scholarly journals Proofs in conflict-driven theory combination

2018 ◽  
Author(s):  
Maria Paola Bonacina ◽  
Stéphane Graham-Lengrand ◽  
Natarajan Shankar
Keyword(s):  
Theory Combination

scholarly journals Delayed theory combination vs. Nelson-Oppen for satisfiability modulo theories: a comparative analysis

2009 ◽  
Vol 55 (1-2) ◽  
pp. 63-99 ◽  
Author(s):  
Roberto Bruttomesso ◽  
Alessandro Cimatti ◽  
Anders Franzen ◽  
Alberto Griggio ◽  
Roberto Sebastiani
Keyword(s):  
Comparative Analysis ◽  
Satisfiability Modulo Theories ◽  
Theory Combination

Efficient Satisfiability Modulo Theories via Delayed Theory Combination

2005 ◽  
pp. 335-349 ◽  
Author(s):  
Marco Bozzano ◽  
Roberto Bruttomesso ◽  
Alessandro Cimatti ◽  
Tommi Junttila ◽  
Silvio Ranise ◽  
...  
Keyword(s):  
Satisfiability Modulo Theories ◽  
Theory Combination

scholarly journals Conflict-Driven Satisfiability for Theory Combination: Lemmas, Modules, and Proofs

2021 ◽  
Author(s):  
Maria Paola Bonacina ◽  
Stéphane Graham-Lengrand ◽  
Natarajan Shankar
Keyword(s):  
Theorem Proving ◽  
Practical Interest ◽  
Interactive Theorem Proving ◽  
Transition System ◽  
Candidate Model ◽  
Inference Systems ◽  
Input Formula ◽  
Theory Combination

AbstractSearch-based satisfiability procedures try to build a model of the input formula by simultaneously proposing candidate models and deriving new formulae implied by the input. Conflict-driven procedures perform non-trivial inferences only when resolving conflicts between formulæ and assignments representing the candidate model. CDSAT (Conflict-Driven SATisfiability) is a method for conflict-driven reasoning in unions of theories. It combines inference systems for individual theories as theory modules within a solver for the union of the theories. This article augments CDSAT with a more general lemma learning capability and with proof generation. Furthermore, theory modules for several theories of practical interest are shown to fulfill the requirements for completeness and termination of CDSAT. Proof generation is accomplished by a proof-carrying version of the CDSAT transition system that produces proof objects in memory accommodating multiple proof formats. Alternatively, one can apply to CDSAT the LCF approach to proofs from interactive theorem proving, by defining a kernel of reasoning primitives that guarantees the correctness by construction of CDSAT proofs.

scholarly journals Theory Combination: Beyond Equality Sharing

2019 ◽  
pp. 57-89 ◽  
Author(s):  
Maria Paola Bonacina ◽  
Pascal Fontaine ◽  
Christophe Ringeissen ◽  
Cesare Tinelli
Keyword(s):  
Theory Combination
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