Parameterised complexity of model checking and satisfiability in propositional dependence logic

Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to be NP-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is FPT. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture.

Polyteam semantics

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatization for the associated implication problem. We relate polyteam semantics to team semantics and investigate in which cases logics over the former can be simulated by logics over the latter. We also characterize the expressive power of poly-dependence logic by properties of polyteams that are downwards closed and definable in existential second-order logic ($\textsf{ESO}$). The analogous result is shown to hold for poly-independence logic and all $\textsf{ESO}$-definable properties. We also relate poly-inclusion logic to greatest fixed point logic.

Antecedents of Technological Diversification: A Resource Dependence Logic

This paper extends resource dependence logic by investigating the antecedents of technological diversification and further identifies its boundary condition. We argue that this resource dependence logic is bound by state ownership through coalitions with firms, a less discussed component of interdependence. The empirical results, based on a panel data analysis of Chinese listed firms, suggest that environmental dynamism positively relates to technological diversification, while environmental munificence negatively relates to technological diversification. These relationships changed when state ownership is considered. The theoretical implications for resource dependence theory and diversification research are discussed.

LOGICS FOR PROPOSITIONAL DETERMINACY AND INDEPENDENCE

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic${\cal D}$and Propositional Independence Logic${\cal I}$are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics${{\cal L}_D}$and${{\cal L}_{\,I\,}}$, based on Kripke semantics, and propose them as alternatives for${\cal D}$and${\cal I}$, respectively. We analyse the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue that${{\cal L}_D}$and${{\cal L}_{\,I\,}}$naturally resolve a range of interpretational problems that arise in${\cal D}$and${\cal I}$. We also obtain sound and complete axiomatizations for${{\cal L}_D}$and${{\cal L}_{\,I\,}}$.

Rigid and Flexible Quantification in Plural Predicate Logic

Noun phrases with overt determiners, such as some apples or a quantity of milk, differ from bare noun phrases like apples or milk in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal for-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial for-adverbials, habituals, and the quantifier all.