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#### SCL with Theory Constraints

##### MPS-Authors

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##### Fulltext (public)

arXiv:2003.04627.pdf

(Preprint), 268KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Bromberger, M., Fiori, A., & Weidenbach, C. (2020). SCL with Theory Constraints. Retrieved from https://arxiv.org/abs/2003.04627.

Cite as: http://hdl.handle.net/21.11116/0000-0007-7AFE-3

##### Abstract

We lift the SCL calculus for first-order logic without equality to the SCL(T)
calculus for first-order logic without equality modulo a background theory. In
a nutshell, the SCL(T) calculus describes a new way to guide hierarchic
resolution inferences by a partial model assumption instead of an a priori
fixed order as done for instance in hierarchic superposition. The model
representation consists of ground background theory literals and ground
foreground first-order literals. One major advantage of the model guided
approach is that clauses generated by SCL(T) enjoy a non-redundancy property
that makes expensive testing for tautologies and forward subsumption completely
obsolete. SCL(T) is a semi-decision procedure for pure clause sets that are
clause sets without first-order function symbols ranging into the background
theory sorts. Moreover, SCL(T) can be turned into a decision procedure if the
considered combination of a first-order logic modulo a background theory enjoys
an abstract finite model property.