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I.: A propositional typicality logic for extending rational consequence (2013)
| Venue: | Trends in Belief Revision and Argumentation Dynamics, Studies in Logic – Logic and Cognitive Systems |
| Citations: | 3 - 2 self |
BibTeX
@INPROCEEDINGS{Booth13i.:a,
author = {Richard Booth and Thomas Meyer and Ivan Varzinczak},
title = {I.: A propositional typicality logic for extending rational consequence},
booktitle = {Trends in Belief Revision and Argumentation Dynamics, Studies in Logic – Logic and Cognitive Systems},
year = {2013},
pages = {123--154},
publisher = {King’s College Publications}
}
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Abstract
abstract. We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical proposi-tional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a given formula holds. The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that KLM-style rational consequence relations can be embedded in our logic. Moreover we show that we can define consequence relations on the language of PTL itself, thereby moving beyond the propositional setting. Building on the exist-ing link between propositional rational consequence and belief revision, we show that the same correspondence holds in the case of rational con-sequence and belief revision defined on the language of PTL. Finally we also investigate different notions of entailment for PTL and propose two appropriate candidates.
Keyphrases
propositional typicality logic rational consequence belief revision exist-ing link propositional setting klm-style preferential reasoning rational con-sequence different notion ranked model appropriate candidate klm-style rational consequence relation consequence relation classical proposi-tional logic typicality operator propositional rational consequence
