A Practical Decision Procedure for Quantifier-Free, Decidable Languages Extended with Restricted Quantifiers - Cristiá, Maximiliano; Rossi, Gianfranco (Journal of automated reasoning, 2024)
Let L X be the language of a first-order, decidable, quantifier-free theory X . Consider the language, L R Q ( X ) , that extends L X with formulas of the form ∀ x ∈ A : ϕ (restricted universal quantifier, RUQ) and ∃ x ∈ A : ϕ (restricted existential quantifier, REQ), where A is a finite set and ϕ is a formula made of X -formulas, RUQ and REQ. That is, L R Q ( X ) admits nested restricted quantifiers. In this paper we present a decision procedure for some expressive fragments of L R Q ( X ) and its implementation as part of the { l o g } (‘setlog’) tool. The usefulness of the approach is shown by reporting on three real-world case studies.