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Refinements to Relation-Theoretic Contraction Principle

Aftab Alam, Reny George, Mohammad Imdad
2022 Axioms  
The aim of this paper is to further refine the relation-theoretic contraction principle by relaxing the conditions of completeness and continuity by replacing their respective relation-theoretic analogues  ...  Moreover, we observe that the notion of d-self-closedness utilized in relation-theoretic contraction principle is more general than the concepts of regularity and strong regularity utilized by earlier  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/axioms11070316 fatcat:xtocehq6xraitgwpgnsslr46li

Descriptor Revision for Conditionals: Literal Descriptors and Conditional Preservation [article]

Kai Sauerwald, Jonas Haldimann, Martin von Berg, Christoph Beierle
2020 arXiv   pre-print
We apply the principle of conditional preservation developed by Kern-Isberner to descriptor revision for conditionals, show how descriptor revision for conditionals under these restrictions can be characterised  ...  This is in contrast to the currently dominating AGM paradigm shaped by Alchourr\'on, G\"ardenfors, and Makinson, where different kinds of changes, like a revision or a contraction, are dealt with separately  ...  Implementation by ChangeOCF We implemented descriptor revision for conditionals and elementary descriptors under the principle of conditional preservation.  ... 
arXiv:2006.01444v1 fatcat:a7msbrn64ncd5i5cd27v54uime

A Conditional Perspective for Iterated Belief Contraction [article]

Kai Sauerwald and Gabriele Kern-Isberner and Christoph Beierle
2019 arXiv   pre-print
According to Boutillier, Darwiche, Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals.  ...  We prove that the new set of postulates conforms semantically to the class of operators like the ones given by Konieczny and Pino P\'erez for iterated contraction.  ...  By using contraposition and the correspondence between contractionals and contractions, the following non-conditional formulation of the principles (C10cond) and (C11cond) can be obtained: (C10) if ¬α  ... 
arXiv:1911.08833v1 fatcat:s2bv3eeaavgxzmlgyy6fn7pamq

The measurement of ranks and the laws of iterated contraction

Matthias Hild, Wolfgang Spohn
2008 Artificial Intelligence  
The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.  ...  Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior.  ...  [25] propose a principle of iterated contraction that they call "Principled Factored Insertion".  ... 
doi:10.1016/j.artint.2008.03.002 fatcat:6u2acqaktzchbmtmxoips3mycq

Metrical fixed point theorems via locally finitely T-transitive binary relations under certain control functions

Aftab Alam, Mohammad Arif, Mohammad Imdad
2019 Miskolc Mathematical Notes  
In this paper, we extend relation-theoretic contraction principle due to Alam and Imdad to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely  ...  T -transitive binary relation, which improves the corresponding fixed point theorems especially due to: Alam and Imdad (J.  ...  The aim of this paper, is to extend relation-theoretic contraction principle due to Alam and Imdad [2] to a suitable class of nonlinear contractions.  ... 
doi:10.18514/mmn.2019.2468 fatcat:57xhqtogj5dgrjshwiho7d5wvi

Nonlinear contractions in metric spaces under locally T-transitive binary relations [article]

Aftab Alam, Mohammad Imdad
2016 arXiv   pre-print
In this paper, we present a variant of Boyd-Wong fixed point theorem in a metric space equipped with a locally T-transitive binary relation, which under universal relation reduces to Boyd-Wong (Proc.  ...  Also, our results extend several other well-known fixed point theorems such as: Alam and Imdad (J. Fixed Point Theory Appl. 17 (4) (2015) 693-702) and Karapinar and Roldan-Lopez-de-Hierro (J.  ...  The authors are also grateful to Professor Mihai Turinici for providing the file of his book chapter.  ... 
arXiv:1512.00348v4 fatcat:n4edb4cm3bgofobtqacm3nw6ti

AGM, Ranking Theory, and the Many Ways to Cope with Examples [chapter]

Wolfgang Spohn
2013 David Makinson on Classical Methods for Non-Classical Problems  
And the other conclusion will be that because of those complexities any inference from such examples to the shape of the basic principles of belief change is premature and problematic.  ...  The paper first explains how the ranking-theoretic belief change or conditionalization rules entail all of the standard AGM belief revision and contraction axioms.  ...  Rankingtheoretic contraction, by contrast, can be iterated (for the complete logic of iterated contraction see Hild and Spohn (2008) ).  ... 
doi:10.1007/978-94-007-7759-0_6 fatcat:jndprl77rngbzdu262h52ci4mi

On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators

Richard Booth, Jake Chandler
2020 Artificial Intelligence  
Darwiche and Pearl's seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision.  ...  In this paper, we supplement the DP postulates and (P) with a number of novel conditions.  ...  Acknowledgements This research was partially supported by the Australian Government through an Australian Research Council Future Fellowship (project number FT160100092) awarded to Jake Chandler.  ... 
doi:10.1016/j.artint.2020.103289 fatcat:qgosdzbpivbbvf5q34cizgmgae

The Tarski–Kantorovitch prinicple and the theory of iterated function systems

Jacek Jachymski, Leslaw Gajek, Piotr Pokarowski
2000 Bulletin of the Australian Mathematical Society  
We show how some results of the theory of iterated function systems can be de rived from the Tarski-Kantorovitch fixed-point principle for maps on partially or dered sets.  ...  As a by-product, we also obtain some new characterisations of continuity of maps on countably compact and sequential spaces.  ...  In this case the countable chain condition of the T-K principle forces the countable compactness of X (see Proposition 4).  ... 
doi:10.1017/s0004972700022243 fatcat:n3grt6lu7bfblnwpmclgnsscpu

Iterated Belief Contraction from First Principles

Abhaya C. Nayak, Randy Goebel, Mehmet A. Orgun
2007 International Joint Conference on Artificial Intelligence  
Importance of contraction for belief change notwithstanding, literature on iterated belief change has by and large centered around the issue of iterated belief revision, ignoring the problem of iterated  ...  We show that this principle is satisfied by the account of iterated belief contraction modelled by Lexicographic State Contraction, and outline its connection with Lexicographic Revision, Darwiche-Pearl's  ...  This is reminiscent of Spohn's account of belief contraction via Ordinal Conditional Functions [Spohn, 1988] , and we take it that this is the relational analogue of Spohn's account of iterated belief  ... 
dblp:conf/ijcai/NayakGO07 fatcat:bmoj7jdww5fufcidku6emjdlfu

Iterated revision and the axiom of recovery: a unified treatment via epistemic states [article]

Samir Chopra, Aditya Ghose, Thomas Meyer
2002 arXiv   pre-print
This provides a framework in which iterated revision becomes possible and makes explicit the connection between iterated belief change and the axiom of recovery.  ...  We provide a representation theorem that connects the semantic conditions that we impose on iterated revision and the additional syntactical properties mentioned.  ...  (R8) says that if a belief is contained in the original knowledge base, then that belief will be preserved under a sequence of revisions which begin with revision followed by contraction and then revision  ... 
arXiv:cs/0207038v1 fatcat:qxwaqi3l75auxfg4gfxh76cxnm

Minimal belief change, Pareto-optimality and logical consequence

Oliver Schulte
2002 Economic Theory  
It is clear that the principle of keeping constant the relative ranking of possible worlds that are consistent with the new information leads to the preservation principle, K*4.  ...  Since the new information q n = \player 2 has defected for the last n rounds" is logically consistent with p, the proposition that 2 will eventually cooperate, by the preservation principle K*4 player  ...  In the remainder of this paper, I always assume that the basic language L is closed under the conditional connective. Consider a belief revision system hK; ¤i that satis¯es the Ramsey test.  ... 
doi:10.1007/s001990100194 fatcat:vk3vt6it7fdbfaob46duf33ixe

Three Scenarios for the Revision of Epistemic States

D. Dubois
2008 Journal of Logic and Computation  
In this case, iteration makes sense, and it corresponds to the revision of a conditional knowledge base describing background information by the addition of new default rules.  ...  We argue that this view of iterated revision is at odds with the claim, made by Gärdenfors and Makinson, that belief revision and non-monotonic reasoning are two sides of the same coin.  ...  They extend the Darwiche-Pearl postulates and preserve the minimal change requirement in the sense that they preserve the plausibility ordering ≥ π among the examples A ∧ B of the input conditionals, its  ... 
doi:10.1093/logcom/exm092 fatcat:6hs23ipoq5aolgdzn642tesaea

On Artifacts and Truth-Preservation

Shawn Standefer
2015 The Australasian Journal of Logic  
In Saving Truth from Paradox, Hartry Field presents and defends a theory of truth with a new conditional.  ...  One way of adjusting the theory adequately responds to the truth-preservation criticism, at the cost of making the validity criticism worse.  ...  I would also like to thank Graham Leach-Krouse and the anonymous referee of this journal for helpful feedback.  ... 
doi:10.26686/ajl.v12i3.2045 fatcat:i4hujdqaxvdlxgzp2jld3wnoly

Dynamic Programming with State-Dependent Discounting [article]

John Stachurski, Junnan Zhang
2020 arXiv   pre-print
We obtain a condition on the discount factor process under which all of the standard optimality results can be recovered. We also show that the condition cannot be significantly weakened.  ...  This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting.  ...  Notice that Proposition 6.2 contains no analogue of the eventual contraction condition in Assumption 2.1.  ... 
arXiv:1908.08800v4 fatcat:4sh232xncben5k5wykjv6asvfi
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