PTL: A Propositional Typicality Logic

Abstract

We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical propositional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a formula holds. The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that 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 existing link between propositional rational consequence and belief revision, we show that the same correspondence holds for rational consequence and belief revision on PTL. We investigate entailment for PTL, and propose two appropriate notions thereof.

This work is based upon research supported by the National Research Foundation. Any opinion, findings and conclusions or recommendations expressed in this material are those of the author(s) and therefore the NRF do not accept any liability in regard thereto. This work was partially funded by Project number 247601, Net2: Network for Enabling Networked Knowledge, from the FP7-PEOPLE-2009-IRSES call.