DIFFERENCE-MAKING CONDITIONALS AND THE RELEVANT RAMSEY TEST

2019 ◽  
pp. 1-32 ◽  
Author(s):  
HANS ROTT
Keyword(s):  
Belief Revision ◽  
Classical Theory ◽  
Belief State ◽  
Conditional Logic ◽  
Counterfactual Analysis ◽  
Ramsey Test ◽  
Difference Making ◽  
Alternative Version ◽  
Almost All

Abstract This article explores conditionals expressing that the antecedent makes a difference for the consequent. A ‘relevantised’ version of the Ramsey Test for conditionals is employed in the context of the classical theory of belief revision. The idea of this test is that the antecedent is relevant to the consequent in the following sense: a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent fails to be accepted if the belief state is revised by the antecedent’s negation. The connective thus defined violates almost all of the traditional principles of conditional logic, but it obeys an interesting logic of its own. The article also gives the logic of an alternative version, the ‘Dependent Ramsey Test,’ according to which a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent is rejected (e.g., its negation is accepted) if the belief state is revised by the antecedent’s negation. This conditional is closely related to David Lewis’s counterfactual analysis of causation.

(DIS)BELIEF CHANGE AND ARGUED FEED-BACK DIALOG

2005 ◽  
Vol 13 (05) ◽  
pp. 511-538
Author(s):  
LAURENT PERRUSSEL ◽  
JEAN-MARC THÉVENIN
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Preference Relation ◽  
Belief State ◽  
Temporal Aspects ◽  
Incoming Information ◽  
Multi Agent

This paper focuses on the features of belief change in a multi-agent context where agents consider beliefs and disbeliefs. Disbeliefs represent explicit ignorance and are useful to prevent agents to entail conclusions due to their ignorance. Agents receive messages holding information from other agents and change their belief state accordingly. An agent may refuse to adopt incoming information if it prefers its own (dis)beliefs. For this, each agent maintains a preference relation over its own beliefs and disbeliefs in order to decide if it accepts or rejects incoming information whenever inconsistencies occur. This preference relation may be built by considering several criteria such as the reliability of the sender of statements or temporal aspects. This process leads to non-prioritized belief revision. In this context we first present the * and − operators which allow an agent to revise, respectively contract, its belief state in a non-prioritized way when it receives an incoming belief, respectively disbelief. We show that these operators behave properly. Based on this we then illustrate how the receiver and the sender may argue when the incoming (dis)belief is refused. We describe pieces of dialog where (i) the sender tries to convince the receiver by sending arguments in favor of the original (dis)belief and (ii) the receiver justifies its refusal by sending arguments against the original (dis)belief. We show that the notion of acceptability of these arguments can be represented in a simple way by using the non-prioritized change operators * and −. The advantage of argumentation dialogs is twofold. First whenever arguments are acceptable the sender or the receiver reconsider its belief state; the main result is an improvement of the reconsidered belief state. Second the sender may not be aware of some sets of rules which act as constraints to reach a specific conclusion and discover them through argumentation dialogs.

scholarly journals Revision and Conditional Inference for Abstract Dialectical Frameworks

2021 ◽  
Author(s):  
Jesse Heyninck ◽  
Gabriele Kern-Isberner ◽  
Tjitze Rienstra ◽  
Kenneth Skiba ◽  
Matthias Thimm
Keyword(s):  
Belief Revision ◽  
Research Topic ◽  
Conditional Inference ◽  
Ramsey Test ◽  
The One ◽  
Exact Relationship ◽  
Nonmonotonic Inference ◽  
Total Preorder

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

Belief revision, epistemic conditionals and the Ramsey test

Synthese ◽  
1992 ◽  
Vol 91 (3) ◽  
pp. 195-237 ◽  
Author(s):  
Sten Lindstr�m ◽  
Wlodzimierz Rabinowicz
Keyword(s):  
Belief Revision ◽  
Ramsey Test

scholarly journals Observations on Darwiche and Pearl's Approach for Iterated Belief Revision

2019 ◽  
Author(s):  
Theofanis Aravanis ◽  
Pavlos Peppas ◽  
Mary-Anne Williams
Keyword(s):  
Belief Revision ◽  
Possible Worlds ◽  
Belief State ◽  
Strong Sense ◽  
Preference Ordering ◽  
Satisfactory Solution ◽  
Entire Class ◽  
Seminal Work ◽  
Iterated Belief Revision ◽  
Belief States

Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The seminal work of Darwiche and Pearl (DP approach, for short) remains the most dominant, despite its well-documented shortcomings. In this article, we make further observations on the DP approach. Firstly, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can be captured by identifying belief states with total preorders over possible worlds, a fact implying that a preference ordering (over possible worlds) is an insufficient representation for a belief state.

scholarly journals Revision by Conditionals: From Hook to Arrow

2020 ◽  
Author(s):  
Jake Chandler ◽  
Richard Booth
Keyword(s):  
Belief Revision ◽  
Independent Interest ◽  
Plug And Play ◽  
Ramsey Test ◽  
Iterated Belief Revision

The belief revision literature has largely focussed on the issue of how to revise one’s beliefs in the light of information regarding matters of fact. Here we turn to an important but comparatively neglected issue: How to model agents capable of acquiring information regarding which rules of inference (‘Ramsey Test conditionals’) they ought to use in reasoning about these facts. Our approach to this second question of so-called ‘conditional revision’ is distinctive insofar as it abstracts from the controversial details of how the address the first. We introduce a ‘plug and play’ method for uniquely extending any iterated belief revision operator to the conditional case. The flexibility of our approach is achieved by having the result of a conditional revision by a Ramsey Test conditional (‘arrow’) determined by that of a plain revision by its corresponding material conditional (‘hook’). It is shown to satisfy a number of new constraints that are of independent interest.

BELIEF-REVISION, THE RAMSEY TEST, MONOTONICITY, AND THE SO-CALLED IMPOSSIBILITY RESULTS

2008 ◽  
Vol 1 (4) ◽  
pp. 402-423
Author(s):  
NEIL TENNANT
Keyword(s):  
Belief Revision ◽  
Impossibility Result ◽  
Rational Belief ◽  
Methodological Error ◽  
Ramsey Test ◽  
Impossibility Results ◽  
Definition Of ◽  
New Diagnosis ◽  
Made In ◽  
Monotonicity Principle

Peter Gärdenfors proved a theorem purporting to show that it is impossible to adjoin to the AGM-postulates for belief-revision a principle of monotonicity for revisions. The principle of monotonicity in question is implied by the Ramsey test for conditionals. So Gärdenfors’ result has been interpreted as demonstrating that it is impossible to combine the Ramsey test for conditionals with the basic postulates for rational belief-revision. It is shown here that this interpretation of Gärdenfors’ result is unwarranted. A new diagnosis is offered of a methodological error made in the statement of the key principle of monotonicity. Crucial applications of this principle in Gärdenfors’ proof require one to regard as revisions what are really expansions. If monotonicity is stated only for genuine revisions, then Gärdenfors’ proof does not go through. Nor can it; for, when the monotonicity principle for revisions is correctly formulated, one can actually establish a contrary consistency result. This requires only a slight adjustment to the postulates of AGM-theory, in order to ensure that the three operations of expansion, contraction, and revision trichotomize the domain of theory-changes. It is further shown that being careful in this way about the proper domains of definition of the three operations of expansion, contraction, and revision also disposes of another, more direct, impossibility result, due to Arló-Costa, that targets the Ramsey test.

scholarly journals Ranking kinematics for revising by contextual information

2021 ◽  
Author(s):  
Meliha Sezgin ◽  
Gabriele Kern-Isberner ◽  
Christoph Beierle
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Contextual Information ◽  
Proof Of Concept ◽  
Ranking Functions ◽  
Ramsey Test ◽  
Local Contexts ◽  
Iterated Belief Revision ◽  
Probability Kinematics ◽  
Set Up

AbstractProbability kinematics is a leading paradigm in probabilistic belief change. It is based on the idea that conditional beliefs should be independent from changes of their antecedents’ probabilities. In this paper, we propose a re-interpretation of this paradigm for Spohn’s ranking functions which we call Generalized Ranking Kinematics as a new principle for iterated belief revision of ranking functions by sets of conditional beliefs with respect to their specific subcontext. By taking into account semantical independencies, we can reduce the complexity of the revision task to local contexts. We show that global belief revision can be set up from revisions on the local contexts via a merging operator. Furthermore, we formalize a variant of the Ramsey-Test based on the idea of local contexts which connects conditional and propositional revision in a straightforward way. We extend the belief change methodology of c-revisions to strategic c-revisions which will serve as a proof of concept.

A Conditional Logic for Belief Revision

1998 ◽  
pp. 294-308 ◽  
Author(s):  
Laura Giordano ◽  
Valentina Gliozzi ◽  
Nicola Olivetti
Keyword(s):  
Belief Revision ◽  
Conditional Logic

scholarly journals Iterated Belief Base Revision: A Dynamic Epistemic Logic Approach

2019 ◽  
Vol 33 ◽  
pp. 3076-3083 ◽  
Author(s):  
Marlo Souza ◽  
Álvaro Moreira ◽  
Renata Vieira
Keyword(s):  
Belief Revision ◽  
Epistemic Logic ◽  
Belief Change ◽  
Dynamic Epistemic Logic ◽  
Belief State ◽  
Revision Operation ◽  
Belief Bases ◽  
Negative Results ◽  
Base Revision ◽  
Iterated Belief Revision

AGM’s belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been largely used to specify the agent’s belief state - whether representing the agent’s ‘explicit beliefs’ or as a computational model for her belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. This work investigates how priority graphs, a syntactic representation of preference relations deeply connected to prioritised bases, can be used to characterise belief change operators, focusing on well-known postulates of Iterated Belief Change. We provide syntactic representations of belief change operators in a dynamic context, as well as new negative results regarding the possibility of representing an iterated belief revision operation using transformations on priority graphs.

Sign in / Sign up

Export Citation Format

Share Document