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111Rationally Functional DependenceJournal of Philosophical Logic 43 (2-3): 603-616. 2014.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 A…Read more
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51Logic of secrets in collaboration networksAnnals of Pure and Applied Logic 162 (12): 959-969. 2011.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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55On modal logic of deductive closureAnnals of Pure and Applied Logic 141 (1): 218-224. 2006.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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206Logic of secrets in collaboration networksAnnals of Pure and Applied Logic 162 (12): 959-969. 2011.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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43Axiomatic theory of betweennessArchive for Mathematical Logic 60 (1): 227-239. 2020.Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.
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101Functional Dependence in Strategic GamesNotre Dame Journal of Formal Logic 57 (3): 341-353. 2016.The article studies properties of functional dependencies between strategies of players in Nash equilibria of multiplayer strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for payoff functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete.
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54The Ryōan-ji axiom for common knowledge on hypergraphsSynthese 191 (14): 3407-3426. 2014.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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University of SouthamptonRegular Faculty
Southampton, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
| Decision Theory and Ethics |
| Game Theory and Ethics |
| Doxastic and Epistemic Logic |