Abstract:
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established.

Abstract:
The paper studies properties of functional dependencies between strategies of players in Nash equilibria of multi-player strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for pay-off functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete.

Abstract:
The paper studies properties of functional dependencies between strategies of players in Nash equilibria of multi-player strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for pay-off functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete.

Abstract:
The notion of interchangeability has been introduced by John Nash in one of his original papers on equilibria. This paper studies properties of Nash equilibria interchangeability in cellular games that model behavior of infinite chain of homogeneous economic agents. The paper shows that there are games in which strategy of any given player is interchangeable with strategies of players in an arbitrary large neighborhood of the given player, but is not interchangeable with the strategy of a remote player outside of the neighborhood. The main technical result is a sound and complete logical system describing universal properties of interchangeability common to all cellular games.

Abstract:
The paper investigates epistemic properties of information flow under communication protocols with a given topological structure of the communication network. The main result is a sound and complete logical system that describes all such properties. The system consists of a variation of the multi-agent epistemic logic S5 extended by a new network-specific Gateway axiom.

Abstract:
The paper investigates properties of the conditional independence relation between pieces of information. This relation is also known in the database theory as embedded multivalued dependency. In 1980, Parker and Parsaye-Ghomi established that the properties of this relation can not be described by a finite system of inference rules. In 1995, Herrmann proved that the propositional theory of this relation is undecidable. The main result of this paper is a complete recursively enumerable axiomatization of this theory.

Abstract:
The paper considers epistemic properties of linear communication chains. It describes a sound and complete logical system that, in addition to the standard axioms of S5 in a multi-modal language, contains two non-trivial axioms that capture the linear structure of communication chains.

Abstract:
Armstrong's axioms of functional dependency form a well-known logical system that captures properties of functional dependencies between sets of database attributes. This article assumes that there are costs associated with attributes and proposes an extension of Armstrong's system for reasoning about budget-constrained functional dependencies in such a setting. The main technical result of this article is the completeness theorem for the proposed logical system. Although the proposed axioms are obtained by just adding cost subscript to the original Armstrong's axioms, the proof of the completeness for the proposed system is significantly more complicated than that for the Armstrong's system.

Abstract:
A collaboration network is a graph formed by communication channels between parties. Parties communicate over these channels to establish secrets, simultaneously enforcing interdependencies between the secrets. The paper studies properties of these interdependencies that are induced by the topology of the network. In previous work, the authors developed a complete logical system for one such property, independence, also known in the information flow literature as nondeducibility. This work describes a complete and decidable logical system for the functional dependence relation between sets of secrets over a collaboration network. The system extends Armstrong's system of axioms for functional dependency in databases.

Abstract:
The octahedral cluster core of the anion in the structure of the title compound, (C16H36N)3[Mo6(C4H9S)6(μ3-Cl)7(μ3-S)]·2H2O, has -3 site symmetry. Two μ3-Cl atoms fully occupy positions in the cluster core, while the remaining six positions are statistically occupied by Cl and S atoms in a 1:5 ratio. The fully occupied Cl-atom positions are located on sites with 3 symmetry, and the N atom of tetrabutylammonium cation is located on a site with 2 symmetry. The structure contains also two disordered solvent water molecules, one of which is located on a threefold rotation axis and the other in a general position, both with an occupancy of 0.25. The water molecules are localized in cavities formed by the tetrabutylammonium cations and the tert-butanethiolate groups. The metal clusters are stacked in a cubic close packing arrangement along [001].