n this paper we study the proof theory of C.I. Lewis’ logics of strict conditional S1- S5 and we propose the first modular and uniform presentation of C.I. Lewis’ systems. In particular, for each logic Sn we present a labelled sequent calculus G3Sn and we discuss its structural properties: every rule is height-preserving invertible and the structural rules of weakening, contraction and cut are admissible. Completeness of G3Sn is established both indirectly via the embedding in the axiomatic system Sn and directly via the extraction of a countermodel out of a failed proof search. Finally, the sequent calculus G3S1 is employed to obtain a syntactic proof of decidability of S1.
Labelled sequent calculi for logics of strict implication
Tesi, Matteo
2022
Abstract
n this paper we study the proof theory of C.I. Lewis’ logics of strict conditional S1- S5 and we propose the first modular and uniform presentation of C.I. Lewis’ systems. In particular, for each logic Sn we present a labelled sequent calculus G3Sn and we discuss its structural properties: every rule is height-preserving invertible and the structural rules of weakening, contraction and cut are admissible. Completeness of G3Sn is established both indirectly via the embedding in the axiomatic system Sn and directly via the extraction of a countermodel out of a failed proof search. Finally, the sequent calculus G3S1 is employed to obtain a syntactic proof of decidability of S1.File | Dimensione | Formato | |
---|---|---|---|
s1_s5_draft (1).pdf
accesso aperto
Tipologia:
Published version
Licenza:
Solo Lettura
Dimensione
535.75 kB
Formato
Adobe PDF
|
535.75 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.