System VER

[Hughes and Cresswell, 1996]

Notes

VER comes from the Latin "Verum". [Hughes and Cresswell, 1996, p67]

In VER, L just means "true". [Hughes and Cresswell, 1996, p67]

It is not possible to add any axioms to the system, that aren't already theorems, without making it inconsistent. [Hughes and Cresswell, 1996, p67]

VER is characterized by frames with one dead end. [Hughes and Cresswell, 1996, p122] (I.E. One irreflexive world [Pledger, personal communication, 12jan2001b])

Every consistent extension of system K which retains the rules US, MP, and Necessitation is contained in either Triv or System Ver, or both. [Hughes and Cresswell, 1996, p67]

If you add the system triv to this system, the result is inconsistent. [Hughes and Cresswell, 1996, p67]

Any consistent extension of system K which is not contained in VER contains the axiom D (Lp>Mp). [Hughes and Cresswell, 1996, p67]

Based on

Verum = System K + Axiom VER [Lp]; [Hughes and Cresswell, 1996, p67]

Basis for


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