•  64
    Logic of secrets in collaboration networks
    with Sara Miner More
    Annals 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
  •  59
    Upper bounds on complexity of Frege proofs with limited use of certain schemata
    Archive for Mathematical Logic 45 (4): 431-446. 2006.
    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…Read more
  •  56
    On interchangeability of Nash equilibria in multi-player strategic games
    with Brittany Nicholls
    Synthese 190 (S1): 1-22. 2013.
    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
  •  50
    Rationally Functional Dependence
    with Brittany Nicholls
    Journal 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
  •  45
    On meta complexity of propositional formulas and propositional proofs
    Archive for Mathematical Logic 47 (1): 35-52. 2008.
    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
  •  41
    Logic of confidence
    with Jia Tao
    Synthese 192 (6): 1821-1838. 2015.
    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
  •  32
    Marketing impact on diffusion in social networks
    with Jia Tao
    Journal of Applied Logic 20 49-74. 2017.
  •  31
    A Dynamic Logic of Data-Informed Knowledge
    with Kaya Deuser, Junli Jiang, and Wenxuan Zhang
    Journal of Philosophical Logic 53 (2): 521-557. 2024.
    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 ax…Read more
  •  29
    An epistemic logic of preferences
    with Anna Ovchinnikova
    Synthese 201 (3): 1-36. 2023.
    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 k…Read more
  •  28
    Everyone knows that someone knows: Quantifiers over epistemic agents
    with Jia Tao
    Review of Symbolic Logic 12 (2): 255-270. 2019.
  •  25
    An epistemic logic of blameworthiness
    with Jia Tao
    Artificial Intelligence 283 (C): 103269. 2020.
  •  25
    Together we know how to achieve: An epistemic logic of know-how
    with Jia Tao
    Artificial Intelligence 262 (C): 279-300. 2018.
  •  25
    The Ryōan-ji axiom for common knowledge on hypergraphs
    with Jeffrey Kane
    Synthese 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
  •  24
    Functional Dependence in Strategic Games
    with Kristine Harjes
    Notre 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.
  •  24
    Price of privacy
    with Jia Tao
    Journal of Applied Logic 20 32-48. 2017.
  •  24
    Knowing-how under uncertainty
    with Jia Tao
    Artificial Intelligence 276 (C): 41-56. 2019.
  •  22
    Symmetry in information flow
    with Jeffrey Kane
    Annals of Pure and Applied Logic 165 (1): 253-265. 2014.
    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
  •  22
    Group Conformity in Social Networks
    with Colby Morrison
    Journal of Logic, Language and Information 29 (1): 3-19. 2020.
    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 …Read more
  •  22
    Independence in Information Spaces
    Studia Logica 100 (5): 953-973. 2012.
    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
  •  21
    Fault tolerance in belief formation networks
    with Sarah Holbrook
    In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence, Springer. pp. 267--280. 2012.
  •  20
    Data-informed knowledge and strategies
    Artificial Intelligence 309 (C): 103727. 2022.
  •  19
    On Modal Logics of Partial Recursive Functions
    Studia Logica 81 (3): 295-309. 2005.
    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 establish…Read more
  •  19
    An Independence Relation for Sets of Secrets
    with Sara Miner More
    Studia Logica 94 (1): 73-85. 2010.
    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.
  •  18
    If You’re Happy, Then You Know It: The Logic of Happiness... and Sadness
    with Sanaz Azimipour
    Logic and Logical Philosophy. forthcoming.
    The article proposes a formal semantics of happiness and sadness modalities in the imperfect information setting. It shows that these modalities are not definable through each other and gives a sound and complete axiomatization of their properties.
  •  15
    On modal logic of deductive closure
    Annals 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
  •  15
    Logic of secrets in collaboration networks
    with Sara More
    Annals 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.
  •  14
    On composition of bounded-recall plans
    with Kaya Deuser
    Artificial Intelligence 289 (C): 103399. 2020.
  •  12
    An Egocentric Logic of Knowing How to Tell Them Apart
    Journal of Symbolic Logic 1-33. forthcoming.
    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 sett…Read more
  •  10
    Counterfactual and seeing-to-it responsibilities in strategic games
    with Jia Tao
    Annals of Pure and Applied Logic 174 (10): 103353. 2023.
  •  10
    Axiomatic theory of betweenness
    with Sanaz Azimipour
    Archive 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.