The inverse method is a saturation-based theorem-proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here, we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability, which is appropriate for constructively ascertaining the unprovability of a formula G by providing a concise countermodel for it; in particular, we prove that the generated countermodels have minimal height. Moreover, we clarify the role of the saturated database obtained as a result of a failed proof search in FRJ(G) by showing how to extract from such a database a derivation witnessing the Intuitionistic validity of the goal.

Duality between Unprovability and Provability in Forward Refutation-search for Intuitionistic Propositional Logic

Fiorentini, Camillo
;
Ferrari, Mauro
2020-01-01

Abstract

The inverse method is a saturation-based theorem-proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here, we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability, which is appropriate for constructively ascertaining the unprovability of a formula G by providing a concise countermodel for it; in particular, we prove that the generated countermodels have minimal height. Moreover, we clarify the role of the saturated database obtained as a result of a failed proof search in FRJ(G) by showing how to extract from such a database a derivation witnessing the Intuitionistic validity of the goal.
2020
2020
proof-search procedures, intuitionistic propositional logic, sequent calculi
Fiorentini, Camillo; Ferrari, Mauro
File in questo prodotto:
File Dimensione Formato  
2020-fiofer-DualityBetweenUnprovabilityAndProvabilityInForwardRefutation-searchForIPL-tocl.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 2.1 MB
Formato Adobe PDF
2.1 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2088064
 Attenzione

L'Ateneo sottopone a validazione solo i file PDF allegati

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 3
social impact