System IPC

[Hackstaff, 1966]


There are structural similarities between IPC and the modal logic system S4. [Hughes and Cresswell 1996, p225] [Zeman, 1973, p231] (Both apparently quoting [McKinsey and Tarski, 1948, p13] which showed that there was a validity preserving mapping between Heyting Propositional Calculus H and S4.) But note that Ian Hacking [Hacking, 1963] proved that the Heyting Propositional Calculus H could also be mapped onto S3

Based on

IPC is Positive Propositional Logic plus the Axioms IP1 [(p>~p)>~p] and IP2 [~p>(p>q)] [Claimed to be from H.Scholz and K.Schröter, as attributed by Church.] [Hackstaff, 1966, p223]


Intuitionist PC [as given by Heyting] is

[Hackstaff, 1966, p223]


IPC is an alternative to Standard PC, in contrast to other popular alternatives:

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