# KF (Lemmon)

## Notes

This system was on these pages for years as the "Marked system",
because I knew of nobody bothering to investigate such a degenerate system.
Well, Lemmon and Scott's famous "Lemmon notes" did, and now
that I've stumbled over them, the system is more interesting
than I would have expected.

The marked system has the axiom F: Lp == Mp.
It is not quite the trivial system, but it is close.

It does sometime show up without a name in exercises in text books.

There are actually a family of degenerate systems with the Lx==Mx
axiom... but since I can't think of any reason anyone would be
interested in any of them, they are all just lumped together here.

This specific system is characterized by a two-world frame in which
the designated world can see only the other world, not itself.
[Pledger,
2001a]

Theoremhood in KF is equivalent in all K whose accessiblity relation (R) is
serial and in addition satisfies the condition

(∀ u, t, t')(uRt & uRt' > (t = t'))

(∀u)(∃!t)uRt

Each world u leads to a *unique* world t.
[Lemmon and Scott,
1977, p60]

## Based on

The system can be formed from the system K
plus the axiom F: (Lp == Mp)
[Lemmon and Scott,
1977, p60]

## Basis for

The trivial system, by adding any of the following:

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© Copyright 2006, by John Halleck, All Rights Reserved.

This page is http://www.cc.utah.edu/~nahaj/logic/structures/systems/marked.html

This page was last modified on September 16th, 2006