: We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say "according to agent i, formula ' holds with probability at least b." The language is powerful enough to allow reasoning about higher-order probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, and consider various properties that might hold of the interrelationship between agents' probability assignments at different states. We provide a complete axiomatization for reasoning about knowledge and probability, prove a small model property, and obtain decision procedures. We then consider the effects of adding common knowledge and a probabilistic variant of common knowledge to the language. A preliminary version of this paper appeared in the Proceedings of the Second Conference on T...

We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the model-checking problem.

: We present a formal model that captures the subtle interaction between knowledge and action in distributed systems. We view a distributed system as a set of runs, where a run is a function from time to global states and a global state is a tuple consisting of an environment state and a local state for each process in the system. This model is a generalization of those used in many previous papers. Actions in this model are associated with functions from global states to global states. A protocol is a function from local states to actions. We extend the standard notion of a protocol by defining knowledge-based protocols, ones in which a process' actions may depend explicitly on its knowledge. Knowledge-based protocols provide a natural way of describing how actions should take place in a distributed system. Finally, we show how the notion of one protocol implementing another can be captured in our model. Some material in this paper appeared in preliminary form in [HF85]. An abridge...

Reasoning about activities in a distributed computer system at the level of the knowledge of individuals and groups allows us to abstract away from many concrete details of the system we are considering. In this paper, we make use of two notions introduced in our recent book to facilitate designing and reasoning about systems in terms of knowledge. The first notion is that of a knowledge-based program. A knowledge-based program is a syntactic object: a program with tests for knowledge. The second notion is that of a context, which captures the setting in which a program is to be executed. In a given context, a standard program (one without tests for knowledge) is represented by (i.e., corresponds in a precise sense to) a unique system. A knowledge-based program, on the other hand, may be represented by no system, one system, or many systems. In this paper, we provide a sufficient condition for a knowledge-based program to be represented in a unique way in a given context. This condit...

While the intuition underlying a zero knowledge proof system [GMR85] is that no "knowledge" is leaked by the prover to the verifier, researchers are just beginning to analyze such proof systems in terms of formal notions of knowledge. In this paper, we show how interactive proof systems motivate a new notion of practical knowledge, and we capture the definition of an interactive proof system in terms of practical knowledge. Using this notion of knowledge, we formally capture and prove the intuition that the prover does not leak any knowledge of any fact (other than the fact being proven) during a zero knowledge proof. We extend this result to show that the prover does not leak any knowledge of how to compute any information (such as the factorization of a number) during a zero knowledge proof. Finally, we de ne the notion of a weak interactive proof in which the prover is limited to probabilistic, polynomial-time computations, and we prove analogous security results for such proof systems. We showthat, in a precise sense, any nontrivial weak interactive proof must be a proof about the prover's knowledge, and show that, under natural conditions, the notions of interactive proofs of knowledge defined in [TW87] and [FFS87] are instances of weak interactive proofs.

: In this survey, I attempt to identify and describe some of the common threads that tie together work in reasoning about knowledge in such diverse fields as philosophy, economics, linguistics, artificial intelligence, and theoretical computer science, with particular emphasis on work of the past five years, particularly in computer science. This articule is essentially the same as one that appears in Handbook of of Logic in Artificial Intelligence and Logic Programming, Vol. 4, D. Gabbay, C. J. Hogger, and J. A. Robinson, eds., Oxford University Press, 1995, pp. 1--34. It is a revised and updated version of a paper entitled "Reasoning about knowledge: a survey circa 1991", which appears in the Encyclopedia of Computer Science and Technology, Vol. 27, Supplement 12 (ed. A. Kent and J. G. Williams), Marcel Dekker, 1993, pp. 275--296. That article, in turn is a revision of an article entitled "Reasoning About Knowledge: An Overview" that appears in Theoretical Aspects of Reasoning Abou...

The syntactic approach to epistemic logic avoids the logical omniscience problem by taking knowledge as primary rather than as defined in terms of possible worlds. In this study, we combine the syntactic approach with modal logic, using transition systems to model reasoning. We use two syntactic epistemic modalities: ‘knowing at least ’ a set of formulae and ‘knowing at most’ a set of formulae. We are particularly interested in models restricting the set of formulae known by an agent at a point in time to be finite. The resulting systems are investigated from the point of view of axiomatization and complexity. We show how these logics can be used to formalise non-omniscient agents who know some inference rules, and study their relationship to other systems of syntactic epistemic logics,

Abstract not found

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning "Yes" to a query about a fact # provides evidence for # being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.

Abstract not found