Premium
A note on the independence of premiss rule
Author(s) -
Ishihara Hajime,
Nemoto Takako
Publication year - 2016
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201500032
Subject(s) - axiom , independence (probability theory) , constructive , mathematics , predicate (mathematical logic) , mathematical economics , intuitionistic logic , discrete mathematics , calculus (dental) , computer science , propositional calculus , programming language , statistics , geometry , process (computing) , medicine , dentistry
In this note, we prove that certain theories of (many‐sorted) intuitionistic predicate logic are closed under the independence of premiss rule (IPR). As corollaries, we show that HA and HA ω extended by some non‐classical axioms and non‐constructive axioms are closed under IPR.