Booth, Richard ![]() ![]() |
Preview |
PDF
- Accepted Post-Print Version
Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (745kB) | Preview |
Abstract
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sen- tence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM- style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains mono- tonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality.
Item Type: | Article |
---|---|
Date Type: | Publication |
Status: | Published |
Schools: | Computer Science & Informatics |
Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
Publisher: | Elsevier |
ISSN: | 0004-3702 |
Date of First Compliant Deposit: | 7 October 2019 |
Date of Acceptance: | 25 September 2019 |
Last Modified: | 12 Nov 2023 18:15 |
URI: | https://orca.cardiff.ac.uk/id/eprint/125890 |
Citation Data
Cited 8 times in Scopus. View in Scopus. Powered By Scopus® Data
Actions (repository staff only)
![]() |
Edit Item |