Results for 'Theory contraction'

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  1.  98
    On the Logic of Theory Change: Contraction Without Recovery. [REVIEW]Eduardo L. Fermé - 1998 - Journal of Logic, Language and Information 7 (2):127-137.
    The postulate of Recovery, among the six postulates for theory contraction, formulated and studied by Alchourrón, Gärdenfors and Makinson is the one that has provoked most controversy. In this article we construct withdrawal functions that do not satisfy Recovery, but try to preserve minimal change, and relate these withdrawal functions with the AGM contraction functions.
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  2.  87
    On the Logic of Theory Change: Contraction Functions and Their Associated Revision Functions.Carlos E. Alchourron & David Makinson - 1982 - Theoria 48 (1):14-37.
    A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.
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  3.  48
    Belief Contraction in the Context of the General Theory of Rational Choice.Hans Rott - 1993 - Journal of Symbolic Logic 59 (4):1426-1450.
    This paper reorganizes and further develops the theory of partial meet contraction which was introduced in a classic paper by Alchourron, Gardenfors, and Makinson. Our purpose is threefold. First, we put the theory in a broader perspective by decomposing it into two layers which can respectively be treated by the general theory of choice and preference and elementary model theory. Second, we reprove the two main representation theorems of AGM and present two more representation results (...)
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  4. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions.Carlos E. Alchourrón, Peter Gärdenfors & David Makinson - 1985 - Journal of Symbolic Logic 50 (2):510-530.
    This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or (...)
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  5. Theory Contraction and Base Contraction Unified.Sven Ove Hansson - 1993 - Journal of Symbolic Logic 58 (2):602-625.
    One way to construct a contraction operator for a theory (belief set) is to assign to it a base (belief base) and an operator of partial meet contraction for that base. Axiomatic characterizations are given of the theory contractions that are generated in this way by (various types of) partial meet base contractions.
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  6.  25
    Theory-Contraction is NP-Complete.Neil Tennant - 2003 - Logic Journal of the IGPL 11 (6):675-693.
    I investigate the problem of contracting a dependency-network with respect to any of its nodes. The resulting contraction must not contain the node in question, but must also be a minimal mutilation of the original network. Identifying successful and minimally mutilating contractions of dependency-networks is non-trivial, especially when non-well-founded networks are to be taken into account. I prove that the contraction problem is NP-complete.1.
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  7.  43
    Theory Contraction Through Base Contraction.André Fuhrmann - 1991 - Journal of Philosophical Logic 20 (2):175 - 203.
  8.  60
    On the Logic of Theory Change: Safe Contraction.Carlos E. Alchourrón & David Makinson - 1985 - Studia Logica 44 (4):405 - 422.
    This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its (...)
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  9.  36
    A Consistent Theory of Attributes in a Logic Without Contraction.Richard B. White - 1993 - Studia Logica 52 (1):113 - 142.
    This essay demonstrates proof-theoretically the consistency of a type-free theoryC with an unrestricted principle of comprehension and based on a predicate logic in which contraction (A (A B)) (A B), although it cannot holds in general, is provable for a wide range ofA's.C is presented as an axiomatic theoryCH (with a natural-deduction equivalentCS) as a finitary system, without formulas of infinite length. ThenCH is proved simply consistent by passing to a Gentzen-style natural-deduction systemCG that allows countably infinite conjunctions and (...)
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  10.  23
    Peter Gärdenfors. Knowledge in Flux. Modeling the Dynamics of Epistemic States. Bradford Books. The MIT Press, Cambridge, Mass., and London, 1988, Xi + 262 Pp. - Carlos E. Alchourrón, Peter Gärdenfors, and David Makinson. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. The Journal of Symbolic Logic, Vol. 50 , Pp. 510–530. [REVIEW]André Fuhrmann - 1992 - Journal of Symbolic Logic 57 (4):1479-1481.
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  11. Dialogue with Deviance: The Hasidic Ethic and the Theory of Social Contraction.Mordechai Rotenberg - 1983 - University Press of America.
     
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  12.  12
    Review: Peter Gardenfors, Knowledge in Flux. Modeling the Dynamics of Epistemic States; Carlos E. Alchourron, Peter Gardenfors, David Makinson, On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. [REVIEW]Andre Fuhrmann - 1992 - Journal of Symbolic Logic 57 (4):1479-1481.
  13.  21
    Possible Worlds Semantics for Partial Meet Multiple Contraction.Maurício D. L. Reis & Eduardo Fermé - 2012 - Journal of Philosophical Logic 41 (1):7-28.
    In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985 ). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989 ), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994 ) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of (...)
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  14.  33
    Four Floors for the Theory of Theory Change: The Case of Imperfect Discrimination.Hans Rott - 2014 - In Eduardo Fermé João Leite (ed.), Logics in Artificial Intelligence: 13th European Conference (JELIA 2014). Springer. pp. 368-382.
    The classical qualitative theory of belief change due to Alchourrón, Gärdenfors and Makinson has been widely known as being characterised by two packages of postulates. While the basic package consists of six postulates and is very weak, the full package that adds two further postulates is very strong. I revisit two classic constructions of theory contraction, viz., relational possible worlds contraction and entrenchment-based contraction and argue that four intermediate levels can be distinguished that play - (...)
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  15.  43
    New Foundations for a Relational Theory of Theory-Revision.Neil Tennant - 2006 - Journal of Philosophical Logic 35 (5):489-528.
    AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions 'J is a contraction of K with respect to A' and 'J is a revision of K with respect to A'. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds (...)
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  16.  26
    Three Floors for the Theory of Theory Change.Hans Rott - 2014 - In Vít Punčochář Michal Dančák (ed.), The Logica Yearbook 2013. College Publications. pp. 187-205.
    The theory of theory change due to Alchourrón, Gärdenfors and Makinson ("AGM") has been widely known as being characterized by two sets of postulates, one being very weak and the other being very strong. Commenting on the three classic constructions of partial meet contraction, safe contraction and entrenchment-based construction, I argue that three intermediate levels can be distinguished that play decisive roles within the AGM theory.
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  17. On the logic of theory change: Contraction functions and their associated revision functions.Carlos E. Alchourrón - 1982 - Theoria 48 (1):14.
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  18.  32
    On the Status of the Postulate of Recovery in the Logic of Theory Change.David Makinson - 1987 - Journal of Philosophical Logic 16 (4):383 - 394.
    Describes and discusses the rather special behaviour of one of the postulates in the AGM account of theory change.
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  19.  89
    A Robust Non-Transitive Logic.Alan Weir - 2015 - Topoi 34 (1):1-9.
    Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and (...)
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  20. Contraction: On the Decision-Theoretical Origins of Minimal Change and Entrenchment.Horacio Arló-Costa & Isaac Levi - 2006 - Synthese 152 (1):129 - 154.
    We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic (...)
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  21.  32
    A Note on Partial Meet Package Contraction.Jun Li - 1998 - Journal of Logic, Language and Information 7 (2):139-142.
    It was shown that finite P-recovery holds for partial meet package contraction in Furhmann and Hansson (1994). However, it is not known if recovery holds for partial meet package contraction in the infinite case. In this paper, I show that recovery does not hold for partial meet package contraction in the infinite case.
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  22.  74
    Coherentist Contraction.Sven Ove Hansson - 2000 - Journal of Philosophical Logic 29 (3):315 - 330.
    A model of coherentist belief contraction is constructed. The outcome of belief contraction is required to be one of the coherent subsets of the original belief set, and a set of plausible properties is proposed for this set of coherent subsets. The contraction operators obtained in this way are shown to coincide with well-known belief base operations. This connection between coherentist and "foundationalist" approaches to belief change has important implications for the philosophical interpretation of models of belief (...)
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  23. A Power Algebra for Theory Change.K. Britz - 1999 - Journal of Logic, Language and Information 8 (4):429-443.
    Various representation results have been established for logics of belief revision, in terms of remainder sets, epistemic entrenchment, systems of spheres and so on. In this paper I present another representation for logics of belief revision, as an algebra of theories. I show that an algebra of theories, enriched with a set of rejection operations, provides a suitable algebraic framework to characterize the theory change operations of systems of belief revision. The theory change operations arise as power operations (...)
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  24.  32
    On the Axiom of Extensionality in the Positive Set Theory.Olivier Esser - 2003 - Mathematical Logic Quarterly 49 (1):97-100.
    This is a study of the relative interpretability of the axiom of extensionality in the positive set theory. This work has to be considered in the line of works of R. O. Gandy, D. Scott and R. Hinnion who have studied the relative interpretability of the axiom of extensionality in set theories of Zermelo and Zermelo-Fraenkel.
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  25.  11
    Hirokawa on Right Weakening and Right Contraction.Susan Rogerson - 2007 - In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic. pp. 237--263.
    In his paper, ìRight Weakening and Right Contraction in LK î, Hirokawa investigates the properties of the structural rules of contraction and weak- ening as they appear in a certain sequent calculus formulation of Örst order classical logic. In what follows we explore the notion of correspondence, in particular with reference to the structural rules in the succedent, and in doing so critically examine the sensitivity of Hirokawaís results to the formulation of the calculus, both with respect to (...)
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  26.  24
    Einstein's Pathway to the Special Theory of Relativity.Galina Weinstein - 2015 - Cambridge Scholars Press.
    This book pieces together the jigsaw puzzle of Einstein's journey to discovering the special theory of relativity. Between 1902 and 1905, Einstein sat in the Patent Office and may have made calculations on old pieces of paper that were once patent drafts. One can imagine Einstein trying to hide from his boss, writing notes on small sheets of paper, and, according to reports, seeing to it that the small sheets of paper on which he was writing would vanish into (...)
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  27.  21
    Foundational Belief Change.Abhaya C. Nayak - 1994 - Journal of Philosophical Logic 23 (5):495 - 533.
    This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to satisfy the "supplementary postulates" of belief contraction. Finally Fuhrmann's construction is appropriately modified so as to yield the desired properties. The new construction may be (...)
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  28.  36
    Infobase Change: A First Approximation. [REVIEW]Thomas Andreas Meyer, Willem Adrian Labuschagne & Johannes Heidema - 2000 - Journal of Logic, Language and Information 9 (3):353-377.
    Generalisations of theory change involving operations on arbitrary sets ofwffs instead of on belief sets (i.e., sets closed under a consequencerelation), have become known as base change. In one view, a base should bethought of as providing more structure to its generated belief set, whichmeans that it can be employed to determine the theory contraction operationassociated with a base contraction operation. In this paper we follow suchan approach as the first step in defining infobase change. We (...)
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  29.  89
    A Survey of Multiple Contractions.André Fuhrmann & Sven Ove Hansson - 1994 - Journal of Logic, Language and Information 3 (1):39-75.
    The AGM theory of belief contraction is extended tomultiple contraction, i.e. to contraction by a set of sentences rather than by a single sentence. There are two major variants: Inpackage contraction all the sentences must be removed from the belief set, whereas inchoice contraction it is sufficient that at least one of them is removed. Constructions of both types of multiple contraction are offered and axiomatically characterized. Neither package nor choice contraction can (...)
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  30.  66
    AGM 25 Years: Twenty-Five Years of Research in Belief Change.Eduardo Fermé & Sven Ove Hansson - 2011 - Journal of Philosophical Logic 40 (2):295 - 331.
    The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), "On the Logic of Theory Change: Partial Meet Contraction and Revision Functions" was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twentyfive years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not (...)
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  31.  24
    Changes of Disjunctively Closed Bases.Sven Ove Hansson - 1993 - Journal of Logic, Language and Information 2 (4):255-284.
    An operator of contraction for a belief set (a theory) can be obtained by assigning to it a belief base and an operator of partial meet contraction for that base. It is argued that closure of the base under disjunction is an intuitively reasonable condition. Axiomatic characterizations are given of the contractions of belief sets that can be generated by (various types of) partial meet contraction on disjunctively closed bases. The corresponding revision operators are also characterized. (...)
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  32.  15
    Recovery Recovered.Stephen Murray Glaister - 2000 - Journal of Philosophical Logic 29 (2):171 - 206.
    The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more (...)
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  33.  17
    Recovery Recovered.StephenMurray Glaister - 2000 - Journal of Philosophical Logic 29 (2):171-206.
    The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more (...)
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  34. Quantum Gravity and Taoist Cosmology: Exploring the Ancient Origins of Phenomenological String Theory.Steven M. Rosen - 2017 - Progress in Biophysics and Molecular Biology 131:34-60.
    In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the (...)
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  35.  36
    Mild Contraction: Evaluating Loss of Information Due to Loss of Belief.Isaac Levi - 2004 - Oxford University Press.
    Isaac Levi's new book develops further his pioneering work in formal epistemology, focusing on the problem of belief contraction, or how rationally to relinquish old beliefs. Levi offers the most penetrating analysis to date of this key question in epistemology, offering a completely new solution and explaining its relation to his earlier proposals. He mounts an argument in favor of the thesis that contracting a state of belief by giving up specific beliefs is to be evaluated in terms of (...)
  36. Contraction and Revision.Shawn Standefer - 2016 - Australasian Journal of Logic 13 (3):58-77.
    An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.
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  37.  48
    How to Be Really Contraction Free.Greg Restall - 1993 - Studia Logica 52 (3):381 - 391.
    A logic is said to be contraction free if the rule from A→(A→B) to A→B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be (...)
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  38.  35
    System of Spheres-Based Multiple Contractions.Eduardo Fermé & Maurício D. L. Reis - 2012 - Journal of Philosophical Logic 41 (1):29-52.
    We propose a new class of multiple contraction operations — the system of spheres-based multiple contractions — which are a generalization of Grove’s system of spheres-based (singleton) contractions to the case of contractions by (possibly non-singleton) sets of sentences. Furthermore, we show that this new class of functions is a subclass of the class of the partial meet multiple contractions.
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  39.  69
    NO Revision and NO Contraction.Gregory Wheeler & Marco Alberti - 2011 - Minds and Machines 21 (3):411-430.
    One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an (...)
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  40.  30
    Norm-System Revision: Theory and Application. [REVIEW]Audun Stolpe - 2010 - Artificial Intelligence and Law 18 (3):247-283.
    This paper generalises classical revision theory of the AGM brand to sets of norms. This is achieved substituting input/output logic for classical logic and tracking the changes. Operations of derogation and amendment—analogues of contraction and revision—are defined and characterised, and the precise relationship between contraction and derogation, on the one hand, and derogation and amendment on the other, is established. It is argued that the notion of derogation, in particular, is a very important analytical tool, and that (...)
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  41. Towards a Coherent Theory of Physics and Mathematics: The Theory–Experiment Connection.Paul Benioff - 2005 - Foundations of Physics 35 (11):1825-1856.
    The problem of how mathematics and physics are related at a foundational level is of interest. The approach taken here is to work towards a coherent theory of physics and mathematics together by examining the theory experiment connection. The role of an implied theory hierarchy and use of computers in comparing theory and experiment is described. The main idea of the paper is to tighten the theory experiment connection by bringing physical theories, as mathematical structures (...)
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  42.  19
    Safe Contraction Revisited.Hans Rott & Sven Ove Hansson - 2014 - In Sven Ove Hansson (ed.), David Makinson on Classical Methods for Non-Classical Problems (Outstanding Contributions to Logic, Vol. 3). Springer. pp. 35-70.
    Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe (...)
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  43.  27
    A Real Lorentz-FitzGerald Contraction.Carlos Barceló & Gil Jannes - 2008 - Foundations of Physics 38 (2):191-199.
    Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and (...)
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  44.  18
    Rationality, Theory Acceptance and Decision Theory.J. Nicolas Kaufmann - 1998 - Principia: An International Journal of Epistemology 2 (1):3-20.
    Following Kuhn's main thesis according to which theory revision and acceptance is always paradigm relative, I propose to outline some possible consequences of such a view. First, asking the question in what sense Bayesian decision theory could serve as the appropriate theory of rationality examined from the point of view of the epistemology of theory acceptance, I argue that Bayesianism leads to a narrow conception of theory acceptance. Second, regarding the different types of theory (...)
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  45. Ordinal Conditional Functions. A Dynamic Theory of Epistemic States.Wolfgang Spohn - 1988 - In W. L. Harper & B. Skyrms (eds.), Causation in Decision, Belief Change, and Statistics, vol. II. Kluwer Academic Publishers.
    It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one (...)
     
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  46.  43
    Contraction-Free Sequent Calculi for Geometric Theories with an Application to Barr's Theorem.Sara Negri - 2003 - Archive for Mathematical Logic 42 (4):389-401.
    Geometric theories are presented as contraction- and cut-free systems of sequent calculi with mathematical rules following a prescribed rule-scheme that extends the scheme given in Negri and von Plato. Examples include cut-free calculi for Robinson arithmetic and real closed fields. As an immediate consequence of cut elimination, it is shown that if a geometric implication is classically derivable from a geometric theory then it is intuitionistically derivable.
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  47.  67
    The Measurement of Ranks and the Laws of Iterated Contraction.Wolfgang Spohn & Matthias Hild - 2008 - Artificial Intelligence 172:1195-1218.
    Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.
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  48.  94
    Paths to Triviality.Tore Fjetland Øgaard - 2016 - Journal of Philosophical Logic 45 (3):237-276.
    This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann (...)
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  49.  47
    How to Give It Up: A Survey of Some Formal Aspects of the Logic of Theory Change.David Makinson - 1985 - Synthese 62 (3):347 - 363.
    The paper surveys some recent work on formal aspects of the logic of theory change. It begins with a general discussion of the intuitive processes of contraction and revision of a theory, and of differing strategies for their formal study. Specific work is then described, notably Gärdenfors'' postulates for contraction and revision, maxichoice contraction and revision functions and the condition of orderliness, partial meet contraction and revision functions and the condition of relationality, and finally (...)
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  50.  48
    A Note on Contraction-Free Logic for Validity.Colin R. Caret & Zach Weber - 2015 - Topoi 34 (1):63-74.
    This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.
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