In the present paper, we consider modal propositional logic and look for the constraints that are imposed to the propositions of the special type Box by the structure of the relevant finite Kripke frame. We translate the usual language of modal propositional logic in terms of notions of commutative algebra, namely polynomial rings, ideals and bases of ideals. We use extensively the perspective obtained in previous works in algebraic statistics. We prove that the constraints on Box can be derived through a binomial ideal containing a toric ideal and we give sufficient conditions under which the toric ideal, together with the fact that the truth values are in 0,1, fully describes the constraints.

Modal operators and toric ideals

R. Camerlo;F. Rapallo
2019

Abstract

In the present paper, we consider modal propositional logic and look for the constraints that are imposed to the propositions of the special type Box by the structure of the relevant finite Kripke frame. We translate the usual language of modal propositional logic in terms of notions of commutative algebra, namely polynomial rings, ideals and bases of ideals. We use extensively the perspective obtained in previous works in algebraic statistics. We prove that the constraints on Box can be derived through a binomial ideal containing a toric ideal and we give sufficient conditions under which the toric ideal, together with the fact that the truth values are in 0,1, fully describes the constraints.
File in questo prodotto:
File Dimensione Formato  
1712.04191.pdf

accesso aperto

Tipologia: Documento in Pre-print
Dimensione 246.14 kB
Formato Adobe PDF
246.14 kB Adobe PDF Visualizza/Apri

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: http://hdl.handle.net/11567/973597
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact