
Pavel NaumovUniversity of Southampton · Department of Electronics and Computer Science (ECS)
Pavel Naumov
Ph.D., Cornell University
About
153
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Introduction
The area of my current interests in foundations of AI ethics. I also published papers on logical systems for reasoning about multiagent systems, coalition strategies, privacy, uncertainty, information flow, formal epistemology, and social networks.
Publications
Publications (153)
Security games are an example of a successful real-world application of game theory. The paper defines blameworthiness of the defender and the attacker in security games using the principle of alternative possibilities and provides a sound and complete logical system for reasoning about blameworthiness in such games. Two of the axioms of this syste...
The paper investigates the second-order blameworthiness or duty to warn modality "one coalition knew how another coalition could have prevented an outcome". The main technical result is a sound and complete logical system that describes the interplay between the distributed knowledge and the duty to warn modalities.
Blameworthiness of an agent or a coalition of agents can be defined in terms of the principle of alternative possibilities: for the coalition to be responsible for an outcome, the outcome must take place and the coalition should be a minimal one that had a strategy to prevent the outcome. In this article we argue that in the settings with imperfect...
An agent, or a coalition of agents, faces an ethical dilemma between several statements if she is forced to make a conscious choice between which of these statements will be true. This paper proposes to capture ethical dilemmas as a modality in strategic game settings with and without limit on sacrifice and for perfect and imperfect information gam...
The paper studies two forms of responsibility, seeing to it and being blamable, in the setting of strategic games with imperfect information. The paper shows that being blamable is definable through seeing to it, but not the other way around. In addition, it proposes a bimodal logical system that describes the interplay between the seeing to it mod...
Common knowledge/belief in rationality is the traditional standard assumption in analysing interaction among agents. This paper proposes a graph-based language for capturing significantly more complicated structures of higher-order beliefs that agents might have about the rationality of the other agents. The two main contributions are a solution co...
Originally proposed by Prior, egocentric logic is a class of logical systems that capture properties of agents rather than of possible worlds. The article proposes a doxastic egocentric system with rigid names for reasoning about beliefs that an agent might have about herself.
Traditionally, knowledge and beliefs are attributed to agents. The article explores an alternative approach where knowledge is informed by data and belief comes from trust in, not necessarily reliable, data. At the core of the article is the modality “if one dataset is trusted, then another dataset informs a belief”. The main technical result is a...
If an agent prefers one kind of agents to the other agents, then the agent has first-order preferences. If the agent prefers agents with one kind of preferences to the other agents, then the agent has second-order preferences. The article proposes a sound, complete, and decidable logical system capable of expressing higher-order preferences.
In many real-world situations, there is often not enough information to know that a certain strategy will succeed in achieving the goal, but there is a good reason to believe that it will. The paper introduces the term "doxastic" for such strategies. The main technical contribution is a sound and complete logical system that describes the interplay...
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.
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 proper...
The article proposes de dicto and de re versions of ‘knowing-who’ modalities as well as studies the interplay between them and modalities ‘knows’ and ‘for all agents’. It shows that neither of these four modalities is definable through a combination of the three others. In addition, a sound and complete logical system describing the properties of d...
An operation is called covert if it conceals the identity of the actor; it is called clandestine if the very fact that the operation is conducted is concealed. The paper proposes a formal semantics of clandestine operations and introduces a sound and complete logical system that describes the interplay between the distributed knowledge modality and...
The article proposes a new approach to reasoning about knowledge and strategies in multiagent systems. It emphasizes data, not agents, as the source of strategic knowledge. The approach brings together Armstrong's functional dependency expression from database theory, a data-informed knowledge modality based on a recent work by Baltag and van Benth...
Prior proposes the term "egocentric" for logical systems that study properties of agents rather than properties of possible worlds. In such a setting, the paper introduces two different modalities capturing de re and de dicto knowledge and proves that these two modalities are not definable through each other.
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...
An operation is called covert if it conceals the identity of the actor; it is called clandestine if the very fact that the operation is conducted is concealed. The paper proposes a formal semantics of clandestine operations and introduces a sound and complete logical system that describes the interplay between the distributed knowledge modality and...
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 tru...
The Agents, Interaction and Complexity research group at the University of Southampton has a long track record of research in multiagent systems (MAS). We have made substantial scientific contributions across learning in MAS, game-theoretic techniques for coordinating agent systems, and formal methods for representation and reasoning. We highlight...
The paper studies the interplay between modalities representing four different types of multistep strategies in the imperfect information setting. It introduces a new "truth set algebra'' technique for proving undefinability, which is significantly different from the existing techniques based on bisimulation. The newly proposed technique is used to...
The Agents, Interaction and Complexity research group at the University of Southampton has a long track record of research in multiagent systems (MAS). We have made substantial scientific contributions across learning in MAS, game-theoretic techniques for coordinating agent systems, and formal methods for representation and reasoning. We highlight...
If an agent, or a coalition of agents, has a strategy, knows that she has a strategy, and knows what the strategy is, then she has a know-how strategy. Several modal logics of coalition power for know-how strategies have been studied before. The contribution of the article is three-fold. First, it proposes a new class of know-how strategies that de...
dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We show that possibilistic logic is the unique logic that can...
Lexicographic inference is a well-known and popular approach to reasoning with non-monotonic conditionals. It is a logic of very high-quality, as it extends rational closure and avoids the so-called drowning problem. It seems, however, this high quality comes at a cost, as reasoning on the basis of lexicographic inference is of high computational c...
The paper studies strategic abilities that rise from restrictions on the information sharing in multi-agent systems. The main technical result is a sound and complete logical system that describes the interplay between the knowledge and the strategic ability modalities.
The article proposes a new approach to reasoning about knowledge and strategies in multiagent systems. It emphasizes data, not agents, as the source of strategic knowledge. The approach brings together Armstrong's functional dependency expression from database theory, a data-informed knowledge modality based on a recent work by Baltag and van Benth...
Discounting future costs and rewards is a common practice in accounting, game theory and machine learning. In spite of this, existing logics for reasoning about strategies with cost and resource constraints do not account for discounting. The article proposes a sound and complete logical system for reasoning about budget-constrained strategic abili...
This paper proposes a novel way to compare classes of strategic games based on their sets of pure Nash equilibria. This approach is then used to relate the classes of zero-sum games, polymatrix, and k-polymatrix games. This paper concludes with a conjecture that k-polymatrix games form an increasing chain of classes.
If an agent, or a coalition of agents, has a strategy, knows that she has a strategy, and knows what the strategy is, then she has a know-how strategy. Several modal logics of coalition power for know-how strategies have been studied before.
The contribution of the article is three-fold. First, it proposes a new class of know-how strategies that d...
An agent, or a coalition of agents, faces an ethical dilemma between several statements if she is forced to make a conscious choice between which of these statements will be true. This paper proposes to capture ethical dilemmas as a modality in strategic game settings with and without limit on sacrifice and for perfect and imperfect information gam...
The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main technical result is a completeness theorem for the proposed system.
The ability of an agent to comprehend a sentence is tightly connected to the agent's prior experiences and background knowledge. The paper suggests to interpret comprehension as a modality and proposes a complete bimodal logical system that describes an interplay between comprehension and knowledge modalities.
Discounting future costs and rewards is a common practice in accounting, game theory, and machine learning. In spite of this, existing logics for reasoning about strategies with cost and resource constraints do not account for discounting. The paper proposes a sound and complete logical system for reasoning about budget-constrained strategic abilit...
Discounting future costs and rewards is a common practice in accounting, game theory, and machine learning. In spite of this, existing logics for reasoning about strategies with cost and resource constraints do not account for discounting. The paper proposes a sound and complete logical system for reasoning about budget-constrained strategic abilit...
The paper investigates an evidence-based semantics for epistemic logics. It is shown that the properties of knowledge obtained from a potentially infinite body of evidence are described by modal logic S5. At the same time, the properties of knowledge obtained from only a finite subset of this body are described by modal logic S4. The main technical...
The article compares two different approaches of incorporating probability into coalition logics. One is based on the semantics of games with stochastic transitions, and the other on games with the stochastic failures. The work gives an example of a non-trivial property of coalition power for the first approach and a complete axiomatization for the...
The article proposes a trimodal logical system that can express the strategic ability of coalitions to learn from their experience. The main technical result is the completeness of the proposed system.
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...
The article proposes a formal semantics of happiness and sadness modalities in imperfect information setting. It shows that these modalities are not definable through each other and gives a sound and complete axiomatization of their properties.
The ability of an agent to comprehend a sentence is tightly connected to the agent's prior experiences and background knowledge. The paper suggests to interpret comprehension as a modality and proposes a complete bimodal logical system that describes an interplay between comprehension and knowledge modalities.
The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main technical result is a completeness theorem for the proposed system.
The ability of an agent to comprehend a sentence is tightly connected to the agent's prior experiences and background knowledge. The paper suggests to interpret comprehension as a modality and proposes a complete bimodal logical system that describes an interplay between comprehension and knowledge modalities.
The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main technical result is a completeness theorem for the proposed system.
The article studies the ability of agents with bounded memory to execute con- secutive composition of plans. It gives an upper limit on the amount of memory required to execute the composed plans and shows that the limit cannot be im- proved. Furthermore, the article shows that there are, essentially, no other univer- sal properties of plans for bo...
Logical systems containing knowledge and know-how modalities have been investigated in several recent works. Independently, epistemic modal logics in which every knowledge modality is labeled with a degree of uncertainty have been proposed. This article combines these two research lines by introducing a bimodal logic containing knowledge and know-h...
If an agent, or a coalition of agents, knows that it has a strategy to achieve a certain outcome, it does not mean that the agent knows what the strategy is. Even if the agent knows what the strategy is, she might not know the price of executing this strategy.
The article considers modality “the coalition not only knows the strategy, but also knows...
Security games are an example of a successful real-world application of game theory. The paper defines blameworthiness of the defender and the attacker in security games using the principle of alternative possibilities and provides a sound and complete logical system for reasoning about blameworthiness in such games. Two of the axioms of this syste...
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 th...
Security games are an example of a successful real-world application of game theory. The paper defines blameworthiness of the defender and the attacker in security games using the principle of alternative possibilities and provides a sound and complete logical system for reasoning about blameworthiness in such games. Two of the axioms of this syste...
The paper investigates the second-order blameworthiness or duty to warn modality "one coalition knew how another coalition could have prevented an outcome". The main technical result is a sound and complete logical system that describes the interplay between the distributed knowledge and the duty to warn modalities.
A coalition of agents, or a single agent, has an ethical dilemma between several statements if each joint action of the coalition forces at least one specific statement among them to be true. For example, any action in the trolley dilemma forces one specific group of people to die. In many cases, agents face ethical dilemmas because they are restri...
The article considers strategies of coalitions that are based on intelligence information about moves of some of the other agents. The main technical result is a sound and complete logical system that describes the interplay between coalition power modality with intelligence and distributed knowledge modality in games with imperfect information.
The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal." The logical properties of this modality depend on whether the modal language allows the empty coalition. The ma...
Resources, Knowledge, and Actions, 2019 ESSLLI Course
There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blamable for a statement if the statement is true, but the coalition had a strategy to prevent it. The main technical result is a sound and complete bimodal logical sy...
Logical systems containing knowledge and know-how modalities have been investigated in several recent works. Independently, epistemic modal logics in which every knowledge modality is labeled with a degree of uncertainty have been proposed. This article combines these two research lines by introducing a bimodal logic containing knowledge and know-h...
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...
A coalition is blameable for an outcome if the coalition had a strategy to prevent it. It has been previously suggested that the cost of prevention, or the cost of sacrifice, can be used to measure the degree of blameworthiness. The paper adopts this approach and proposes a modal logical system for reasoning about the degree of blameworthiness. The...
The article generalizes the standard threshold models of diffusion in social networks by introducing the notion of recalcitrant agents, i.e., agents that are fully resistant to the diffusion process. The focus of the article is on capturing a ternary influence relation between groups of agents: agents in one group can indirectly influence agents in...
There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blamable for a statement if the statement is true, but the coalition had a strategy to prevent it. The main technical result is a sound and complete bimodal logical sy...
Blameworthiness of an agent or a coalition of agents is often defined in terms of the principle of alternative possibilities: for the coalition to be responsible for an outcome, the outcome must take place and the coalition should have had a strategy to prevent it. In this paper we argue that in the settings with imperfect information, not only sho...
There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blamable for a statement if the statement is true, but the coalition had a strategy to prevent it. The main technical result is a sound and complete bimodal logical sy...
There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blam-able for a statement if the statement is true, but the coalition had a strategy to prevent it. The main technical result is a sound and complete bimodal logical s...
Strategies, Knowledge, and Know-How, course slides
Social Networks for Logicians, course slides
The paper studies navigability by machines with bounded recall in mazes with imperfect information. The main result is a sound and complete logical system for the relation "there is a machine with at most n states that can navigate from a set of classes of indistinguishable rooms X to a set of classes of indistinguishable rooms Y''. The axioms of t...
The paper introduces a notion of a transition system with catastrophic failures where in each state and under each action profile of the agents the system might either transition to a next state or fail with a given probability. The main technical result is a sound and complete axiomatization of modality "coalition has a strategy to survive with a...
The article studies navigability of an autonomous agent in a maze where some rooms may be indistinguishable. In a previous work the authors have shown that the properties of navigability in such a setting depend on whether an agent has perfect recall. Navigability by strategies with perfect recall is a transitive relation and navigability by memory...
The existence of a coalition strategy to achieve a goal does not necessarily mean that the coalition has enough information to know how to follow the strategy. Neither does it mean that the coalition knows that such a strategy exists. The article studies an interplay between the distributed knowledge, coalition strategies, and coalition "know-how"...
The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall is captured in the system by a single axiom. The main technical results are the soundness and the completeness...
The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong's axioms from database theory. If the assumption of perfect recall is omitted, then Armstrong's transitivity axiom is not valid, but it can be replaced by a weaker principle. The ma...
The fact that a coalition has a strategy does not mean that the coalition knows what the strategy is. If the coalition knows the strategy, then such a strategy is called a know-how strategy of the coalition. The paper proposes the notion of a second-order know-how strategy for the case when one coalition knows what the strategy of another coalition...
Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of dist...
The article investigates an influence relation between two sets of agents in a social network. It proposes a logical system that captures propositional properties of this relation valid in all threshold models of social networks with the same structure. The logical system consists of Armstrong axioms for functional dependence and an additional Ligh...
The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall is captured in the system by a single axiom. The main technical results are the soundness and the completeness...
The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong's axioms from database theory. If the assumption of perfect recall is omitted, then Armstrong's transitivity axiom is not valid, but it can be replaced by a weaker principle. The ma...
Although first proposed in the database theory as properties of functional dependencies between attributes, Armstrong's axioms capture general principles of information flow by describing properties of dependencies between sets of pieces of information. This article generalizes Armstrong's axioms to a setting in which there is a cost associated wit...
The paper introduces a notion of a budget-constrained multiagent transition system that associates two financial parameters with each transition: a pre-transition minimal budget requirement and a post-transition profit. The paper proposes a new modal language for reasoning about such a system. The language uses a modality labeled by agent as well a...
The existence of a coalition strategy to achieve a goal does not necessarily mean that the coalition has enough information to know how to follow the strategy. Neither does it mean that the coalition knows that such a strategy exists. The paper studies an interplay between the distributed knowledge, coalition strategies, and coalition "know-how" st...
The existence of a coalition strategy to achieve a goal does not necessarily mean that the coalition has enough information to know how to follow the strategy. Neither does it mean that the coalition knows that such a strategy exists. The paper studies an interplay between the distributed knowledge, coalition strategies, and coalition "know-how" st...
The article studies navigability of an autonomous agent in a maze where some rooms may be indistinguishable. In a previous work the authors have shown that the properties of navigability in such a setting depend on whether an agent has perfect recall. Navigability by an agent with perfect recall is a transitive relation and without is not transitiv...
The existence of a coalition strategy to achieve a goal does not necessarily mean that the coalition has enough information to know how to follow the strategy. Neither does it mean that the coalition knows that such a strategy exists. The article studies an interplay between the distributed knowledge, coalition strategies, and coalition "know-how"...
The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong's axioms from the database theory. If the assumption of perfect recall is omitted, then Armstrong's transitivity axiom is not valid, but it can be replaced by two new weaker princip...
The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall is captured in the system by a single axiom. The main technical results are the soundness and the completeness...
The article investigates an evidence-based semantics for epistemic logics in which pieces of evidence are interpreted as equivalence relations on the epistemic worlds. It is shown that the properties of knowledge obtained from potentially infinitely many pieces of evidence are described by modal logic S5. At the same time, the properties of knowled...
The paper proposes a bimodal logic that describes an interplay between coalition strategies and distributed knowledge. Unlike the existing literature, the paper assumes that a strategy must be not only executable but also verifiable. That is, the strategy of a coalition should be based only on the information distributively known by the coalition a...
The article proposes a logical framework for reasoning about agents’ ability to protect their privacy by hiding certain information from a privacy intruder. It is assumed that the knowledge of the intruder is derived from the observation of pieces of evidence and that there is a cost associated with the elimination of the evidence. The logical fram...
Although first proposed in the database theory as properties of functional dependencies between attributes, Armstrong's axioms capture general principles of information flow by describing properties of dependencies between sets of pieces of information. This paper generalizes Armstrong's axioms to a setting in which there is a cost associated with...
The article proposes a way to add marketing into the standard threshold model of social networks. Within this framework, the article studies logical properties of the influence relation between sets of agents in social networks. Two different forms of this relation are considered: one for promotional mar- keting and the other for preventive marketi...