Is Horn clause logic decidable?

[Kreinovich, Vladik]

See, e.g., https://www.ii.uni.wroc.pl/~jma/csl93.pdf and references therein

-----Original Message-----
From: FOM [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Daniel Schwartz
Sent: Saturday, October 16, 2021 4:00 PM
To: fom at cs.nyu.edu
Subject: Is Horn clause logic decidable?

I have been told that Horn Clause Logic, considered as a subsystem of First-Order Logic, is undecidable.  More exactly, if S is a set of Horn clauses and P is an atom, then whether P is derivable from S is undecidable.

However, I have never seen a proof of this and have been unable to find any discussion of it.

Would anyone know whether this statemnt is true, and could you provide a refernce?

Thanks and best regards,

Dan Schwartz

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