Satisfaction classes in nonstandard models of first-order arithmetic

A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively saturated. A proof of this fact is presented in detail in such a way that it is adaptable to a language with function symbols. The idea that a satisfaction class can only see finitely deep in a formula is extended to terms. The definition gives rise to new notions of valuations of nonstandard terms; these are investigated. The notion of a free satisfaction class is introduced, it is a satisfaction class free of existential assumptions on nonstandard terms. It is well known that pathologies arise in some satisfaction classes. Ideas of how to remove those are presented in the last chapter. This is done mainly by adding inference rules to M-logic. The consistency of many of these extensions is left as an open question.Comment: Thesis for the degree of licentiate of philosophy, 74 pages, 4 figure

Characterizing Quantifier Extensions of Dependence Logic

We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.Comment: 9 page

Expansions, omitting types, and standard systems

Recursive saturation and resplendence are two important notions in models of arithmetic. Kaye, Kossak, and Kotlarski introduced the notion of arithmetic saturation and argued that recursive saturation might not be as rigid as first assumed. In this thesis we give further examples of variations of recursive saturation, all of which are connected with expandability properties similar to resplendence. However, the expandability properties are stronger than resplendence and implies, in one way or another, that the expansion not only satisfies a theory, but also omits a type. We conjecture that a special version of this expandability is in fact equivalent to arithmetic saturation. We prove that another of these properties is equivalent to \beta-saturation. We also introduce a variant on recursive saturation which makes sense in the context of a standard predicate, and which is equivalent to a certain amount of ordinary saturation. The theory of all models which omit a certain type p(x) is also investigated. We define a proof system, which proves a sentence if and only if it is true in all models omitting the type p(x). The complexity of such proof systems are discussed and some explicit examples of theories and types with high complexity, in a special sense, are given. We end the thesis by a small comment on Scott's problem. We prove that, under the assumption of Martin's axiom, every Scott set of cardinality <2^{\aleph_0} closed under arithmetic comprehension which has the countable chain condition is the standard system of some model of PA. However, we do not know if there exists any such uncountable Scott sets.Comment: Doctoral thesi

The propositional logic of teams

Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team semantic constructions have been used to generate expressively enriched logics still conserving nice properties, such as compactness or decidability. In contrast, these logics fail to be substitutional, limiting any algebraic treatment, and rendering schematic uniform proof systems impossible. This shortcoming can be attributed to the flatness principle, commonly adhered to when generating team semantics. Investigating the formation of team semantics from algebraic semantics, and disregarding the flatness principle, we present the logic of teams, LT, a substitutional logic for which important propositional team logics are axiomatisable as fragments. Starting from classical propositional logic and Boolean algebras, we give semantics for LT by considering the algebras that are powersets of Boolean algebras B, equipped with internal (point-wise) and external (set-theoretic) connectives. Furthermore, we present a well-motivated complete and sound labelled natural deduction system for LT.Comment: 28 page

Dependence logic with generalized quantifiers : Axiomatizations

Peer reviewe

Contributions of lean production to the development of sustainable business practices in the food industry : the case of Arla Foods

Corporations in the food industry are under pressure from stakeholders to take responsibility for their social and environmental impact (Garnett, 2013). In the struggle, several initiatives have been implemented where the aim is to find a balance between financial, social as well as environmental aspects (Amani et al., 2015). Lean production is an initiative where the aim is to increase productivity and efficiency by the elimination of waste (Kovach & Cho, 2011). One of the cornerstones of lean production is to focus on a long term philosophy where value should be created for society as well as for the corporation (Liker, 2004). This means that if lean production is used as intended, it could lead to the creation of shared value. Shared value implicates that corporations take into account social, environmental and financial aspects when building strategies, and that focus should be on creating value in these three aspects (Porter & Kramer, 2011). Therefore, the aim in this study is to explain the role of lean production in developing sustainable business practices in the food industry. The study is based on a qualitative approach where Arla Foods, a global dairy cooperative, poses as case company. Managers at Arla Foods have been interviewed and their perceptions from working with lean production makes the foundation for the analysis. The material is analyzed using a theoretical framework that builds on lean production as described by Liker (2004) and shared value by Porter and Kramer (2011). The theoretical framework suggests that lean production could lead to the creation of shared value. This is also supported by the empirical evidence that shows that shared value is created because a long term philosophy is implemented where values in social, environmental and financial aspects are created. The empirical evidence also shows that the main incentive with lean production is to lower corporate costs and increase productivity and efficiency, why the values created for society seems to be spin-offs from the financial benefits. However, when striving to minimize corporate costs, benefits for society are created as well. More specifically, lean production leads to lowered use of energy and water as well as lowered levels of food waste and emission. Lean production also increases the well-being, motivation, health and work safety among employees. This study contributes to a growing number of research focusing on the relation between lean production and sustainable development in the food industry. It makes a theoretical contribution by showing that a corporation can generate benefits for society when applying lean production. Empirically it contributes by showing how managers in the food industry perceive the work on lean in relation to sustainable development. The results of the study could be used to create strategies for managing sustainability issues in the food industry.Företag inom livsmedelsindustrin är under press från intressenter att ta ansvar för de sociala och miljömässiga konsekvenserna som deras aktiviteter ger upphov till (garnett, 2013). Flera initiativ har genomförts med syftet att hitta en balans mellan ekonomiska, sociala och miljömässiga aspekter (Amani et al., 2015). Lean production är ett initiativ där syftet är att öka produktiviteten och effektiviteten inom företag genom eliminering av olika typer av slöseri (Kovach & Cho, 2011). En av hörnstenara i lean production är att skapa en långsiktig filosofi där värde inte bara ska skapas för företaget, utan även för samhället som det verkar i (Liker, 2004). Om lean production används som Liker (2004) förespråkar skulle det därför kunna användas för att skapa shared value. Shared value är ett begrepp som utvecklats av Porter och Kramer (2011) och innebär att företag ska ta hänsyn till sociala, miljömässiga och ekonomiska aspekter när de bygger sina strategier. Fokus ska vara att skapa värde i dessa tre aspekter. Syftet med studien är därför att förklara betydelsen av lean i utvecklingen av hållbara affärsmetoder inom livsmedelsindustrin. Studien genomförs med en kvalitativ ansats där Arla Foods, ett globalt mejerikooperativ, står som fallföretag. Personer med ansvar för lean production inom Arla Foods har intervjuats och deras uppfattningar av att arbeta på lean i förhållande till en hållbar utveckling utgör grunden för analysen. Materialet analyseras med hjälp av ett teoretisk ramverk bestående av lean production så som beskrivits av Liker (2004) och shared value av Porter and Kramer (2011). Den teoretiska referensramen föreslår att lean kan leda till skapandet av shared value. Detta stöds också av de empiriska bevisen som visar att shared value skapas eftersom en långsiktig filosofi är tillämpad där värden i sociala, miljömässiga och ekonomiska aspekter skapas. De empiriska bevisen visar också att det primära incitamentet med lean production är att sänka företagskostnader och öka produktiviteten och effektiviteten, varför de värden som skapas för samhället verkar vara bieffekter av de ekonomiska värdena som skapas. När företaget strävar efter att minimera kostnader skapas fördelar för samhället också. Mer specifikt leder lean produktion till sänkt användning av energi och vatten samt sänkta nivåer av matavfall och utsläpp. Lean production ökar också välbefinnande, motivation, hälsa och arbetssäkerhet bland de anställda. Denna studie bidrar till den växande litteratur av forskning som fokuserar på förhållandet mellan lean production och hållbar utveckling inom livsmedelsindustrin. Den ger ett teoretisk bidrag genom att visa att ett företag kan skapa fördelar för samhället genom att tillämpa lean production. Empiriskt bidrar studien genom att visa hur managers inom livsmedelsindustrin uppfattar arbetet med lean production. Resultatet av studien kan användas för att skapa strategier för att hantera hållbarhetsfrågor inom livsmedelsindustrin