Integrating Cardinality Constraints into Constraint Logic Programming with Sets

@article{Cristia2021IntegratingCC,
  title={Integrating Cardinality Constraints into Constraint Logic Programming with Sets},
  author={Maximiliano Cristi'a and Gianfranco Rossi},
  journal={ArXiv},
  year={2021},
  volume={abs/2102.05422}
}
Formal reasoning about finite sets and cardinality is important for many applications, including software verification, where very often one needs to reason about the size of a given data structure. The Constraint Logic Programming tool $$\{ log\} $$ provides a decision procedure for deciding the satisfiability of formulas involving very general forms of finite sets, although it does not provide cardinality constraints. In this paper we adapt and integrate a decision procedure for… 

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References

SHOWING 1-10 OF 50 REFERENCES
Efficient Automated Reasoning About Sets and Multisets with Cardinality Constraints
  • R. Piskac
  • Computer Science, Mathematics
    IJCAR
  • 2020
TLDR
This presentation outlines an efficient decision procedure for reasoning about multisets with cardinality constraints and describes how to translate constraints to constraints in an extension of quantifier-free linear integer arithmetic, which is called LIA*.
Rewrite rules for a solver for sets, binary relations and partial functions
  • 2019
A pearl on SAT and SMT solving in Prolog
Decision Procedures for Multisets with Cardinality Constraints
TLDR
A polynomial-space algorithm for deciding expressive quantifier-free constraints on multisets with cardinality operators and a proof that adding quantifiers to a constraint language containing subset and cardinality Operators yields undecidable constraints.
Combining Multisets with Integers
TLDR
This work presents a decision procedure for a constraint language combining multisets of ur-elements, the integers, and an arbitrary first-order theory T of the ur- elements using the Nelson-Oppen combination method.
Combining Sets with Integers
We present a decision procedure for a constraint language combining stratified sets of ur-elements with integers in the presence of a cardinality operator. Our decision procedure is an extension of
Log
Logics for Sizes with Union or Intersection
TLDR
This paper presents the most basic logics for reasoning about the sizes of sets that admit either the union of terms or the intersection of terms, and presents a sound, complete, and polynomial-time decidable proof system for these logics.
Deciding Boolean Algebra with Presburger Arithmetic
TLDR
An algorithm for deciding the first-order multisorted theory BAPA, which combines Boolean algebras of sets of uninterpreted elements (BA) and Presburger arithmetic operations (PA), is described and it is shown that it has optimal alternating time complexity and that it matches the complexity of PA.
OFAI clp(Q,R) Manual
TLDR
This Manual documents a Prolog implementation of clp(Q,R), based on SICStus featuring extensible uniication via attributed variables, at least as complete as other existingclp(R) implementations.
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5
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