order logic and its existential fragment. Translations are useful for showing relationships between the expressive powers of logics. Also, by inspecting the form of the translated formulas, one can see how an aspect of one logic can be expressed in the other logic. The thesis makes preliminary investigations into proof theory of dependence logic. Attempts focus on finding a complete proof system for a modest yet nontrivial fragment of dependence logic. A key problem is identified and addressed in adapting a known proof system of classical propositional logic to become a proof system for the fragment, namely that the rule of contraction is needed but is unsound in its unrestricted form. A proof system is suggested for the fragment and its completeness conjectured. Finally, the thesis investigates the very foundation of dependence logic. An alternative semantics called 1-semantics is suggested for the syntax of dependence logic. There are several key differences between 1-semantics and other semantics of dependence logic. 1-semantics is derived from first order semantics by a natural type shift. Therefore 1-semantics reflects an established semantics in a coherent manner. Negation in 1-semantics is a semantic operation and satisfies the law of excluded middle. A translation is provided from unrestricted formulas of existential second order logic into 1-semantics. Also game theoretic semantics are considerd in the light of 1-semantics.

Exploring Customer Value Formation: A Customer Dominant Logic Perspective

This paper extends current discussions about value creation and proposes a customer dominant value perspective. A customer-dominant marketing logic positions the customer in the center, rather than the service provider/producer or the interaction or the system. The focus is shifted from the company´s service processes involving the customer, to the customer´s multi-contextual value formation, involving the company. It is argued that value is not always an active process of creation; instead value is embedded and formed in the highly dynamic and multi-contextual reality and life of the customer. This leads to a need to look beyond the current line of visibility where visible customer-company interactions are focused to the invisible and mental life of the customer. From this follows a need to extend the temporal scope, from exchange and use even further to accumulated experiences in the customer´s life. The aim of this paper is to explore value formation from a customer dominant logic perspective. This is done in three steps: first, value formation is contrasted to earlier views on the company’s role in value creation by using a broad ontologically driven framework discussing what, how, when, where and who. Next, implications of the proposed characteristics of value formation compared to earlier approaches are put forward. Finally, some tentative suggestions of how this perspective would affect marketing in service companies are presented. As value formation in a CDL perspective has a different focus and scope than earlier views on value it leads to posing questions about the customer that reveals earlier hidden aspects of the role of a service for the customer. This insight might be used in service development and innovation.

Rethinking Service Companies’ Business Logic: Do We Need a Customer-Dominant Logic as a Guideline?

Purpose –This paper explores and expands the roles of customers and companies in creating value by introducing a new a customer-based approach to service. The customer’s logic is examined as being the foundation of a customer-based marketing and business logic. Design/methodology/approach – The authors argue that both goods-dominant logics and service-dominant logics are provider-dominant. Contrasting the customer-dominant logic with provider-dominant logics, the paper examines the creation of service value from the perspectives of value-in-use, the customer’s own context, and the customer’s experience of service. Findings –Moving from a provider-dominant logic to a customer-dominant logic uncovered five major challenges to service marketers: Company involvement, company control in co-creation, visibility of value creation, locus of customer experience, and character of customer experience. Research limitations/implications – The paper is exploratory. It presents and discusses a conceptual model and suggests implications for research and practice. Practical implications –Awareness of the mechanisms of customer logic will provide businesses with new perspectives on the role of the company in their customer’s lives. We propose that understanding the customer’s logic should represent the starting-point for the marketer’s business logic. Originality/value – The paper increases the understanding of how the customer’s logic underpins the customer-dominant business logic. By exploring consequences of applying a customer-dominant logic, we suggest further directions for theoretical and empirical research.

Re-Conceptualizing Value-Creation From Industrial Business Logic to Service Business Logic

There is an urgent interest in marketing to move away from neo-classical value definitions suggesting that value creation is a process of exchanging goods for money. In the present paper, value creation is conceptualized as an integration of two distinct, yet closely coupled processes. First, actors co-create what this paper calls an underlying basis of value. This is done by interactively re-configuring resources. By relating and combining resources, activity sets, and risks across actor boundaries in novel ways actors create joint productivity gains – a concept very similar to density (Normann, 2001). Second, actors engage in a process of signification and evaluation. Signification implies co-constructing the meaning and worth of joint productivity gains co-created through interactive resource re-configuration, as well as sharing those gains through a pricing mechanism as value to involved actors. The conceptual framework highlights an all-important dynamics associated with ´value creation´ and ´value´ - a dynamics the paper claims has eluded past marketing research. The paper argues that the framework presented here is appropriate for the interactive service perspective, where value and value creation are not objectively given, but depend on the power of involved actors´ socially constructed frames to mobilize resources across actor boundaries in ways that ´enhance system well-being´ (Vargo et al., 2008). The paper contributes to research on Service Logic, Service-Dominant Logic, and Service Science.

Towards Service Logic: The Unique Contribution of Value Co-Creation

The underpinning logic of value co-creation in service logic is analysed. It is observed that three of the ten foundational premises of the so-called service-dominant logic are problematic and do not support an understanding of value-co-creation and creation that is meaningful for theoretical development and decision making in business and marketing practice. Without a thorough understanding of the interaction concept, the locus and nature of value co-creation cannot be identified. Based on the analysis in the present article it is observed that a unique contribution of a service perspective on business (service logic) is not that customers always are co-creators of value, but that under certain circumstances the service provider gets opportunities to co-create value together with its customers. Finally, the three problematic premises are reformulated accordingly.

What Can A Service Logic Offer Marketing Theory

The goods-dominated marketing model has major shortcomings as a guiding marketing theory. Its marketing mix approach is mainly geared towards buying and does not include consumption as an integral part of marketing theory. Although it is during the process of consuming goods and services that value is generated for customers and the foundation for repeat purchasing and customer relationships are laid, this process is left outside the scope of marketing. The focus in service marketing is not on a product but on interactions in service encounters. Consumption has become an integral part of a holistic marketing model. Other than standardized goods-based value propositions can be better understood when taking a servicebased approach. It is concluded that marketing based on a goods logic is but a special case of marketing based on a service logic and applicable only in certain contexts with standardized products.

Marketing and the Logic of Service: Value Facilitation, Value Creation and Co-creation, and Their Marketing Implications

The discussion of a service-dominant logic has made the findings of decades of service marketing research a topic of interest for marketing at large. Some fundamental aspects of the logic such as value creation and its marketing implications are more complex than they have been treated as so far and need to be further developed to serve marketing theory and practice well. Following the analysis in the present article it is argued that although customers are co-producers in service processes, according to the value-in-use notion adopted in the contemporary marketing and management literature they are fundamentally the creators of value for themselves. Furthermore, it is concluded that although by providing goods and services as input resources into customers’ consumption and value-generating processes firms are fundamentally value facilitators, interactions with customers that exist or can be created enable firms to engage themselves with their customers’ processes and thereby they become co-creators of value with their customers. As marketing implications it is observed that 1) the goal of marketing is to support customers’ value creation, 2) following a service logic and due to the existence of interactions where the firm’s and the customer’s processes merge into an integrated joint value creation process, the firm is not restricted to making value propositions only, but can directly and actively influence the customer’s value fulfilment as well and extend its marketing process to include activities during customer-firm interactions, and 3) although all goods and services are consumed as service, customers’ purchasing decisions can be expected to be dependant of whether they have the skills and interest to use a resource, such as a good, as service or want to buy extended market offerings including process-related elements. Finally, the analysis concludes with five service logic theses.