Pavel Naumov

The paper considers a commonly used axiomatization of the classical propositional logic and studies how different axiom schemata in this system contribute to proof complexity of the logic. The existence of a polynomial bound on proof complexity of every statement provable in this logic is a well-known open question.The axiomatization consists of three schemata. We show that any statement provable using unrestricted number of axioms from the first of the three schemata and polynomially-bounded in size set of axioms from the other schemata, has a polynomially-bounded proof complexity. In addition, it is also established, that any statement, provable using unrestricted number of axioms from the remaining two schemata and polynomially-bounded in size set of axioms from the first scheme, also has a polynomially-bounded proof complexity

Two different types of functional dependencies are compared: dependencies that are functional due to the laws of nature and dependencies that are functional if all involved agents behave rationally. The first type of dependencies was axiomatized by Armstrong. This article gives a formal definition of the second type of functional dependencies in terms of strategic games and describes a sound and complete axiomatization of their properties. The axiomatization is significantly different from the Armstrong’s axioms

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.

With agents relying more and more on information from central servers rather than their own sensors, knowledge becomes property not of a specific agent but of the data that the agents can access. The article proposes a dynamic logic of data-informed knowledge that describes an interplay between three modalities and one relation capturing the properties of this form of knowledge. The main technical results are the undefinability of two dynamic operators through each other, a sound and complete axiomatisation, and a model checking algorithm.

The article studies preferences of agents in a setting with imperfect information. For such a setting, the authors propose a new class of preferences. It is said that an agent prefers one statement over another if, among all indistinguishable worlds, the agent prefers the worlds where the first statement is true to those where the second one is true. The main technical result is a sound and complete logical system describing the interplay between a binary modality capturing preferences and the knowledge modality. The proof of completeness is using a newly proposed “tumbled pairs” technique.

Diffusion in social networks is a result of agents’ natural desires to conform to the behavioral patterns of their peers. In this article we show that the recently proposed “propositional opinion diffusion model” could be used to model an agent’s conformity to different social groups that the same agent might belong to, rather than conformity to the society as whole. The main technical contribution of this article is a sound and complete logical system describing the properties of the influence relation in this model. The logical system is an extension of Armstrong’s axioms from database theory by one new axiom that captures the topological structure of the network.

Traditionally, the formulae in modal logic express properties of possible worlds. Prior introduced “egocentric” logics that capture properties of agents rather than of possible worlds. In such a setting, the article proposes the modality “know how to tell apart” and gives a complete logical system describing the interplay between this modality and the knowledge modality. An important contribution of this work is a new matrix-based technique for proving completeness theorems in an egocentric setting.