Handling Transitive Relations in First-Order Automated Reasoning
Journal article, 2021

We present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and transitive relations in general. We show how such relations can be discovered syntactically in an input theory, and how they can be expressed in alternative ways. We experimentally evaluate different such ways on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain types of binary relations.


Automated theorem proving

Transitive relations

Binary relations

First-order logic

Automated reasoning



Koen Claessen

Chalmers, Computer Science and Engineering (Chalmers), Functional Programming

Ann Lillieström

Chalmers, Computer Science and Engineering (Chalmers), CSE Verksamhetsstöd, Data Science Research Engineers

Journal of Automated Reasoning

0168-7433 (ISSN) 1573-0670 (eISSN)

Vol. 65 8 1097-1124

Subject Categories


Medical Ethics

Computer Science



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Latest update

4/5/2022 5