Hypersequent Calculi for Lewis' Conditional Logics with Uniformity and Reflexivity [chapter]

Marianna Girlando, Björn Lellmann, Nicola Olivetti, Gian Luca Pozzato
2017 Lecture Notes in Computer Science  
We present the first internal calculi for Lewis' conditional logics characterized by uniformity and reflexivity, including non-standard internal hypersequent calculi for a number of extensions of the logic VTU. These calculi allow for syntactic proofs of cut elimination and known connections to S5. We then introduce standard internal hypersequent calculi for all these logics, in which sequents are enriched by additional structures to encode plausibility formulas as well as diamond formulas.
more » ... e calculi provide both a decision procedure for the respective logics and constructive countermodel extraction from a failed proof search attempt. This paper is a preliminary version accepted for the conference TABLEAUX 2017.
doi:10.1007/978-3-319-66902-1_8 fatcat:ren4zmqudjf2zkrxxdd3pa4oue