Knowledge, Certainty, Belief, and Conditionalisation (abbreviated version)

Lamarre, Philippe; Shoham, Yoav

doi:10.1016/b978-1-4832-1452-8.50134-2

Cited by 31 publications

(38 citation statements)

References 6 publications

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“…In this paper we employ one such model: a plausibility structure consisting of a set of states and a single plausibility ordering (which is reflexive, transitive and connected) w v that says "v is at least as plausible as w." Originally used as a semantics for conditionals (cf. [24]), these plausibility models have been extensively used by logicians [34,35,8], game theorists [12] and computer scientists [14,23] to represent rational agents' (all-out) beliefs. We thus take for granted that they provide a natural model of beliefs in games:…”

Section: Describing An Informational Contextmentioning

confidence: 99%

A Dynamic Analysis of Interactive Rationality

Pacuit¹,

Roy²

2016

Logic, Epistemology, and the Unity of Science

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Abstract. Epistemic game theory has shown the importance of informational contexts in understanding strategic interaction. We propose a general framework to analyze how such contexts may arise. The idea is to view informational contexts as the fixed-points of iterated, "rational responses" to incoming information about the agents' possible choices. We show general conditions for the stabilization of such sequences of rational responses, in terms of structural properties of both the decision rule and the information update policy. Background and MotivationAn increasingly popular 3 view is that "the fundamental insight of game theory [is] that a rational player must take into account that the players reason about each other in deciding how to play" [6, pg. 81]. Exactly how the players (should) incorporate the fact that they are interacting with other (actively reasoning) agents into their own decision making process is the subject of much debate. A variety of frameworks explicitly model the reasoning of rational agents in a strategic situation. Key examples include Brian Skyrms' models of "dynamic deliberation" [32], Ken Binmore's analysis of "eductive reasoning" [11], and Robin Cubitt and Robert Sugden's "common modes of reasoning" [17]. Although the details of these frameworks are quite different they share a common line of thought: In contrast to classical game theory, solution concepts are no longer the basic object of study. Instead, the "rational solutions" of a game are the result of individual (rational) decisions in specific informational "contexts".This perspective on the foundations of game theory is best exemplified by the so-called epistemic program in game theory (cf. [15]). The central thesis here is that the basic mathematical model of a game should include an explicit parameter describing the players' informational attitudes. However, this broadly decision-theoretic stance does not simply reduce the question of decision-making in interaction to that of rational decision making in the face of uncertainty or ignorance. Crucially, higher-order information (belief about beliefs, etc.)

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Section: Describing An Informational Contextmentioning

confidence: 99%

A Dynamic Analysis of Interactive Rationality

Pacuit¹,

Roy²

2016

Logic, Epistemology, and the Unity of Science

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“…The description of the agent's doxastic state can be enriched if we also consider what the agent would believe if she was confronted with new evidence about the current situation. This has led Lamarre and Shoham in (Lamarre and Shoham, 1994) to define two operators of conditional belief, B ψ φ and B ψ w φ. 13 The semantics of these operators of conditional belief is based on the semantics of default statements.…”

Section: Remarkmentioning

confidence: 99%

“…The authors of (Friedman and Halpern, 1997) and (Lamarre and Shoham, 1994) interpret a default statement ψ ⊃ φ as a conditional belief statement: 'the agent believes φ, given assumption ψ' or more precisely 'if ψ were announced to the agent, she would believe that φ held (before the announcement)'. Given this intended interpretation, the notion of strong belief Bφ (resp.…”

Section: Remarkmentioning

confidence: 99%

“…This quest for reasoning principles somehow vanished in the 1980's when epistemic logic was taken over by computer scientists to address other problems related to various applications. In the early 1990's, however, new interaction axioms relating knowledge and conditional belief were elicited by some researchers in artificial intelligence (Moses and Shoham, 1993;Lamarre and Shoham, 1994).…”

Section: Introductionmentioning

confidence: 99%

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Principles of Knowledge, Belief and Conditional Belief

Aucher

2014

Logic, Argumentation &Amp; Reasoning

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International audienceWe review and examine in this paper the validity of the different axioms (and inference rules) of knowledge and belief and relating knowledge to belief which have been proposed in the epistemic !epistemic logic literature. In doing so, we encounter many of the problems that epistemic !epistemic logic has had to face in its relatively short (modern) history and provide relevant pointers for more details. We also contribute to this area by providing conditions under which the notion of belief can be formally defined in terms of knowledge , and vice versa. We also prove that certain convoluted axioms dealing only with the notion of knowledge can be derived from understandable interaction axioms relating knowledge and conditional belief

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“…Early seminal work includes that of Gärdenfors [1988], Alchourron, Gärdenfors and Makinson [1985] (after whom "AGM revision" is named), and Katsuno and Mendelzon [1991], who introduced the distinction between belief revision and belief update. The material in the chapter on knowledge, certainty, and belief is based on Boutilier [1992] and Lamarre and Shoham [1994]. The material in the section on belief fusion is based on Maynard-Reid and Shoham [2001] and Maynard-Zhang and Lehmann [2003].…”

Section: History and Referencesmentioning

confidence: 99%