Paper Info
Title
Beyond System P - Hilbert-Style Convergence Results for Conditional Logics with a Connexive Twist.
Abstract
The paper has three aims. Firstly, the convergence result of conditional logics for Systems P and R is extended; based on a Hilbert style axiomatization it is proved that Lewis's System V and Burgess's variant system, System V*, are nothing but Lehmann and Magidor's System R. Secondly, it is shown that connexive principles are the center stage of axiomatizations of System P and System R. They introduce a proof-theoretic dependency of two core principles of System P and System R - Cautious Monotonicity and Rational Monotonicity - even when the connexive principles are formulated as default rules. Thirdly, the impossibility result for an extension of classical conditional logics by unrestricted connexive principles is strengthened. It is shown that such an impossibility result ensues even when Principle Refl is given up, where the latter asserts that 'if A then A' is a theorem. As a consequence, on pain of inconsistency any complete classical conditional logic can include connexive principles only in a restricted form, where classical conditional logics are minimal conditional logics that take classical propositional calculus to govern propositional connectives other than conditionals. Implications of the strengthened impossibility result are discussed.
Year
Venue
Field
2016
JOURNAL OF APPLIED LOGICS-IFCOLOG JOURNAL OF LOGICS AND THEIR APPLICATIONS
Convergence (routing),Twist,Pure mathematics,Mathematics
DocType
Volume
Issue
Journal
3
SP3
ISSN
Citations 
PageRank 
2055-3706
0
0.34
References 
Authors
0
1
Name
Order
Citations
PageRank
Matthias Unterhuber100.34