Section: New Software and Platforms

The Redlog Computer Logic System

Functional Description

Redlog is an integral part of the interactive computer algebra system Reduce. It supplements Reduce's comprehensive collection of powerful methods from symbolic computation by supplying more than 100 functions on first-order formulas. Redlog has been publicly available since 1995 and is constantly being improved. The name Redlog stands for Reduce Logic System. Andreas Dolzmann from Schloss Dagstuhl Leibniz-Zentrum für Informatik is a co-developer of Redlog.

Reduce and Redlog are open-source and freely available under a modified BSD license at http://reduce-algebra.sourceforge.net/ . The Redlog homepage is located at http://www.redlog.eu/ . Redlog generally works with interpreted first-order logic in contrast to free first-order logic. Each first-order formula in Redlog must exclusively contain atoms from one particular Redlog-supported theory, which corresponds to a choice of admissible functions and relations with fixed semantics. Redlog-supported theories include Nonlinear Real Arithmetic (Real Closed Fields), Presburger Arithmetic, Parametric QSAT, and many more.

Effective quantifier elimination procedures for the various supported theories establish an important class of methods available in Redlog. For the theories supported by Redlog, quantifier elimination procedures immediately yield decision procedures. Besides these quantifier elimination-based decision methods there are specialized, and partly incomplete, decision methods, which are tailored to input from particular fields of application.

In 2015 there was further significant progress with the identification of bifurcations in biochemical models based on real reasoning [17] , [33] . With existential real quantifier elimination Redlog can now produce unsatisfiable cores in the infeasible case [27] . This is of considerable relevance in the course of using Redlog as a theory solver in SMT contexts, e.g., within the SMArT project (section 9.2 ).

Redlog is a widely accepted tool and highly visible in mathematics, informatics, engineering and the sciences. The seminal article on Redlog [4] has received more than 300 citations in the scientific literature so far.