Is Horn clause logic decidable?

Kreinovich, Vladik vladik at
Mon Oct 18 00:17:06 EDT 2021

See, e.g., and references therein

-----Original Message-----
From: FOM [mailto:fom-bounces at] On Behalf Of Daniel Schwartz
Sent: Saturday, October 16, 2021 4:00 PM
To: fom at
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

Dr. Daniel G. Schwartz                            Office    850-644-5875
Dept. of Computer Science, MC 4530                CS Dept   850-644-4029
Florida State University                          Fax       850-644-0058
Tallahassee, FL 32306-4530                        schwartz at

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