Attainable Knowledge

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 knowledge obtained from only a finite number of pieces of evidence are described by modal logic S4. The main technical result is a sound and complete bi-modal logical system that describes properties of these two modalities and their interplay

Marketing Impact on Diffusion in Social Networks

The paper proposes a way to add marketing into the standard threshold model of social networks. Within this framework, the paper 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 marketing and the other for preventive marketing. In each case a sound and complete logical system describing properties of the influence relation is proposed. Both systems could be viewed as extensions of Armstrong's axioms of functional dependency from the database theory

Knowledge and Blameworthiness

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 article we argue that in the settings with imperfect information, not only should the coalition have had a strategy, but it also should have known that it had a strategy, and it should have known what the strategy was. The main technical result of the article is a sound and complete bimodal logic that describes the interplay between knowledge and blameworthiness in strategic games with imperfect information

Blameworthiness in Strategic Games

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 system that describes properties of blameworthiness in one-shot games

The Budget-Constrained Functional Dependency

Armstrong's axioms of functional dependency form a well-known logical system that captures properties of functional dependencies between sets of database attributes. This article assumes that there are costs associated with attributes and proposes an extension of Armstrong's system for reasoning about budget-constrained functional dependencies in such a setting. The main technical result of this article is the completeness theorem for the proposed logical system. Although the proposed axioms are obtained by just adding cost subscript to the original Armstrong's axioms, the proof of the completeness for the proposed system is significantly more complicated than that for the Armstrong's system

Topics in Knowledge Bases: Epistemic Ontologies and Secrecy-preserving Reasoning

Applications of ontologies/knowledge bases (KBs) in many domains (healthcare, national security, intelligence) have become increasingly important. In this dissertation, we focus on developing techniques for answering queries posed to KBs under the open world assumption (OWA). In the first part of this dissertation, we study the problem of query answering in KBs that contain epistemic information, i.e., knowledge of different experts. We study ALCKm, which extends the description logic ALC by adding modal operators of the basic multi-modal logic Km. We develop a sound and complete tableau algorithm for answering ALCKm queries w.r.t. an ALCKm knowledge base with an acyclic TBox. We then consider answering ALCKm queries w.r.t. an ALCKm knowledge base in which the epistemic operators correspond to those of classical multi-modal logic S4m and provide a sound and complete tableau algorithm. Both algorithms can be implemented in PSpace. In the second part, we study problems that allow autonomous entities or organizations (collectively called querying agents) to be able to selectively share information. In this scenario, the KB must make sure its answers are informative but do not disclose sensitive information. Most of the work in this area has focused on access control mechanisms that prohibit access to sensitive information (secrets). However, such an approach can be too restrictive in that it prohibits the use of sensitive information in answering queries against knowledge bases even when it is possible to do so without compromising secrets. We investigate techniques for secrecy-preserving query answering (SPQA) against KBs under the OWA. We consider two scenarios of increasing difficulty: (a) a KB queried by a single agent; and (b) a KB queried by multiple agents where the secrecy policies can differ across the different agents and the agents can selectively communicate the answers that they receive from the KB with each other subject to the applicable answer sharing policies. We consider classes of KBs that are of interest from the standpoint of practical applications (e.g., description logics and Horn KBs). Given a KB and secrets that need to be protected against the querying agent(s), the SPQA problem aims at designing a secrecy-preserving reasoner that answers queries without compromising secrecy under OWA. Whenever truthfully answering a query risks compromising secrets, the reasoner is allowed to hide the answer to the query by feigning ignorance, i.e., answering the query as Unknown . Under the OWA, the querying agent is not able to infer whether an Unknown answer to a query is obtained because of the incomplete information in the KB or because secrecy protection mechanism is being applied. In each scenario, we provide a general framework for the problem. In the single-agent case, we apply the general framework to the description logic EL and provide algorithms for answering queries as informatively as possible without compromising secrecy. In the multiagent case, we extend the general framework for the single-agent case. To model the communication between querying agents, we use a communication graph, a directed acyclic graph (DAG) with self-loops, where each node represents an agent and each edge represents the possibility of information sharing in the direction of the edge. We discuss the relationship between secrecy-preserving reasoners and envelopes (used to protect secrets) and present a special case of the communication graph that helps construct tight envelopes in the sense that removing any information from them will leave some secrets vulnerable. To illustrate our general idea of constructing envelopes, Horn KBs are considered

A model for storage and query of cascading beliefs in multilevel security database

A database consists of an object space that is information about objects in (some part of) the real world. Every object existing in the real world has properties, including an identity that uniquely distinguishes it from other objects. In a belief database multiple subjects are hypothesized. Subjects have varying beliefs about existence, identities, and other properties of objects. A multilevel security database is a belief database where the subjects form a hierarchy. The upper users can see the object space of lower users but the lower users cannot. In fact lower users may not even be aware of upper users. This paper presents a skeleton based model for storage and query of a multilevel security database. This model follows the parametric approach proposed by Gadia. As in all works in the parametric approach, the central focus of this framework is to support most natural query of data