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Abstract
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Given a class
of finite Kripke frames, we consider the uniform distribution on the frames from
with
states. A formula is
almost surely valid in
if the probability that it is valid in a random
-frame with
states
tends to
as
tends to infinity. The formulas that are almost surely valid in
form
a normal modal logic.
We find complete and sound axiomatizations for the logics of
almost-sure validities in the classes of finite frames defined by the logics
,
,
,
,
, and
.
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Keywords
modal logic, Kripke semantics, asymptotic probability,
random graphs, Euclidean relations, Grzegorczyk's logic
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Mathematical Subject Classification
Primary: 03B45
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Milestones
Received: 19 June 2024
Revised: 9 August 2024
Accepted: 21 November 2024
Published: 31 December 2024
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Publishers). |
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