A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Formal Power Analysis of Systems-on-Chip

The design methods and languages targeted to modern System-on-Chip designs are facing tremendous pressure of the ever-increasing complexity, power, and speed requirements. To estimate any of these three metrics, there is a trade-off between accuracy and abstraction level of detail in which a system under design is analyzed. The more detailed the description, the more accurate the simulation will be, but, on the other hand, the more time consuming it will be. Moreover, a designer wants to make decisions as early as possible in the design flow to avoid costly design backtracking. To answer the challenges posed upon System-on-chip designs, this thesis introduces a formal, power aware framework, its development methods, and methods to constraint and analyze power consumption of the system under design. This thesis discusses on power analysis of synchronous and asynchronous systems not forgetting the communication aspects of these systems. The presented framework is built upon the Timed Action System formalism, which offer an environment to analyze and constraint the functional and temporal behavior of the system at high abstraction level. Furthermore, due to the complexity of System-on-Chip designs, the possibility to abstract unnecessary implementation details at higher abstraction levels is an essential part of the introduced design framework. With the encapsulation and abstraction techniques incorporated with the procedure based communication allows a designer to use the presented power aware framework in modeling these large scale systems. The introduced techniques also enable one to subdivide the development of communication and computation into own tasks. This property is taken into account in the power analysis part as well. Furthermore, the presented framework is developed in a way that it can be used throughout the design project. In other words, a designer is able to model and analyze systems from an abstract specification down to an implementable specification.

The Importance of Semantics: Visual World Studies on Drawing Inferences and Resolving Anaphors

The present thesis investigated the importance of semantics in generating inferences during discourse processing. Three aspects of semantics, gender stereotypes, implicit causality information and proto-role properties, were used to investigate whether semantics is activated elaboratively during discourse comprehension and what its relative importance is in backward inferencing compared to discourse/structural cues. Visual world eye-tracking studies revealed that semantics plays an important role in both backward and forward inferencing: Gender stereotypes and implicit causality information is activated elaboratively during online discourse comprehension. Moreover, gender stereotypes, implicit causality and proto-role properties of verbs are all used in backward inferencing. Importantly, the studies demonstrated that semantic cues are weighed against discourse/structural cues. When the structural cues consist of a combination of cues that have been independently shown to be important in backward inferencing, semantic effects may be masked, whereas when the structural cues consist of a combination of fewer prominent cues, semantics can have an earlier effect than structural factors in pronoun resolution. In addition, the type of inference matters, too: During anaphoric inferencing semantics has a prominent role, while discourse/structural salience attains more prominence during non-anaphoric inferencing. Finally, semantics exhibits a strong role in inviting new inferences to revise earlier made inferences even in the case the additional inference is not needed to establish coherence in discourse. The findings are generally in line with the Mental Model approaches. Two extended model versions are presented that incorporate the current findings into the earlier literature. These models allow both forward and backward inferencing to occur at any given moment during the course of processing; they also allow semantic and discourse/structural cues to contribute to both of these processes. However, while the Mental Model 1 does not assume interactions between semantic and discourse/structural factors in forward inferencing, the Mental Model 2 does assume such a link.

Tool-supported invariant-based programming

The development of correct programs is a core problem in computer science. Although formal verification methods for establishing correctness with mathematical rigor are available, programmers often find these difficult to put into practice. One hurdle is deriving the loop invariants and proving that the code maintains them. So called correct-by-construction methods aim to alleviate this issue by integrating verification into the programming workflow. Invariant-based programming is a practical correct-by-construction method in which the programmer first establishes the invariant structure, and then incrementally extends the program in steps of adding code and proving after each addition that the code is consistent with the invariants. In this way, the program is kept internally consistent throughout its development, and the construction of the correctness arguments (proofs) becomes an integral part of the programming workflow. A characteristic of the approach is that programs are described as invariant diagrams, a graphical notation similar to the state charts familiar to programmers. Invariant-based programming is a new method that has not been evaluated in large scale studies yet. The most important prerequisite for feasibility on a larger scale is a high degree of automation. The goal of the Socos project has been to build tools to assist the construction and verification of programs using the method. This thesis describes the implementation and evaluation of a prototype tool in the context of the Socos project. The tool supports the drawing of the diagrams, automatic derivation and discharging of verification conditions, and interactive proofs. It is used to develop programs that are correct by construction. The tool consists of a diagrammatic environment connected to a verification condition generator and an existing state-of-the-art theorem prover. Its core is a semantics for translating diagrams into verification conditions, which are sent to the underlying theorem prover. We describe a concrete method for 1) deriving sufficient conditions for total correctness of an invariant diagram; 2) sending the conditions to the theorem prover for simplification; and 3) reporting the results of the simplification to the programmer in a way that is consistent with the invariantbased programming workflow and that allows errors in the program specification to be efficiently detected. The tool uses an efficient automatic proof strategy to prove as many conditions as possible automatically and lets the remaining conditions be proved interactively. The tool is based on the verification system PVS and i uses the SMT (Satisfiability Modulo Theories) solver Yices as a catch-all decision procedure. Conditions that were not discharged automatically may be proved interactively using the PVS proof assistant. The programming workflow is very similar to the process by which a mathematical theory is developed inside a computer supported theorem prover environment such as PVS. The programmer reduces a large verification problem with the aid of the tool into a set of smaller problems (lemmas), and he can substantially improve the degree of proof automation by developing specialized background theories and proof strategies to support the specification and verification of a specific class of programs. We demonstrate this workflow by describing in detail the construction of a verified sorting algorithm. Tool-supported verification often has little to no presence in computer science (CS) curricula. Furthermore, program verification is frequently introduced as an advanced and purely theoretical topic that is not connected to the workflow taught in the early and practically oriented programming courses. Our hypothesis is that verification could be introduced early in the CS education, and that verification tools could be used in the classroom to support the teaching of formal methods. A prototype of Socos has been used in a course at Åbo Akademi University targeted at first and second year undergraduate students. We evaluate the use of Socos in the course as part of a case study carried out in 2007.

Formal and informal mechanisms for knowledge protection and sharing

The most important knowledge in firms is mostly tacit and embedded in individuals within the organization. This background knowledge that firms possess is used for creation of new knowledge and innovations. As firms today greatly concentrate on their core competencies, they need external knowledge from various collaboration partners. Thus, collaborative relationship governance, as well as control (use of appropriability mechanisms) over background (the input from each firm in innovative activities) and foreground knowledge (the output of collaboration activities) is needed in order to successfully create and capture value from innovative activities without losing core knowledge and competitiveness. Even though research has concentrated on knowledge protection and knowledge sharing, studies that combine both of these views and examine the effects of sharing and protection on value creation and capture have been rather limited. Studies have mainly focused on the protection of the output of innovation while forgetting the protection of the input of innovation. On the other hand, as the research concentrating on the output of innovation tends to favor formal mechanisms, informal mechanisms have remained more unknown to researchers as well as managers. This research aims to combine the perspectives of knowledge sharing and knowledge protection and their relationship with value creation and value capture. The sharing and protection are viewed from two points of view: the use of appropriability mechanisms, as well as governance of the collaborative relationship. The study consists of two parts. The first part introduces the research topic and discusses the overall results. The second part comprises six complementary research publications. Both qualitative and quantitative research methods are used in the study. In terms of results, the findings enhance understanding of the combined use of formal and informal mechanisms for knowledge protection and sharing. Informal mechanisms appear to be emphasized in the protection of background knowledge, and thus are prerequisites for innovation, whereas formal mechanisms are relied on more for protecting the results of innovative activities. However, the simultaneous use of the formal and informal mechanisms that are relevant to the particular industry and innovation context is recommendedthroughout the collaborative innovation process. Further, the study adds to the current knowledge on HRM as an appropriability mechanism: on the firm level its uses include assessing and hedging against employee-related risks such as knowledge leaking and knowledge leaving. A further contribution is to the research on HRM protection and its interrelations with other appropriability mechanisms, its constituents, and its potential use in the area of knowledge protection.

Of pearls and pigs : a conceptual-semantic Tiernet approach to formal representation of structure and variation of phraseological units

"Helmiä sioille", pärlor för svin, säger man på finska om någonting bra och fint som tas emot av en mottagare som inte vill eller har ingen förmåga att förstå, uppskatta eller utnyttja hela den potential som finns hos det mottagna föremålet, är ointresserad av den eller gillar den inte. För sådana relativt stabila flerordiga uttryck, som är lagrade i språkbrukarnas minnen och som demonstrerar olika slags oregelbundna drag i sin struktur använder man inom lingvistiken bl.a. termerna "idiom" eller "fraseologiska enheter". Som en oregelbundenhet kan man t.ex. beskriva det faktum att betydelsen hos uttrycket inte är densamma som man skulle komma till ifall man betraktade det som en vanlig regelbunden fras. En annan oregelbundenhet, som idiomforskare har observerat, ligger i den begränsade förmågan att varieras i form och betydelse, som många idiom har jämfört med regelbundna fraser. Därför talas det ofta om "grundform" och "grundbetydelse" hos idiom och variationen avses som avvikelse från dessa. Men när man tittar på ett stort antal förekomstexempel av idiom i språkbruk, märker man att många av dem tillåter variation, t.o.m. i sådan utsträckning att gränserna mellan en variant och en "grundform" suddas ut, och istället för ett idiom råkar vi plötsligt på en "familj" av flera besläktade uttryck. Allt detta väcker frågan om hur dessa uttryck egentligen ska vara representerade i språket. I avhandlingen utförs en kritisk granskning av olika tidigare tillvägagångssätt att beskriva fraseologiska enheter i syfte att klargöra vilka svårigheter deras struktur och variation erbjuder för den lingvistiska teorin. Samtidigt presenteras ett alternativt sätt att beskriva dessa uttryck. En systematisk och formell modell som utvecklas i denna avhandling integrerar en beskrivning av idiom på många olika språkliga nivåer och skildrar deras variation i form av ett nätverk och som ett resultat av samspel mellan idiomets struktur och kontexter där det förekommer, samt av interaktion med andra fasta uttryck. Modellen bygger på en fördjupande, språkbrukbaserad analys av det finska idiomet "X HEITTÄÄ HELMIÄ SIOILLE" (X kastar pärlor för svin).

Making Sense of Shared Leadership. A case study of leadership processes and practices without formal leadership structure in the team context

Leadership is essential for the effectiveness of the teams and organizations they are part of. The challenges facing organizations today require an exhaustive review of the strategic role of leadership. In this context, it is necessary to explore new types of leadership capable of providing an effective response to new needs. The presentday situations, characterized by complexity and ambiguity, make it difficult for an external leader to perform all leadership functions successfully. Likewise, knowledge-based work requires providing professional groups with sufficient autonomy to perform leadership functions. This study focuses on shared leadership in the team context. Shared leadership is seen as an emergent team property resulting from the distribution of leadership influence across multiple team members. Shared leadership entails sharing power and influence broadly among the team members rather than centralizing it in the hands of a single individual who acts in the clear role of a leader. By identifying the team itself as a key source of influence, this study points to the relational nature of leadership as a social construct where leadership is seen as social process of relating processes that are co-constructed by several team members. Based on recent theoretical developments concerned with relational, practice-based and constructionist approaches to the study of leadership processes, this thesis proposes the study of leadership interactions, working processes and practices to focus on the construction of direction, alignment and commitment. During the research process, critical events, activities, working processes and practices of a case team have been examined and analyzed with the grounded theory –approach in the terms of shared leadership. There are a variety of components to this complex process and a multitude of factors that may influence the development of shared leadership. The study suggests that the development process of shared leadership is a common sense -making process and consists of four overlapping dimensions (individual, social, structural, and developmental) to work with as a team. For shared leadership to emerge, the members of the team must offer leadership services, and the team as a whole must be willing to rely on leadership by multiple team members. For these individual and collective behaviors to occur, the team members must believe that offering influence to and accepting it from fellow team members are welcome and constructive actions. Leadership emerges when people with differing world views use dialogue and collaborative learning to create spaces where a shared common purpose can be achieved while a diversity of perspectives is preserved and valued. This study also suggests that this process can be supported by different kinds of meaning-making and process tools. Leadership, then, does not reside in a person or in a role, but in the social system. The built framework integrates the different dimensions of shared leadership and describes their relationships. This way, the findings of this study can be seen as a contribution to the understanding of what constitutes essential aspects of shared leadership in the team context that can be of theoretical value in terms of advancing the adoption and development process of shared leadership. In the real world, teams and organizations can create conditions to foster and facilitate the process. We should encourage leaders and team members to approach leadership as a collective effort that the team can be prepared for, so that the response is rapid and efficient.

Proactive and Preventive Student Welfare Activities in Finnish Preschool and Elementary School: Handling of Transition to Formal Schooling and a National Anti-Bullying Program as Examples

Prerequisites and effects of proactive and preventive psycho-social student welfare activities in Finnish preschool and elementary school were of interest in the present thesis. So far, Finnish student welfare work has mainly focused on interventions and individuals, and the voluminous possibilities to enhance well-being of all students as a part of everyday school work have not been fully exploited. Consequently, in this thesis three goals were set: (1) To present concrete examples of proactive and preventive psycho-social student welfare activities in Finnish basic education; (2) To investigate measurable positive effects of proactive and preventive activities; and (3) To investigate implementation of proactive and preventive activities in ecological contexts. Two prominent phenomena in preschool and elementary school years—transition to formal schooling and school bullying—were chosen as examples of critical situations that are appropriate targets for proactive and preventive psycho-social student welfare activities. Until lately, the procedures concerning both school transitions and school bullying have been rather problem-focused and reactive in nature. Theoretically, we lean on the bioecological model of development by Bronfenbrenner and Morris with concentric micro-, meso-, exo- and macrosystems. Data were drawn from two large-scale research projects, the longitudinal First Steps Study: Interactive Learning in the Child–Parent– Teacher Triangle, and the Evaluation Study of the National Antibullying Program KiVa. In Study I, we found that the academic skills of children from preschool–elementary school pairs that implemented several supportive activities during the preschool year developed more quickly from preschool to Grade 1 compared with the skills of children from pairs that used fewer practices. In Study II, we focused on possible effects of proactive and preventive actions on teachers and found that participation in the KiVa antibullying program influenced teachers‘ self-evaluated competence to tackle bullying. In Studies III and IV, we investigated factors that affect implementation rate of these proactive and preventive actions. In Study III, we found that principal‘s commitment and support for antibullying work has a clear-cut positive effect on implementation adherence of student lessons of the KiVa antibullying program. The more teachers experience support for and commitment to anti-bullying work from their principal, the more they report having covered KiVa student lessons and topics. In Study IV, we wanted to find out why some schools implement several useful and inexpensive transition practices, whereas other schools use only a few of them. We were interested in broadening the scope and looking at local-level (exosystem) qualities, and, in fact, the local-level activities and guidelines, along with teacherreported importance of the transition practices, were the only factors significantly associated with the implementation rate of transition practices between elementary schools and partner preschools. Teacher- and school-level factors available in this study turned out to be mostly not significant. To summarize, the results confirm that school-based promotion and prevention activities may have beneficial effects not only on students but also on teachers. Second, various top-down processes, such as engagement at the level of elementary school principals or local administration may enhance implementation of these beneficial activities. The main message is that when aiming to support the lives of children the primary focus should be on adults. In future, promotion of psychosocial well-being and the intrinsic value of inter- and intrapersonal skills need to be strengthened in the Finnish educational systems. Future research efforts in student welfare and school psychology, as well as focused training for psychologists in educational contexts, should be encouraged in the departments of psychology and education in Finnish universities. Moreover, a specific research centre for school health and well-being should be established.

Scheduling of guarded command based models

Formal methods provide a means of reasoning about computer programs in order to prove correctness criteria. One subtype of formal methods is based on the weakest precondition predicate transformer semantics and uses guarded commands as the basic modelling construct. Examples of such formalisms are Action Systems and Event-B. Guarded commands can intuitively be understood as actions that may be triggered when an associated guard condition holds. Guarded commands whose guards hold are nondeterministically chosen for execution, but no further control flow is present by default. Such a modelling approach is convenient for proving correctness, and the Refinement Calculus allows for a stepwise development method. It also has a parallel interpretation facilitating development of concurrent software, and it is suitable for describing event-driven scenarios. However, for many application areas, the execution paradigm traditionally used comprises more explicit control flow, which constitutes an obstacle for using the above mentioned formal methods. In this thesis, we study how guarded command based modelling approaches can be conveniently and efficiently scheduled in different scenarios. We first focus on the modelling of trust for transactions in a social networking setting. Due to the event-based nature of the scenario, the use of guarded commands turns out to be relatively straightforward. We continue by studying modelling of concurrent software, with particular focus on compute-intensive scenarios. We go from theoretical considerations to the feasibility of implementation by evaluating the performance and scalability of executing a case study model in parallel using automatic scheduling performed by a dedicated scheduler. Finally, we propose a more explicit and non-centralised approach in which the flow of each task is controlled by a schedule of its own. The schedules are expressed in a dedicated scheduling language, and patterns assist the developer in proving correctness of the scheduled model with respect to the original one.

Formal development and quantitative verification of dependable systems

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Theorizing Formal and Informal Feedback Practices in Management Accounting Through Three Dimensions

The purpose of this doctoral thesis is to widen and develop our theoretical frameworks for discussion and analyses of feedback practices in management accounting, particularly shedding light on its formal and informal aspects. The concept of feedback in management accounting has conventionally been analyzed within cybernetic control theory, in which feedback flows as a diagnostic or comparative loop between measurable outputs and pre-set goals (see e.g. Flamholtz et al. 1985; Flamholtz 1996, 1983), i.e. as a formal feedback loop. However, the everyday feedback practices in organizations are combinations of formal and informal elements. In addition to technique-driven feedback approaches (like budgets, measurement, and reward systems) we could also categorize social feedback practices that managers see relevant and effective in the pursuit of organizational control. While cybernetics or control theories successfully capture rational and measured aspects of organizational performance and offer a broad organizational context for the analysis, many individual and informal aspects remain vague and isolated. In order to discuss and make sense of the heterogeneous field of interpretations of formal and informal feedback, both in theory and practice, dichotomous approaches seem to be insufficient. Therefore, I suggest an analytical framework of formal and informal feedback with three dimensions (3D’s): source, time, and rule. Based on an abductive analysis of the theoretical and empirical findings from an interpretive case study around a business unit called Division Steelco, the 3Dframework and formal and informal feedback practices are further elaborated vis-á-vis the four thematic layers in the organizational control model by Flamholtz et al. (1985; Flamholtz 1996, 1983): core control system, organizational structure, organizational culture, and external environment. Various personal and cultural meanings given to the formal and informal feedback practices (“feedback as something”) create multidimensional interpretative contexts. Multidimensional frameworks aim to capture and better understand both the variety of interpretations and their implications to the functionality of feedback practices, important in interpretive research.