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Communication Dans Un Congrès Année : 2023

A Strict Constrained Superposition Calculus for Graphs

Rachid Echahed
Mnacho Echenim
Mehdi Mhalla
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Résumé

We propose a superposition-based proof procedure to reason on equational first order formulas defined over graphs. First, we introduce the considered graphs that are directed labeled graphs with lists of roots standing for pins or interfaces for replacements. Then the syntax and semantics of the considered logic are defined. The formulas at hand are clause sets built on equations and disequations on graphs. Afterwards, a sound and complete proof procedure is provided, and redundancy criteria are introduced to dismiss useless clauses and improve the efficiency of the procedure. In a first step, a set of inferences rules is provided in the case of uninterpreted labels. In a second step, the proposed rules are lifted to take into account labels defined as terms interpreted in some arbitrary theory. Particular formulas of interest are Horn clauses, for which stronger redundancy criteria can be devised. Essential differences with the usual term superposition calculus are emphasized.
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Dates et versions

hal-03978913 , version 1 (08-02-2023)
hal-03978913 , version 2 (19-03-2023)

Identifiants

  • HAL Id : hal-03978913 , version 2

Citer

Rachid Echahed, Mnacho Echenim, Mehdi Mhalla, Nicolas Peltier. A Strict Constrained Superposition Calculus for Graphs. FOSSACS 2023: 26th International Conference on Foundations of Software Science and Computation Structures, Apr 2023, Paris, France. ⟨hal-03978913v2⟩
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