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Knowledge and Common Knowledge in a Distributed Environment
- Journal of the ACM
, 1984
"... : Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system&apo ..."
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Cited by 578 (55 self)
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: Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system's state of knowledge. This paper presents a general framework for formalizing and reasoning about knowledge in distributed systems. We argue that states of knowledge of groups of processors are useful concepts for the design and analysis of distributed protocols. In particular, distributed knowledge corresponds to knowledge that is "distributed" among the members of the group, while common knowledge corresponds to a fact being "publicly known". The relationship between common knowledge and a variety of desirable actions in a distributed system is illustrated. Furthermore, it is shown that, formally speaking, in practical systems common knowledge cannot be attained. A number of weaker variants...
A Nonstandard Approach to the Logical Omniscience Problem
- Artificial Intelligence
, 1990
"... We introduce a new approach to dealing with the well-known logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which ..."
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Cited by 54 (4 self)
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We introduce a new approach to dealing with the well-known logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit'belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL. 1
Knowledge, belief and time
- Theoretical Computer Science
, 1988
"... Abstract. In the conclusion of [7] Halpern and Moses expressed their interest in a logical system in which one could talk about knowledge and belief (and belief about knowledge, knowledge about belief and so on), We investigate such systems. In the first part of the paper knowledge and belief, witho ..."
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Cited by 52 (8 self)
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Abstract. In the conclusion of [7] Halpern and Moses expressed their interest in a logical system in which one could talk about knowledge and belief (and belief about knowledge, knowledge about belief and so on), We investigate such systems. In the first part of the paper knowledge and belief, without time, are considered. Common knowledge and common belief are defined and compared. A logical system and a family of models are proposed, a completeness result is proved and a decision procedure described. In the second part of the paper, time is considered. Different notions of beliefs are distinguished, obeying different properties of persistence. One interpretation of belief which obeys a very strong persistence axiom is put forward and used in the analysis of the “wise men ” puzzle. 1.
Reasoning about knowledge: An overview
- Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning About Knowledge
, 1986
"... Abstract: In this overview paper, I will 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 sciencce. I will briefly discuss so ..."
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Cited by 34 (3 self)
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Abstract: In this overview paper, I will 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 sciencce. I will briefly discuss some of the more recent work, particularly in computer science, and suggest some lines for future research.
A logic of intention
- In: Proc. of IJCAI-99
, 1999
"... There is a lot of research on formalization of intention. The common idea of these theories is to interprete intention as an unary modal operator in Kripkean semantics. These theories suffer from the side-effect problem seriously. We introduce an alternative approach by establishing a nonclassical l ..."
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Cited by 7 (3 self)
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There is a lot of research on formalization of intention. The common idea of these theories is to interprete intention as an unary modal operator in Kripkean semantics. These theories suffer from the side-effect problem seriously. We introduce an alternative approach by establishing a nonclassical logic of intention. This logic is based on a novel non-Kripkean semantics which embodies some cognitive features. We show that this logic does provide a formal specification and a decidable inference mechanism of intention consequences. All and only the instances of sideeffects, except ones in absorbent forms, are forbidden
Neutrosophy in Situation Analysis
"... In situation analysis (SA), an agent observing a scene receives information from heterogeneous sources of information including for example remote sensing devices, human reports and databases. The aim of this agent is to reach a certain level of awareness of the situation in order to make decisions. ..."
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Cited by 3 (0 self)
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In situation analysis (SA), an agent observing a scene receives information from heterogeneous sources of information including for example remote sensing devices, human reports and databases. The aim of this agent is to reach a certain level of awareness of the situation in order to make decisions. For the purpose of applications, this state of awareness can be conceived as a state of knowledge in the classical epistemic logic sense. Considering the logical connection between belief and knowledge, the challenge for the designer is to transform the raw, imprecise, conflictual and often paradoxical information received from the different sources into statements understandable by both man and machines. Hence, quantitative (i.e. measuring the world) and qualitative (i.e. reasoning about the structure of the world) information processing coexist in SA. A great challenge in SA is the conciliation of both aspects in mathematical and logical frameworks. As a consequence, SA applications need frameworks general enough to take into account the different types of uncertainty and information present in the SA context, doubled with a semantics allowing meaningful reasoning on situations. The aim of this paper is to evaluate the capacity of neutrosophic logic and Dezert- Smarandache theory (DSmT) to cope with the ontological and epistemological problems of SA.
N-TUPLE ALGEBRA-BASED PROBABILISTIC LOGIC
, 2008
"... The concept of “probabilistic logic ” known in artificial intelligence needs a more thorough substantiation. A new approach to constructing probabilistic logic based on the N-tuple algebra developed by the author is proposed. A brief introduction is given to the N-tuple algebra and its properties th ..."
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Cited by 1 (1 self)
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The concept of “probabilistic logic ” known in artificial intelligence needs a more thorough substantiation. A new approach to constructing probabilistic logic based on the N-tuple algebra developed by the author is proposed. A brief introduction is given to the N-tuple algebra and its properties that provide efficient paralleling of algorithms for solving problems of logical analysis of systems in computer implementation are generalized. Methods for solving direct and inverse problems of probabilistic simulation of logical systems are considered.
Guillaume Aucher An Internal Version of
"... Abstract. Representing an epistemic situation involving several agents obviously depends on the modeling point of view one takes. We start by identifying the types of modeling points of view which are logically possible. We call the one traditionally followed by epistemic logic the perfect external ..."
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Abstract. Representing an epistemic situation involving several agents obviously depends on the modeling point of view one takes. We start by identifying the types of modeling points of view which are logically possible. We call the one traditionally followed by epistemic logic the perfect external approach, because there the modeler is assumed to be an omniscient and external observer of the epistemic situation. In the rest of the paper we focus on what we call the internal approach, where the modeler is one of the agents involved in the situation. For this approach we propose and axiomatize a logical formalism based on epistemic logic. This leads us to formalize some intuitions about the internal approach and about its connections with the external ones. Finally, we show that our internal logic is decidable and PSPACE-complete.
Logical Omniscience As Infeasibility
"... Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, al ..."
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Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. Keywords: epistemic logic, logical omniscience, justification logic, complexity theory
A GUIDE TO THE MODAL LOGICS OF KNOWLEDGE AND BELIEF:
"... Abstract: We review and re-examine possible-worlds semantics for propositional logics of knowledge and belief with four particular points of emphasis: (1) we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief, (2) we show ..."
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Abstract: We review and re-examine possible-worlds semantics for propositional logics of knowledge and belief with four particular points of emphasis: (1) we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief, (2) we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system, (3) we discuss how notions of common knowledge and implicit knowledge among a group of agents fit into the possible-worlds framework, and (4) we consider to what extent the possible-worlds approach is a viable one for modelling knowledge and belief. As far as complexity is concerned, we show among other results that while the problem of deciding satisfiability of an S5 formula with one knower is NP-complete, the problem for many knowers is PSPACE-complete. Adding an implicit knowledge operator does not change the complexity substantially, but once a common knowledge operator is added to the language, the problem becomes complete for exponential time. 1.
