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Joseph Y. Halpern

Publications and source records attributed to Joseph Y. Halpern.

At least 163 records · Page 9Linked to original sources
arXiv2005

Probabilistic Algorithmic Knowledge

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 ϕprovides evidence for ϕbeing true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.

cs.AI↗
arXiv2005

Causes and Explanations: A Structural-Model Approach. Part II: Explanations

We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion paper. Essentially, an explanation is a fact that is not known for certain but, if found to be true, would constitute an actual cause of the fact to be explained, regardless of the agent's initial uncertainty. We show that the definition handles well a number of problematic examples from the literature.

cs.AI↗
arXiv2005

Causes and Explanations: A Structural-Model Approach, Part I: Causes

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficulties in the traditional account.

cs.AI↗
arXiv2005

When Ignorance is Bliss

It is commonly-accepted wisdom that more information is better, and that information should never be ignored. Here we argue, using both a Bayesian and a non-Bayesian analysis, that in some situations you are better off ignoring information if your uncertainty is represented by a set of probability measures. These include situations in which the information is relevant for the prediction task at hand. In the non-Bayesian analysis, we show how ignoring information avoids dilation, the phenomenon that additional pieces of information sometimes lead to an increase in uncertainty. In the Bayesian analysis, we show that for small sample sizes and certain prediction tasks, the Bayesian posterior based on a noninformative prior yields worse predictions than simply ignoring the given information.

cs.AI↗
arXiv2005

Interactive Unawareness Revisited

We analyze a model of interactive unawareness introduced by Heifetz, Meier and Schipper (HMS). We consider two axiomatizations for their model, which capture different notions of validity. These axiomatizations allow us to compare the HMS approach to both the standard (S5) epistemic logic and two other approaches to unawareness: that of Fagin and Halpern and that of Modica and Rustichini. We show that the differences between the HMS approach and the others are mainly due to the notion of validity used and the fact that the HMS is based on a 3-valued propositional logic.

cs.AI↗
arXiv2005

Secrecy in Multiagent Systems

We introduce a general framework for reasoning about secrecy and privacy requirements in multiagent systems. Our definitions extend earlier definitions of secrecy and nondeducibility given by Shannon and Sutherland. Roughly speaking, one agent maintains secrecy with respect to another if the second agent cannot rule out any possibilities for the behavior or state of the first agent. We show that the framework can handle probability and nondeterminism in a clean way, is useful for reasoning about asynchronous systems as well as synchronous systems, and suggests generalizations of secrecy that may be useful for dealing with issues such as resource-bounded reasoning. We also show that a number of well-known attempts to characterize the absence of information flow are special cases of our definitions of secrecy.

cs.CR↗
arXiv2004

Intransitivity and Vagueness

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox.

cs.AI↗
arXiv2004

Sleeping Beauty Reconsidered: Conditioning and Reflection in Asynchronous Systems

A careful analysis of conditioning in the Sleeping Beauty problem is done, using the formal model for reasoning about knowledge and probability developed by Halpern and Tuttle. While the Sleeping Beauty problem has been viewed as revealing problems with conditioning in the presence of imperfect recall, the analysis done here reveals that the problems are not so much due to imperfect recall as to asynchrony. The implications of this analysis for van Fraassen's Reflection Principle and Savage's Sure-Thing Principle are considered.

cs.AI↗
arXiv2004

Anonymity and Information Hiding in Multiagent Systems

We provide a framework for reasoning about information-hiding requirements in multiagent systems and for reasoning about anonymity in particular. Our framework employs the modal logic of knowledge within the context of the runs and systems framework, much in the spirit of our earlier work on secrecy [Halpern and O'Neill 2002]. We give several definitions of anonymity with respect to agents, actions, and observers in multiagent systems, and we relate our definitions of anonymity to other definitions of information hiding, such as secrecy. We also give probabilistic definitions of anonymity that are able to quantify an observer s uncertainty about the state of the system. Finally, we relate our definitions of anonymity to other formalizations of anonymity and information hiding, including definitions of anonymity in the process algebra CSP and definitions of information hiding using function views.

cs.CR↗
arXiv2004

A Knowledge-Theoretic Analysis of Uniform Distributed Coordination and Failure Detectors

It is shown that, in a precise sense, if there is no bound on the number of faulty processes in a system with unreliable but fair communication, Uniform Distributed Coordination (UDC) can be attained if and only if a system has perfect failure detectors. This result is generalized to the case where there is a bound t on the number of faulty processes. It is shown that a certain type of generalized failure detector is necessary and sufficient for achieving UDC in a context with at most t faulty processes. Reasoning about processes' knowledge as to which other processes are faulty plays a key role in the analysis.

cs.DC↗
arXiv2003

Representation Dependence in Probabilistic Inference

Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For example, the principle of maximum entropy has been subjected to much criticism due to its representation dependence. There has, however, been almost no work investigating representation dependence. In this paper, we formalize this notion and show that it is not a problem specific to maximum entropy. In fact, we show that any representation-independent probabilistic inference procedure that ignores irrelevant information is essentially entailment, in a precise sense. Moreover, we show that representation independence is incompatible with even a weak default assumption of independence. We then show that invariance under a restricted class of representation changes can form a reasonable compromise between representation independence and other desiderata, and provide a construction of a family of inference procedures that provides such restricted representation independence, using relative entropy.

cs.AI↗
arXiv2003

What Causes a System to Satisfy a Specification?

Even when a system is proven to be correct with respect to a specification, there is still a question of how complete the specification is, and whether it really covers all the behaviors of the system. Coverage metrics attempt to check which parts of a system are actually relevant for the verification process to succeed. Recent work on coverage in model checking suggests several coverage metrics and algorithms for finding parts of the system that are not covered by the specification. The work has already proven to be effective in practice, detecting design errors that escape early verification efforts in industrial settings. In this paper, we relate a formal definition of causality given by Halpern and Pearl [2001] to coverage. We show that it gives significant insight into unresolved issues regarding the definition of coverage and leads to potentially useful extensions of coverage. In particular, we introduce the notion of responsibility, which assigns to components of a system a quantitative measure of their relevance to the satisfaction of the specification.

cs.LO↗
arXiv2003

Responsibility and blame: a structural-model approach

Causality is typically treated an all-or-nothing concept; either A is a cause of B or it is not. We extend the definition of causality introduced by Halpern and Pearl [2001] to take into account the degree of responsibility of A for B. For example, if someone wins an election 11--0, then each person who votes for him is less responsible for the victory than if he had won 6--5. We then define a notion of degree of blame, which takes into account an agent's epistemic state. Roughly speaking, the degree of blame of A for B is the expected degree of responsibility of A for B, taken over the epistemic state of an agent.

cs.AI↗
arXiv2003

Great Expectations. Part I: On the Customizability of Generalized Expected Utility

We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker's beliefs are represented by plausibility measures, and the decision maker's tastes are represented by general (i.e.,not necessarily real-valued) utility functions. We show that every agent, ``rational'' or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage's postulates corresponds to constraints on GEU.

cs.AI↗
arXiv2003

Using Counterfactuals in Knowledge-Based Programming

This paper adds counterfactuals to the framework of knowledge-based programs of Fagin, Halpern, Moses, and Vardi. The use of counterfactuals is illustrated by designing a protocol in which an agent stops sending messages once it knows that it is safe to do so. Such behavior is difficult to capture in the original framework because it involves reasoning about counterfactual executions, including ones that are not consistent with the protocol. Attempts to formalize these notions without counterfactuals are shown to lead to rather counterintuitive behavior.

cs.DC↗
arXiv2003

A logic for reasoning about upper probabilities

We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.

cs.AI↗
arXiv2003

Modeling Belief in Dynamic Systems, Part I: Foundations

Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better understanding of belief change can be gained from examining appropriate semantic models. In this paper we propose a general framework in which to model belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes p if he knows that p is more plausible than its negation. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin for modeling knowledge in multi-agent systems. We then examine the problem of ``minimal change''. This notion can be captured by using prior plausibilities, an analogue to prior probabilities, which can be updated by ``conditioning''. We show by example that conditioning on a plausibility measure can capture many scenarios of interest. In a companion paper, we show how the two best-studied scenarios of belief change, belief revisionand belief update, fit into our framework.

cs.AI↗