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  1. Pavel Naumov & Jia Tao (2015). Logic of Confidence. Synthese 192 (6):1821-1838.
    The article studies knowledge in multiagent systems where data available to the agents may have small errors. To reason about such uncertain knowledge, a formal semantics is introduced in which indistinguishability relations, commonly used in the semantics for epistemic logic S5, are replaced with metrics to capture how much two epistemic worlds are different from an agent’s point of view. The main result is a logical system sound and complete with respect to the proposed semantics.
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  2. Jeffrey Kane & Pavel Naumov (2014). Symmetry in Information Flow. Annals of Pure and Applied Logic 165 (1):253-265.
    The article investigates information flow properties of symmetric multi-party protocols. It gives a sound and complete axiomatic system for properties of the functional dependence predicate that are common to all protocols with the same group of symmetries.
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  3. Jeffrey Kane & Pavel Naumov (2014). The Ryōan-Ji Axiom for Common Knowledge on Hypergraphs. Synthese 191 (14):3407-3426.
    The article studies common knowledge in communication networks with a fixed topological structure. It introduces a non-trivial principle, called the Ryōan-ji axiom, which captures logical properties of common knowledge of all protocols with a given network topology. A logical system, consisting of the Ryōan-ji axiom and two additional axioms, is proven to be sound and complete.
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  4. Pavel Naumov & Brittany Nicholls (2014). Rationally Functional Dependence. Journal of Philosophical Logic 43 (2-3):603-616.
    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.
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  5. Pavel Naumov & Brittany Nicholls (2013). On Interchangeability of Nash Equilibria in Multi-Player Strategic Games. Synthese 190 (S1):1-22.
    The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory.
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  6. Sarah Holbrook & Pavel Naumov (2012). Fault Tolerance in Belief Formation Networks. In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence. Springer 267--280.
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  7. Pavel Naumov (2012). Independence in Information Spaces. Studia Logica 100 (5):953-973.
    Three different types of interdependence between pieces of information, or "secrets", are discussed and compared. Two of them, functional dependence and non-deducibility, have been studied and axiomatized before. This article introduces a third type of interdependence and provides a complete and decidable axiomatization of this new relation.
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  8. Sara Miner More & Pavel Naumov (2011). Logic of Secrets in Collaboration Networks. Annals of Pure and Applied Logic 162 (12):959-969.
    The article proposes Logic of Secrets in Collaboration Networks, a formal logical system for reasoning about a set of secrets established over a fixed configuration of communication channels. The system’s key feature, a multi-channel relation called independence, is a generalization of a two-channel relation known in the literature as nondeducibility. The main result is the completeness of the proposed system with respect to a semantics of secrets.
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  9. Sara Miner More & Pavel Naumov (2010). An Independence Relation for Sets of Secrets. Studia Logica 94 (1):73 - 85.
    A relation between two secrets, known in the literature as nondeducibility , was originally introduced by Sutherland. We extend it to a relation between sets of secrets that we call independence . This paper proposes a formal logical system for the independence relation, proves the completeness of the system with respect to a semantics of secrets, and shows that all axioms of the system are logically independent.
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  10. Pavel Naumov (2010). Sara Miner More. Studia Logica 94:1-13.
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  11. Pavel Naumov (2008). On Meta Complexity of Propositional Formulas and Propositional Proofs. Archive for Mathematical Logic 47 (1):35-52.
    A new approach to defining complexity of propositional formulas and proofs is suggested. Instead of measuring the size of these syntactical structures in the propositional language, the article suggests to define the complexity by the size of external descriptions of such constructions. The main result is a lower bound on proof complexity with respect to this new definition of complexity.
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  12. Pavel Naumov (2006). On Modal Logic of Deductive Closure. Annals of Pure and Applied Logic 141 (1):218-224.
    A new modal logic is introduced. It describes properties of provability by interpreting modality as a deductive closure operator on sets of formulas. Logic is proven to be decidable and complete with respect to this semantics.
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  13. Pavel Naumov (2006). Upper Bounds on Complexity of Frege Proofs with Limited Use of Certain Schemata. Archive for Mathematical Logic 45 (4):431-446.
    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 (...)
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  14. Pavel Naumov (2005). On Modal Logics of Partial Recursive Functions. Studia Logica 81 (3):295 - 309.
    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.
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