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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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
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Abstract	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.
AbstractList	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. Let LX be the language of a first-order, decidable, quantifier-free theory X. Consider the language, LRQ(X), that extends LX 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, LRQ(X) admits nested restricted quantifiers. In this paper we present a decision procedure for some expressive fragments of LRQ(X) and its implementation as part of the {log} (‘setlog’) tool. The usefulness of the approach is shown by reporting on three real-world case studies.
ArticleNumber	23
Author	Rossi, Gianfranco Cristiá, Maximiliano
Author_xml	– sequence: 1 givenname: Maximiliano surname: Cristiá fullname: Cristiá, Maximiliano email: cristia@cifasis-conicet.gov.ar organization: Universidad Nacional de Rosario and CIFASIS (CONICET-UNR) – sequence: 2 givenname: Gianfranco surname: Rossi fullname: Rossi, Gianfranco organization: Università di Parma
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Cites_doi	10.1007/s10817-021-09602-2 10.1017/S1471068421000521 10.2178/jsl/1164060452 10.1007/978-3-540-73595-3_13 10.1007/s10817-006-9062-x 10.1002/cpa.3160340203 10.1017/S1471068415000290 10.1007/s10817-021-09589-w 10.1007/11817963_11 10.1007/978-3-319-06251-8_11 10.1002/malq.19960420105 10.1007/978-1-4757-3452-2 10.1007/s10472-009-9153-6 10.1145/1066100.1066102 10.1145/3625230 10.1007/s10817-023-09666-2 10.1007/978-3-642-02658-4_25 10.1007/978-3-031-55248-9_3 10.1016/j.tcs.2014.03.021 10.1017/S1471068406002730 10.1007/978-3-662-54577-5_5 10.1093/comjnl/bxab030 10.1145/365151.365169 10.1007/978-3-642-59207-2 10.1007/s10817-019-09520-4 10.1007/978-3-642-40561-7_16 10.1007/978-3-319-07512-9_1 10.1002/cpa.3160460104 10.2178/jsl/1344862166 10.19153/cleiej.21.2.3 10.1007/978-3-540-45069-6_34 10.1007/s10817-020-09577-6 10.1002/malq.19920380110 10.1007/978-3-319-07512-9_6 10.1090/S0002-9939-1988-0938682-2
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Snippet	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... Let LX be the language of a first-order, decidable, quantifier-free theory X. Consider the language, LRQ(X), that extends LX with formulas of the form ∀x∈A:ϕ...
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Title	A Practical Decision Procedure for Quantifier-Free, Decidable Languages Extended with Restricted Quantifiers
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