Conditional logics of normality: a modal approach
TL;DR: A family of modal logics is presented in which a conditional connective is defined for statements of normality and its properties are examined, and it is demonstrated that two of the most important conditional approaches are equivalent to fragments of the authors' conditional logics ofnormality.
About: This article is published in Artificial Intelligence.The article was published on 1994-07-01. It has received 246 citations till now. The article focuses on the topics: Non-monotonic logic & T-norm fuzzy logics.
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TL;DR: This work shows how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added, and obtains complete logics for concrete mechanisms of belief revision based on compositional reduction axioms.
Abstract: We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations.
408 citations
Book•
12 Jun 2014TL;DR: A new view of logic as a theory of information-driven agency and intelligent interaction between many agents is developed, unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory.
Abstract: This book develops a new view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.
393 citations
01 Jan 1994
TL;DR: A logical calculus is developed that employs the basic elements of classical decision theory, namely probabilities, utilities and actions, but exploits qualitative information about these elements directly for the derivation of goals.
Abstract: We present a logic for representing and reasoning with qualitative statements of preference and normality and describe how these may interact in decision making under uncertainty. Our aim is to develop a logical calculus that employs the basic elements of classical decision theory, namely probabilities, utilities and actions, but exploits qualitative information about these elements directly for the derivation of goals. Preferences and judgements of normality are captured in a modal/conditional logic, and a simple model of action is incorporated. Without quantitative information, decision criteria other than maximum expected utility are pursued. We describe how techniques for conditional default reasoning can be used to complete information about both preferences and normality judgements, and we show how maximin and maximax strategies can be expressed in our logic.
348 citations
Cites background from "Conditional logics of normality: a ..."
...The properties of the connective I are identical to those of the conditional connective ) defined in [2, 7] for default reasoning (see also Section 4)....
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...The logic of conditional normality statements can be given a probabilistic interpretationas described in [7]....
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...4 These truth conditions can be expressed in LB (see [3, 7]): I(BjA) df $2:A _$3(A ^2(A B)): (1)...
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...(4)Of course, nothing in our models forces the existence of such minimal A-worlds, but our definition is adequate in this case as well [7]....
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...This conditional is exactly that defined in [3, 7], and the associated logic is equivalent to a number of other systems (e....
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TL;DR: A complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms that can model changing obligations, conflicting commands, or ‘regret' and is concluded that the dynamic framework is viable, while admitting a further extension to more numerical ‘utility update'.
Abstract: Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ‘upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or ‘regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with preferences between actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical ‘utility update'.
213 citations
TL;DR: A model of iterated belief revision is described that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent, and ensures that an agent makes as few changes as possible to the conditional component of its belief set.
Abstract: We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a “virtual’ manner, using uniterated revision.
184 citations
References
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Book•
01 Jan 1974TL;DR: The authors described three heuristics that are employed in making judgements under uncertainty: representativeness, availability of instances or scenarios, and adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available.
Abstract: This article described three heuristics that are employed in making judgements under uncertainty: (i) representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; (ii) availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and (iii) adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty.
31,082 citations
TL;DR: This paper proposes a logic for default reasoning, develops a complete proof theory and shows how to interface it with a top down resolution theorem prover, and provides criteria under which the revision of derived beliefs must be effected.
4,146 citations
TL;DR: The authors formalizes such conjectural reasoning and shows that the objects they can determine to have certain properties or relations are the only objects that do, which is a common assumption in human and intelligent computer programs.
1,892 citations
01 Jan 1968
TL;DR: A conditional sentence expresses a proposition which is a function of two other propositions, yet not one which is truth function of those propositions as mentioned in this paper, which has given rise to a number of philosophical problems.
Abstract: A conditional sentence expresses a proposition which is a function of two other propositions, yet not one which is a truth function of those propositions I may know the truth values of “Willie Mays played in the American League” and “Willie Mays hit four hundred” without knowing whether or not Mays, would have hit four hundred if he had played in the American League This fact has tended to puzzle, displease, or delight philosophers, and many have felt that it is a fact that calls for some comment or explanation It has given rise to a number of philosophical problems; I shall discuss three of these
1,725 citations
01 Jan 1977
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.
Abstract: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead (as in classical logic) to irrelevant conclusions. The actual form of the four-valued logic is ‘deduced’ from an interplay of this motivating consideration with certain ideas of Dana Scott concerning ‘approximation lattices.’
1,477 citations