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In this paper we study changes of beliefs in a ranking-theoretic setting using non-extremal implausibility thresholds for belief. We represent implausibilities as ranks and introduce natural rank changes subject to a minimal change criterion. We show that many of the traditional AGM postulates for revision and contraction are preserved, except for the postulate of Preservation which is invalid. The diagnosis for belief contraction is similar, but not exactly the same. We demonstrate that the one-shot versions of both revision and contraction can be represented as revisions based on semiorders, but in two subtly different ways. We provide sets of postulates that are sound and complete in the sense that they allow us to prove representation theorems. We show that, and explain why, the classical duality between revision and contraction, as exhibited by the Levi and Harper identities, is partly broken by threshold-based belief changes. We also study the logic of iterated threshold-based revision and contraction. The traditional Darwiche-Pearl postulates for iterated revision continue to hold, as well as two additional postulates that characterize ranking-based revision as a restricted 'improvement' operator. We investigate the dual notion of iterated threshold-based belief contraction and provide a new set of postulates for it, characterizing contraction as a restricted 'degrading' operator. [ABSTRACT FROM AUTHOR]

Günther recently suggested a 'new' conditional. This conditional is not new, as already remarked by Wansing and Omori. It is just David Lewis' forgotten alternative 'doctored' conditional and part of a larger class termed neutral conditionals. In this paper, I answer some questions raised by Wansing and Omori, concerning the motivation, the logic, the connexive flavor and contra-classicality of such neutralized conditionals. The main message being: Neutralizing a vacuist conditional avoids (some) paradoxes of strict implication, changes the logic essentially only by Aristotle's Thesis, makes strong connexivity impossible, and remains in the realm of non-contra-classical logics. [ABSTRACT FROM AUTHOR]

In some recent works, Crupi and Iacona proposed an analysis of 'if' based on Chrysippus' idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic. [ABSTRACT FROM AUTHOR]

Standard conditionals φ > ψ, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is 'model-implied' by the antecedent. I motivate these conditionals logically, and also doxastically by properties of conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis' weakest system V, in that ID (φ > φ) or even CN (φ > Τ) are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by V to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries. [ABSTRACT FROM AUTHOR]