# A Model Generation Style Completeness Proof for Constraint Tableaux with Superposition

@inproceedings{Giese2002AMG, title={A Model Generation Style Completeness Proof for Constraint Tableaux with Superposition}, author={Martin Giese}, booktitle={TABLEAUX}, year={2002} }

We present a calculus that integrates equality handling by superposition into a free variable tableau calculus. We prove completeness of this calculus by an adaptation of the model generation [2,15] technique commonly used for completeness proofs of resolution calculi. The calculi and the completeness proof are compared to earlier results of Degtyarev and Voronkov [7].

## 17 Citations

### Superposition-based Equality Handling for Analytic Tableaux

- MathematicsJournal of Automated Reasoning
- 2006

We present a variant of the basic ordered superposition rules to handle equality in an analytic free-variable tableau calculus. We prove completeness of this calculus by an adaptation of the model…

### The Hyper Tableaux Calculus with Equality

- Mathematics
- 2008

In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the hyper tableau…

### The Hyper Tableaux Calculus with Equality and an Application to Finite Model Computation

- MathematicsJ. Log. Comput.
- 2010

This article shows how to integrate a modern treatment of equality in the hyper tableau calculus based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for superposition are drawn from a set of positive unit clauses, and superposition inferences into positive literals is restricted into (positive) unit clauses only.

### Hyper Tableaux with Equality

- MathematicsCADE
- 2007

This paper shows how to integrate a modern treatment of equality in the hyper tableau calculus based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for paramodulation are drawn from a set of positive unit clauses, the candidate model.

### Saturation Up to Redundancy for Tableau and Sequent Calculi

- Computer ScienceLPAR
- 2006

This technique can be used to easily show the completeness of optimized calculi that contain destructive rules e.g. for simplification, rewriting with equalities, etc., which is not easily done with a standard Hintikka-style completeness proof.

### Connection Tableaux with Lazy Paramodulation

- Computer ScienceJournal of Automated Reasoning
- 2007

This paper presents a new connection tableau calculus for logic with equality based on a lazy form of paramodulation where parts of the unification step become auxiliary subgoals in a tableau and may be subjected to subsequent paramodulations.

### The Disconnection Tableau Calculus

- Mathematics, Computer ScienceJournal of Automated Reasoning
- 2006

This paper gives a comprehensive presentation of the disconnection tableau calculus, a proof method for formulas in classical first-order clause logic that uses unification in such a manner that important proof-theoretic advantages of the classical tableAU calculus are preserved.

### Integration of Equality Reasoning into the Disconnection Calculus

- Computer ScienceTABLEAUX
- 2002

The disconnection tableau calculus represents a new confluent framework well suited for the integration of a large class of different methods for equality handling, as demonstrated in this paper.

### The Model Evolution Calculus

- Computer ScienceCADE
- 2003

In addition to being a more faithful lifting of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, one of FDPLL’s optimizations, and so has the potential of leading to much faster implementations.

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