Journal of Philosophical Logic

, Volume 43, Issue 5, pp 903–942 | Cite as

Preferential Semantics using Non-smooth Preference Relations

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Abstract

This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation ≺ . They are equivalent to Shoham’s so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After discussing this type of semantics, we focus on some concrete proposals from the literature, checking a number of meta-theoretic properties and elaborating on their intuitive motivation. As it turns out, many of their meta-properties only hold in case ≺ is transitive. To tackle this problem, we propose slight modifications of each of the systems, showing the resulting logics to behave better at the intuitive level and in metatheoretic terms, for arbitrary ≺ .

Keywords

Preferential semantics Smoothness Transitivity Selection function 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of ScienceGhent UniversityGentBelgium

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