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arxiv: 2605.22716 · v1 · pith:747AD5CHnew · submitted 2026-05-21 · 💻 cs.AI · cs.LO

Parametric Modular Answer Set Programs Made Declarative

Jorge Fandinno , Yuliya Lierler , Torsten Schaub This is my paper

Pith reviewed 2026-05-22 04:59 UTC · model grok-4.3

classification 💻 cs.AI cs.LO
keywords modular answer set programmingparametric logic programscollective controlintensionality statementsclingodeclarative modularityASP semantics
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The pith

Parametric modular logic programs let answer set programming define subprograms with parameters and intensionality statements.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces parametric modular logic programs as a new formalism in first-order answer set programming. This approach supports defining subprograms that accept parameters and include statements about which predicates are intensional. The formalism is shown to capture the semantics of clingo programs that use collective control for structuring and instantiating subprograms. A reader would care because the work supplies theoretical foundations for modular ASP while linking it directly to existing non-modular programs without requiring solver changes.

Core claim

Parametric modular logic programs, which incorporate parameters for subprogram definitions and intensionality statements, capture the full semantics of clingo-programs with collective control and thereby render modular answer set programming declarative.

What carries the argument

Parametric modular logic programs, a formalism that defines subprograms equipped with parameters and intensionality statements to structure and instantiate answer set programs.

If this is right

  • Modular answer set programs can be written and understood using only standard declarative syntax.
  • Parameterized subprograms become reusable across different contexts while preserving semantics.
  • Collective control features in existing solvers receive a formal declarative account.
  • Modular and traditional non-modular answer set programs become connected through a shared theoretical framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Developers could build modular ASP libraries that instantiate automatically for different problem instances.
  • The same parametric approach might extend to other logic programming languages that lack built-in modularity.
  • Debugging tools could exploit the intensionality statements to isolate which parts of a subprogram affect the overall answer sets.

Load-bearing premise

The new formalism accurately and completely reproduces the behavior of clingo programs with collective control without adding unintended restrictions or demanding changes to solver implementations.

What would settle it

A concrete clingo program using collective control whose stable models differ from the models computed under the parametric modular logic program semantics.

read the original abstract

In this paper, we explore the concept of modularity in first-order answer set programming (ASP). We introduce a new formalism called parametric modular logic programs, which allows defining subprograms with parameters and intensionality statements. We demonstrate how this formalism can capture the semantics of clingo-programs with collective control, a feature that enables structuring and instantiating subprograms. We provide theoretical foundations for modular ASP, illustrate its usefulness, and connect to traditional non-modular ASP.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces parametric modular logic programs as a new formalism extending first-order answer set programming. Subprograms can be defined with parameters and intensionality statements; the central claim is that this formalism declaratively captures the semantics of clingo programs that use collective control for structuring and instantiating subprograms. Theoretical foundations are provided and connections to traditional non-modular ASP are drawn.

Significance. If the equivalence to clingo collective control holds without unintended restrictions or solver changes, the work would supply a useful declarative layer for modular ASP, aiding program structuring in knowledge-representation applications. The explicit link to an existing solver feature strengthens practical relevance.

major comments (2)
  1. [demonstration paragraph / abstract] Abstract and demonstration section: the assertion that parametric modular logic programs 'correctly and completely capture the semantics of clingo-programs with collective control' is load-bearing yet unsupported by any visible equivalence proof, mapping, or counter-example check; without this, the central claim remains unverified.
  2. [formal definition section] Definition of parametric modular logic programs: it is unclear whether the intensionality statements or parameter mechanism introduce restrictions on answer-set existence or minimality that are absent from standard clingo collective control; a concrete comparison (e.g., via a small program example) is required.
minor comments (2)
  1. [abstract] The abstract states that usefulness is illustrated, yet no concrete example program or output comparison appears in the visible text; adding one short worked example would improve readability.
  2. [preliminaries] Notation for intensionality statements should be introduced with a small table or running example to avoid ambiguity when connecting to traditional ASP.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comments point by point below, indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: Abstract and demonstration section: the assertion that parametric modular logic programs 'correctly and completely capture the semantics of clingo-programs with collective control' is load-bearing yet unsupported by any visible equivalence proof, mapping, or counter-example check; without this, the central claim remains unverified.

    Authors: The demonstration section provides several worked examples that map clingo programs using collective control to equivalent parametric modular logic programs, along with an informal correspondence argument. We acknowledge that an explicit formal equivalence theorem would make the central claim more robust. In the revised manuscript we will add a dedicated subsection containing a formal mapping, a proof sketch of semantic equivalence, and a brief verification against potential counter-examples. revision: yes

  2. Referee: Definition of parametric modular logic programs: it is unclear whether the intensionality statements or parameter mechanism introduce restrictions on answer-set existence or minimality that are absent from standard clingo collective control; a concrete comparison (e.g., via a small program example) is required.

    Authors: The intensionality statements and parameter mechanism are defined to replicate the collective control feature of clingo without imposing additional constraints on answer-set existence or minimality. To clarify this alignment we will augment the formal definition section with a small, self-contained program example. The example will compute the answer sets under both the parametric modular formalism and the corresponding clingo program, demonstrating that the sets coincide exactly. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper introduces parametric modular logic programs as a new formalism extending traditional non-modular ASP, with a demonstration that it captures clingo collective control semantics. No load-bearing step reduces by construction to a fitted input, self-citation, or renamed prior result; the central definitions and theoretical foundations are developed independently and connected to existing ASP without the derivation collapsing into its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The paper introduces the new formalism itself; no free parameters or invented entities beyond the core definitions are visible in the abstract. Standard mathematical logic axioms are assumed as background.

axioms (1)
  • standard math Standard semantics of first-order answer set programs
    Invoked when connecting the new formalism to traditional non-modular ASP.
invented entities (1)
  • parametric modular logic programs no independent evidence
    purpose: To define subprograms with parameters and intensionality statements
    Core new formalism introduced to capture clingo collective control declaratively.

pith-pipeline@v0.9.0 · 5598 in / 1244 out tokens · 26928 ms · 2026-05-22T04:59:34.540348+00:00 · methodology

discussion (0)

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supports
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extends
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unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

  1. [1]

    Cabalar, J

    P. Cabalar, J. Fandinno, and Y. Lierler. Modular answer set programming as a formal specification language. Theory and Practice of Logic Programming, 20 0 (5): 0 767--782, 2020

    work page 2020

  2. [2]

    Dimopoulos, M

    Y. Dimopoulos, M. Gebser, P. L \"u hne, J. Romero, and T. Schaub. plasp 3: Towards effective ASP planning. In M. Balduccini and T. Janhunen, editors, Proceedings of the Fourteenth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'17), volume 10377 of Lecture Notes in Artificial Intelligence, pages 286--300. Springer-Verlag, 2017

    work page 2017

  3. [3]

    Fandinno and Y

    J. Fandinno and Y. Lierler. Splitting answer set programs with respect to intensionality statements. In B. Williams, Y. Chen, and J. Neville, editors, Proceedings of the Thirty-seventh National Conference on Artificial Intelligence (AAAI'23), pages 6338--6345. AAAI Press, 2023

    work page 2023

  4. [4]

    Fandinno, V

    J. Fandinno, V. Lifschitz, P. L \"u hne, and T. Schaub. Verifying tight logic programs with anthem and vampire. Theory and Practice of Logic Programming, 20 0 (5): 0 735--750, 2020

    work page 2020

  5. [5]

    Fandinno, V

    J. Fandinno, V. Lifschitz, and N. Temple. Locally tight programs. Theory and Practice of Logic Programming, 24 0 (5): 0 942--972, 2024

    work page 2024

  6. [6]

    Fandinno, Z

    J. Fandinno, Z. Hansen, Yu. Lierler, Ch. Glinzer, J. Heuer, T. Schaub, T. Stolzmann, and V. Lifschitz. ANTHEM 2.0: Automated reasoning for answer set programming. Theory Pract. Log. Program., 25 0 (4): 0 668--684, 2025

    work page 2025

  7. [7]

    Ferraris, J

    P. Ferraris, J. Lee, and V. Lifschitz. A new perspective on stable models. In M. Veloso, editor, Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI'07), pages 372--379. AAAI/MIT Press, 2007

    work page 2007

  8. [8]

    Ferraris, J

    P. Ferraris, J. Lee, and V. Lifschitz. Stable models and circumscription. Artificial Intelligence, 175 0 (1): 0 236--263, 2011

    work page 2011

  9. [9]

    Gebser, R

    M. Gebser, R. Kaminski, B. Kaufmann, and T. Schaub. Clingo = ASP + control: Extended report. Technical report, Universit \"a t Potsdam, 2014. URL http://www.cs.uni-potsdam.de/wv/pdfformat/gekakasc14a.pdf

    work page 2014

  10. [10]

    Gebser, R

    M. Gebser, R. Kaminski, B. Kaufmann, and T. Schaub. Multi-shot ASP solving with clingo. Theory and Practice of Logic Programming, 19 0 (1): 0 27--82, 2019. doi:10.1017/S1471068418000054

    work page doi:10.1017/s1471068418000054 2019

  11. [11]

    Gelfond and V

    M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In R. Kowalski and K. Bowen, editors, Proceedings of the Fifth International Conference and Symposium of Logic Programming (ICLP'88), pages 1070--1080. MIT Press, 1988. doi:10.1201/b10397-6

    work page doi:10.1201/b10397-6 1988

  12. [12]

    Hansen and Yu

    Z. Hansen and Yu. Lierler. Sm-based semantics for answer set programs containing conditional literals and arithmetic. In PADL , volume 15537 of Lecture Notes in Computer Science, pages 71--87. Springer, 2025

    work page 2025

  13. [13]

    Harrison and Yu

    A. Harrison and Yu. Lierler. First-order modular logic programs and their conservative extensions. Theory and Practice of Logic programming, 32nd Int'l. Conference on Logic Programming (ICLP) Special Issue, 2016

    work page 2016

  14. [14]

    Janhunen, E

    T. Janhunen, E. Oikarinen, H. Tompits, and S. Woltran. Modularity aspects of disjunctive stable models. In C. Baral, G. Brewka, and J. Schlipf, editors, Proceedings of the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'07), volume 4483 of Lecture Notes in Artificial Intelligence, pages 175--187. Springer-Verlag, 2007

    work page 2007

  15. [15]

    Lifschitz

    V. Lifschitz. Transforming gringo rules into formulas in a natural way. In W. Faber, G. Friedrich, M. Gebser, and M. Morak, editors, Proceedings of the Seventeenth European Conference on Logics in Artificial Intelligence (JELIA'21), volume 12678 of Lecture Notes in Computer Science, pages 421--434. Springer-Verlag, 2021

    work page 2021

  16. [16]

    Lifschitz and H

    V. Lifschitz and H. Turner. Splitting a logic program. In Pascal Van Hentenryck, editor, Proceedings of International Conference on Logic Programming ( ICLP ) , pages 23--37, 1994

    work page 1994

  17. [17]

    Lifschitz, L

    V. Lifschitz, L. Morgenstern, and D. Plaisted. Knowledge representation and classical logic. In Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter, editors, Handbook of Knowledge Representation, pages 3--88. Elsevier, 2008. URL http://www.cs.utexas.edu/users/ai-lab?lif08b

    work page 2008

  18. [18]

    Oikarinen and T

    E. Oikarinen and T. Janhunen. Modular equivalence for normal logic programs. In Gerhard Brewka, Silvia Coradeschi, Anna Perini, and Paolo Traverso, editors, Proceedings of the 17th European Conference on Artificial Intelligence, ECAI 2006, pages 412--416, Amsterdam, The Netherlands, 2006. IOS Press

    work page 2006

  19. [19]

    Oikarinen and T

    E. Oikarinen and T. Janhunen. Achieving compositionality of the stable model semantics for S models programs. Theory and Practice of Logic Programming, 5--6: 0 717--761, 2008

    work page 2008

  20. [20]

    Pearce and A

    D. Pearce and A. Valverde. Towards a first order equilibrium logic for nonmonotonic reasoning. In J. Alferes and J. Leite, editors, Proceedings of the Ninth European Conference on Logics in Artificial Intelligence (JELIA'04), volume 3229 of Lecture Notes in Computer Science, pages 147--160. Springer-Verlag, 2004. doi:10.1007/978-3-540-30227-8\_15

    work page doi:10.1007/978-3-540-30227-8 2004

  21. [21]

    Pearce and A

    D. Pearce and A. Valverde. A first order nonmonotonic extension of constructive logic. Studia Logica, 30 0 (2-3): 0 321--346, 2005

    work page 2005