On Variants of Dependence Logic : Axiomatizability and Expressiveness

Dependence logic is a novel logical formalism that has connections to database theory, statistics, linguistics, social choice theory, and physics. Its aim is to provide a systematic and mathematically rigorous tool for studying notions of dependence and independence in different areas. Recently many variants of dependence logic have been studied in the contexts of first-order, modal, and propositional logic. In this thesis we examine independence and inclusion logic that are variants of dependence logic extending first-order logic with so-called independence or inclusion atoms, respectively. The work consists of two parts in which we study either axiomatizability or expressivity hierarchies regarding these logics. In the first part we examine whether there exist some natural parameters of independence and inclusion logic that give rise to infinite expressivity or complexity hierarchies. Two main parameters are considered. These are arity of a dependency atom and number of universal quantifiers. We show that for both logics, the notion of arity gives rise to strict expressivity hierarchies. With respect to number of universal quantifiers however, strictness or collapse of the corresponding hierarchies turns out to be relative to the choice of semantics. In the second part we turn attention to axiomatizations. Due to their complexity, dependence and independence logic cannot have a complete recursively enumerable axiomatization. Hence, restricting attention to partial solutions, we first axiomatize all first-order consequences of independence logic sentences, thus extending an analogous result for dependence logic. We also consider the class of independence and inclusion atoms, and show that it can be axiomatized using implicit existential quantification. For relational databases this implies a sound and complete axiomatization of embedded multivalued and inclusion dependencies taken together. Lastly, we consider keys together with so-called pure independence atoms and prove both positive and negative results regarding their finite axiomatizability.Riippuvuuslogiikka on formalismi, joka tutkii muodollisen logiikan viitekehyksessä riippuvuuden ja riippumattomuuden käsitteitä. Koska nämä käsitteet ilmenevät myös monilla muilla eri tieteenaloilla, riippuvuuslogiikan tutkimus kytkeytyy muun muassa tietokantateoriaan, tilastotieteeseen, kielitieteeseen, sosiaalisen valinnan teoriaan ja fysiikkaan. Ideana riippuvuuslogiikassa on laajentaa tunnettuja muodollisen logiikan kieliä erilaisilla riippuvuuden käsitteillä. Propositio-, modaali- ja predikaattilogiikoille voidaan kaikille määritellä laajennoksia, joissa riippuvuuksia ilmaistaan uusien atomikaavojen avulla. Tämä väitöskirja tarkastelee kahta tällaista ensimmäisen kertaluvun predikaattilogiikan laajennosta. Toisessa uudet atomikaavat kuvaavat riippumattomuuden, ja toisessa sisältyvyyden käsitteitä. Saatuja laajennoksia kutsutaan riippumattomuuslogiikaksi ja inkluusiologiikaksi. Tutkielma jakautuu kahteen osaan. Ensimmäisessä osassa tarkastellaan edellä mainittujen logiikoiden ilmaisuvoimaan ja laskennalliseen vaativuuteen liittyviä hierarkioita. Kyseiset hierarkiat saadaan rajoittamalla joko uusien atomikaavojen kokoa tai universaalikvanttorien lukumäärää. Toisessa osassa tutkitaan riippumattomuus- ja inkluusiologiikan muodollista päättelyä. Tarkastelun kohteena on muodollisen päättelyn kehittäminen riippumattomuuslogiikan ensimmäisen kertaluvun seurauksille sekä erilaisille kokoelmille uusia atomikaavoja. Jälkimmäiseen tapaukseen kehitetty muodollisen päättelyn teoria soveltuu erityisesti relationaalisten tietokantojen riippuvuuskäsitteiden implikaatio-ongelmiin

A Neocolonial Warp of Outmoded Hierarchies, Curricula and Disciplinary Technologies in Trinidad’s Educational System

I re-appropriate the image of a space-time warp and its notion of disorientation to argue that colonialism created a warp in Trinidad’s educational system. Through an analysis of school violence and the wider network of structural violence in which it is steeped, I focus on three outmoded aspects as evidence of this warp--hierarchies, curricula and disciplinary technologies--by using data (interviews, documents and observations) from a longitudinal case study at a secondary school in Trinidad. Colonialism was about exclusion, alienation, violence, control and order, and this functionalism persists today; I therefore contend that hierarchies, curricula and disciplinary technologies are all enforcers of these tenets of (neo)colonialism in Trinidad’s schools. I conclude with some nascent thoughts on a Systemic Restorative Praxis (SRP) model as a way of de-stabilizing the warp, by stitching together literature/approaches from systems thinking, restorative justice and Freirean notions of praxis. SRP implies that colonialism (and this modern-day warp) has rendered much psychic and material damage, and that any intervention to address structural violence has to be systemic and iterative in scope and process, include healing, be participatory, and foster an ethic of horizontalization in human relations

Centre-periphery tensions regarding Central and Eastern Europe

Security issues have played an important role in widening the European Union with eight Central and Eastern European economies. The time since have proved these concerns to be correct. The present North-South tension within the Euro-zone highlights even more the West-East tensions inherent in the international relations since the Eastern enlargement. Various divisions – political and economic alike – have already been felt throughout the whole period of 2004-20122 (Balázs, J.1985, 1993, 1995, 1996). The worldwide economic crisis of 2008, however, has revealed even more the hidden tensions in these relations. The political events after the 2010 election in Hungary, those in Romania in 2012, the continuous anti-EU declarations of the Czech president present ample evidence to the fact: the enlargement has been based more on political wishes and will than on firm economic reasoning. The outcome is constant struggle between the parties to keep face and save the state of the European Union. Ongoing political and economic struggles around Greece, Portugal and Spain are other forms of fundamental problems within the European Union. It is worthwhile, hence to study the almost forgotten centre – periphery relations in this respect

Hierarchies, relational contracts and new forms of outsourcing.

We observe that economic restructuring is significantly changing organizational governance. On the one hand, we witness an increase in mergers & acquisitions, which substitutes markets for hierarchies and, on the other hand, we see an increase in outsourcing and subcontracting activities, appearing to replace hierarchies by markets. However, there is evidence that an increasing part of outsourcing activities mix hierarchies with market forms of governance. The key argument of this paper is that firms have established governance structures based on markets, hierarchies and self-enforcing relational contracts so that they are able to keep a substantial amount of control despite of sourcing out labour. Furthermore, we argue that such hierarchical forms of outsourcing produce dependency. Using empirical evidence of the Austrian insurance industry, it is demonstrated that dependency is created, firstly, by the contractual restriction of alternative uses of resources, secondly, by support measures that bind the upstream party closely to the downstream party, thirdly, by relationship-specific investments made by the upstream party, and fourthly, by authority elements.

Balancing risks and rewards: the logic of violence

Violence is widespread throughout the natural world, prominent examples being predatory violence between species, seasonal violent competition for mating rights and territories within species and food competition both within and between species. These interactions are generally between unrelated individuals with no social connection. There are, however, examples of violent behaviour which occurs within groups of individuals who otherwise cooperate to live, have significant social bonds and may also be related, and that is the primary focus of this paper. Examples are in the establishment and maintenance of dominance hierarchies, or in infanticide, where (usually) incoming males attempt to kill existing infants in a group. Such violence can seem paradoxical, but in fact is often perfectly logical for the individual perpetrating the violence, as distinct from the group as a whole. We discuss such situations from the perspective of evolutionary game theory, and also consider wider questions of interspecific violence

The Expressive Power of k-ary Exclusion Logic

In this paper we study the expressive power of k-ary exclusion logic, EXC[k], that is obtained by extending first order logic with k-ary exclusion atoms. It is known that without arity bounds exclusion logic is equivalent with dependence logic. By observing the translations, we see that the expressive power of EXC[k] lies in between k-ary and (k+1)-ary dependence logics. We will show that, at least in the case of k=1, the both of these inclusions are proper. In a recent work by the author it was shown that k-ary inclusion-exclusion logic is equivalent with k-ary existential second order logic, ESO[k]. We will show that, on the level of sentences, it is possible to simulate inclusion atoms with exclusion atoms, and this way express ESO[k]-sentences by using only k-ary exclusion atoms. For this translation we also need to introduce a novel method for "unifying" the values of certain variables in a team. As a consequence, EXC[k] captures ESO[k] on the level of sentences, and we get a strict arity hierarchy for exclusion logic. It also follows that k-ary inclusion logic is strictly weaker than EXC[k]. Finally we will use similar techniques to formulate a translation from ESO[k] to k-ary inclusion logic with strict semantics. Consequently, for any arity fragment of inclusion logic, strict semantics is more expressive than lax semantics.Comment: Preprint of a paper in the special issue of WoLLIC2016 in Annals of Pure and Applied Logic, 170(9):1070-1099, 201