# Modular Proof Systems for Partial Functions with Weak Equality

@inproceedings{Ganzinger2004ModularPS, title={Modular Proof Systems for Partial Functions with Weak Equality}, author={Harald Ganzinger and Viorica Sofronie-Stokkermans and Uwe Waldmann}, booktitle={IJCAR}, year={2004} }

The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. Modularity means that inferences are pure, only involving clauses over the alphabet of either one, but not both, of the theories. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combinedâ€¦Â

## 16 Citations

### Reasoning in combinations of theories

- Computer Science
- 2010

The reductive approach outlined above has become particularly relevant in recent years due to the rise of powerful solvers for background theories common in verification tasks.

### On Hierarchical Reasoning in Combinations of Theories

- MathematicsIJCAR
- 2010

It is shown that combinations of extensions of theories which are local in this extended sense also have a locality property and hence allow modular and hierarchical reasoning and hence obtain parameterized decidability and complexity results for many (combinations of) theories important in verification.

### Hierarchical Reasoning in Local Theory Extensions and Applications

- Computer Science2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
- 2014

The way the authors used the possibility of hierarchical reasoning in local theory extensions in various application areas such as automated reasoning in mathematics, verification of reactive, real time and hybrid systems, and description logics is discussed.

### Combining Nonstably Infinite Theories

- MathematicsJournal of Automated Reasoning
- 2005

Two extensions of the Nelsonâ€“Oppen method are described that address the problem of combining theories that are not stably infinite, and exchange not only equalities between shared variables but also certain cardinality constraints.

### Hierarchic Reasoning in Local Theory Extensions

- MathematicsCADE
- 2005

It is shown that for special types of extensions of a base theory, which is called local, efficient hierarchic reasoning is possible, for an extension of a theory, to express the decidability and complexity of the universal theory of $\mathcal{T}_{1}$ in terms of the decideability resp.

### Applications of Hierarchical Reasoning in the Verification of Complex Systems

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2007

### System Description: H-PILoT (Version 1.9)

- Computer ScienceArXiv
- 2010

H-PILoT (Hierarchical Proving by Instantiation in Local Theory extensions) provides a decision procedure for testing satisfiability of ground formulae, and can also be used for model generation.

### On Invariant Synthesis for Parametric Systems

- Mathematics, Computer ScienceCADE
- 2019

An algorithm for symbol elimination in theory extensions is used to devise a method for iteratively strengthening certain classes of safety properties to obtain invariants of the system.

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