A Practical Decision Procedure for Quantifier-Free, Decidable Languages Extended with Restricted Quantifiers

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 i...

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Bibliographic Details
Published in:Journal of automated reasoning Vol. 68; no. 4; p. 23
Main Authors: Cristiá, Maximiliano, Rossi, Gianfranco
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2024
Springer Nature B.V
Subjects:
Artificial Intelligence
Case studies
Computer Science
Language
Logic programming
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Semantics
Symbolic and Algebraic Manipulation
Syntax
Theory X
Variables
Set theory
Constraint logic programming
Restricted quantifiers
ISSN:0168-7433, 1573-0670
Online Access:Get full text
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Summary: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.
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ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-024-09713-6