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arxiv: 2605.29965 · v2 · pith:SWUFTWSFnew · submitted 2026-05-28 · 💻 cs.AI

Meta-Programming for Linear-time Temporal Answer Set Programming

Susana Hahn , Amad\'e Nemes , Javier Romero , Torsten Schaub This is my paper

Pith reviewed 2026-07-01 07:46 UTC · model grok-4.3

classification 💻 cs.AI
keywords meta-programminganswer set programmingtemporal logicequilibrium logicclingoTELMELDEL
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The pith

A meta-programming framework lets one declarative system handle multiple temporal variants of answer set programming.

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

The paper develops a meta-programming approach to implement the semantics of several temporal extensions to answer set programming in a single declarative system. This addresses the rigidity of optimized ASP solvers that makes it hard to test new logical designs for non-monotonic reasoning over time. The method augments clingo with type specifications and nesting support for modalities, then applies a transformation pipeline to keep nested time operators intact during grounding. It demonstrates the approach through meta-encodings for linear-time, metric, and dynamic temporal equilibrium logics and supplies a tool to run the workflow.

Core claim

A flexible meta-programming framework operationalizes the semantics of varied temporal logics through a unified, declarative framework by extending clingo's theory grammar with formal type specifications and nesting capabilities, and using a transformation pipeline that protects nested modalities from stable-model-based simplifications during grounding. This is shown by implementing meta-encodings for TEL, MEL, and DEL, with accounts of features for interval constraints and Fischer-Ladner closure.

What carries the argument

The transformation pipeline that protects nested modalities from stable-model-based simplifications during grounding, together with clingo's augmented theory grammar for formal type specifications and nesting.

If this is right

  • Meta-encodings become possible for TEL, MEL, and DEL within the same framework.
  • Interval constraints of MEL can be managed through declarative features of the framework.
  • The Fischer-Ladner closure for DEL can be incorporated into the meta-encodings.
  • The metasp system encapsulates the full workflow for using these encodings.

Where Pith is reading between the lines

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

  • Researchers could prototype additional temporal logic variants more quickly by changing meta-encodings rather than solver internals.
  • Similar protection techniques for complex expressions might apply to other ASP extensions that need special grounding behavior.
  • Applications such as planning or verification could switch between temporal semantics with less implementation effort.

Load-bearing premise

The transformation pipeline must correctly prevent stable-model simplifications from affecting nested modalities so that the computed models match the intended temporal logic semantics.

What would settle it

An example program containing nested modalities in one of the temporal logics where the meta-encoding and grounding steps produce stable models that violate the expected behavior under the original logic's semantics.

Figures

Figures reproduced from arXiv: 2605.29965 by Amad\'e Nemes, Javier Romero, Susana Hahn, Torsten Schaub.

Figure 1
Figure 1. Figure 1: Comparison of runtime and solving time of [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
read the original abstract

The development of temporal extensions of Answer Set Programming (ASP) has led to the emergence of non-monotonic linear-time (TEL), dynamic (DEL), and metric (MEL) temporal equilibrium logics. However, the inherent rigidity of highly optimized ASP systems often hinders the rapid exploration and implementation of alternative logical designs. In this work, we propose a flexible meta-programming framework that operationalizes the semantics of varied temporal logics through a unified, declarative framework. Our approach extends standard ASP meta-programming by augmenting clingo's theory grammar with formal type specifications and nesting capabilities. To ensure semantic correctness, we introduce a transformation pipeline that protects nested modalities from stable-model-based simplifications during grounding. We demonstrate the extensibility of our framework by implementing meta-encodings for TEL, MEL, and DEL. We provide a comprehensive account of TEL and highlight the key features for managing the interval constraints of MEL and the Fischer-Ladner closure in DEL. Finally, we introduce the metasp system, a versatile tool that encapsulates this workflow.

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

1 major / 1 minor

Summary. The paper proposes a meta-programming framework extending clingo's theory grammar with formal type specifications and nesting capabilities to operationalize the semantics of temporal equilibrium logics (TEL, MEL, DEL) in a unified declarative way. It introduces a transformation pipeline to protect nested modalities from stable-model simplifications during grounding, provides meta-encodings for the three logics with accounts of TEL features, MEL interval constraints, and DEL Fischer-Ladner closure, and presents the metasp system as an implementation tool.

Significance. If the central claim of semantic correctness holds, the framework would enable flexible, rapid exploration of alternative temporal logic designs without the constraints of highly optimized ASP solvers, offering a reusable declarative approach for non-monotonic temporal reasoning. The explicit meta-encodings and system implementation could support reproducibility and extension by others in the ASP and temporal logic communities.

major comments (1)
  1. [Abstract / Implementation sections] The abstract asserts semantic correctness of the transformation pipeline for protecting nested modalities, but provides no verification details, edge-case handling, or empirical checks; this leaves the load-bearing claim of correctness without demonstrated support and requires addition of proofs, test cases, or comparisons in the relevant implementation sections.
minor comments (1)
  1. [Framework description] Clarify the exact grammar extensions to clingo's theory language and how they interact with existing ASP grounding.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the framework's potential impact. We address the single major comment point-by-point below.

read point-by-point responses

  1. Referee: [Abstract / Implementation sections] The abstract asserts semantic correctness of the transformation pipeline for protecting nested modalities, but provides no verification details, edge-case handling, or empirical checks; this leaves the load-bearing claim of correctness without demonstrated support and requires addition of proofs, test cases, or comparisons in the relevant implementation sections.

    Authors: We agree that the abstract's claim of semantic correctness for the grounding protection pipeline requires stronger support than currently provided. While the manuscript describes the pipeline's design (type specifications, nesting, and protection transformations) and demonstrates it via the TEL/MEL/DEL meta-encodings, it does not include explicit proofs, systematic edge-case analysis (e.g., deeply nested modalities or interactions with clingo's simplifications), or empirical comparisons. In revision we will add a dedicated subsection in the implementation section containing: (1) a formal argument establishing that the pipeline preserves stable-model semantics for nested temporal formulas by construction, (2) a set of targeted test cases exercising edge cases, and (3) runtime comparisons between protected and unprotected encodings on the metasp benchmarks. These additions will be placed before the system description. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework is self-contained implementation

full rationale

The paper describes a meta-programming extension to clingo for encoding temporal logics (TEL, MEL, DEL) via type specifications, nesting, and a transformation pipeline to protect modalities. No equations, predictions, or first-principles results are presented that reduce by construction to fitted inputs or self-citations. The central contribution is an extensible declarative framework and tool (metasp), with no load-bearing uniqueness theorems, ansatzes smuggled via prior self-citation, or renaming of known results as novel derivations. The work is an independent software realization of existing semantics and is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As an implementation and tool paper, the abstract mentions no free parameters, mathematical axioms, or invented entities; the contribution is a software framework rather than a theoretical derivation.

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Reference graph

Works this paper leans on

28 extracted references · 14 canonical work pages

  1. [1]

    Aguado, P

    F. Aguado, P. Cabalar, G. P \'e rez, C. Vidal, and M. Di \'e guez. Temporal logic programs with variables. Theory and Practice of Logic Programming, 17 0 (2): 0 226--243, 2017

    2017

  2. [2]

    Aguado, P

    F. Aguado, P. Cabalar, M. Di \'e guez, G. P \'e rez, T. Schaub, A. Schuhmann, and C. Vidal. Linear-time temporal answer set programming. Theory and Practice of Logic Programming, 23 0 (1): 0 2--56, 2023. doi:10.1017/S1471068421000557

    work page doi:10.1017/s1471068421000557 2023

  3. [3]

    Alur and T

    R. Alur and T. Henzinger. Logics and models of real time: A survey. In Real-Time: Theory in Practice, pages 74--106. Springer-Verlag, 1992

    1992

  4. [4]

    Balai, M

    E. Balai, M. Gelfond, and Y. Zhang. Towards answer set programming with sorts. In P. Cabalar and T. Son, editors, Proceedings of the Twelfth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'13), volume 8148 of Lecture Notes in Artificial Intelligence, pages 135--147. Springer-Verlag, 2013

    2013

  5. [5]

    Banbara, B

    M. Banbara, B. Kaufmann, M. Ostrowski, and T. Schaub. Clingcon: The next generation. Theory and Practice of Logic Programming, 17 0 (4): 0 408--461, 2017. doi:10.1017/S1471068417000138

    work page doi:10.1017/s1471068417000138 2017

  6. [6]

    Becker, P

    A. Becker, P. Cabalar, M. Di \'e guez, S. Hahn, J. Romero, and T. Schaub. Compiling metric temporal answer set programming. In lpnmr24 , pages 15--29. doi:10.1007/978-3-031-74209-5_2

    work page doi:10.1007/978-3-031-74209-5_2

  7. [7]

    Becker, P

    A. Becker, P. Cabalar, M. Di \'e guez, T. Schaub, and A. Schuhmann. Metric temporal equilibrium logic over timed traces. Theory and Practice of Logic Programming, 24 0 (3): 0 425--452, 2024 b . doi:10.1017/S1471068424000139

    work page doi:10.1017/s1471068424000139 2024

  8. [8]

    Behrens, R

    J. Behrens, R. Kaminski, T. Schaub, T. Son, J. S vancara, and P. Wanko. Routing and scheduling in answer set programming applied to multi-agent path finding: Preliminary report. CoRR, abs/2403.12153, 2024. URL https://arxiv.org/abs/2403.12153

    work page arXiv 2024

  9. [9]

    Beiser, S

    A. Beiser, S. Hahn, and T. Schaub. ASP -driven user-interaction with clinguin. In P. Cabalar and T. Swift, editors, Technical Communications of the Fortieth International Conference on Logic Programming (ICLP'24), EPTCS , 2024

    2024

  10. [10]

    Cabalar and S

    P. Cabalar and S. Demri. Automata-based computation of temporal equilibrium models. In G. Vidal, editor, Proceedings of the Twenty-first International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR'11), volume 7225 of Lecture Notes in Computer Science, pages 57--72. Springer-Verlag, 2011

    2011

  11. [11]

    Cabalar, D

    P. Cabalar, D. Pearce, and A. Valverde. Safety preserving transformations for general answer set programs. In D. D e Schreye, editor, Proceedings of the Nineteenth International Symposium on Logic Based Program Synthesis and Transformation (LOPSTR'09), volume 6037 of Lecture Notes in Computer Science, pages 132--146. Springer-Verlag, 2010

    2010

  12. [12]

    Cabalar, R

    P. Cabalar, R. Kaminski, P. Morkisch, and T. Schaub. telingo = ASP + time. In M. Balduccini, Y. Lierler, and S. Woltran, editors, Proceedings of the Fifteenth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'19), volume 11481 of Lecture Notes in Artificial Intelligence, pages 256--269. Springer-Verlag, 2019. doi:10.1007/978-...

    work page doi:10.1007/978-3-030-20528-7_19 2019

  13. [13]

    Cabalar, M

    P. Cabalar, M. Di \'e guez, F. Laferriere, and T. Schaub. Implementing dynamic answer set programming over finite traces. In G. D e Giacomo, A. Catal \'a , B. Dilkina, M. Milano, S. Barro, A. Bugar \' n, and J. Lang, editors, Proceedings of the Twenty-fourth European Conference on Artificial Intelligence (ECAI'20), pages 656--663. IOS Press, 2020. doi:10....

    work page doi:10.3233/faia200151 2020

  14. [14]

    Cuteri, G

    A. Cuteri, G. Mazzotta, R. Pe \ n aloza, and F. Ricca. Automata-based ltl _f satisfiability checking via ASP . In D. Aineto, R. De Benedictis, M. Maratea, M. Mittelmann, G. Monaco, E. Scala, L. Serafini, I. Serina, F. Spegni, E. Tosello, A. Umbrico, and M. Vallati, editors, Workshop Proceedings of the Twenty-third International Conference of the Italian A...

    2024

  15. [15]

    D e Giacomo and M

    G. D e Giacomo and M. Vardi. Linear temporal logic and linear dynamic logic on finite traces. In F. Rossi, editor, Proceedings of the Twenty-third International Joint Conference on Artificial Intelligence (IJCAI'13), pages 854--860. IJCAI/AAAI Press, 2013

    2013

  16. [16]

    Dodaro, G

    C. Dodaro, G. Gupta, and M. Martinez, editors. Proceedings of the Seventeenth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'24), volume 15245 of Lecture Notes in Artificial Intelligence, 2024. Springer-Verlag. doi:10.1007/978-3-031-74209-5

    work page doi:10.1007/978-3-031-74209-5 2024

  17. [17]

    Fionda, A

    V. Fionda, A. Ielo, and F. Ricca. Ltlf2asp: Ltlf bounded satisfiability in ASP . In lpnmr24 , pages 373--386. doi:10.1007/978-3-031-74209-5_28

    work page doi:10.1007/978-3-031-74209-5_28

  18. [18]

    Fischer and R

    M. Fischer and R. Ladner. Propositional dynamic logic of regular programs. Journal of Computer and System Sciences, 18 0 (2): 0 194--211, 1979

    1979

  19. [19]

    Gebser, R

    M. Gebser, R. Kaminski, and T. Schaub. Complex optimization in answer set programming. Theory and Practice of Logic Programming, 11 0 (4-5): 0 821--839, 2011

    2011

  20. [20]

    Hahn, A Nemes, J

    S. Hahn, A Nemes, J. Romero, and T. Schaub. . https://potassco.org/metasp, 2026

    2026

  21. [21]

    Heljanko and I

    K. Heljanko and I. Niemel \"a . Bounded LTL model checking with stable models. Theory and Practice of Logic Programming, 3 0 (4-5): 0 519--550, 2003

    2003

  22. [22]

    Kaminski, J

    R. Kaminski, J. Romero, T. Schaub, and P. Wanko. How to build your own ASP -based system?! Theory and Practice of Logic Programming, 23 0 (1): 0 299--361, 2023. doi:10.1017/S1471068421000508

    work page doi:10.1017/s1471068421000508 2023

  23. [23]

    Levesque, R

    H. Levesque, R. Reiter, Y. Lesp \'e rance, F. Lin, and R. Scherl. GOLOG : A logic programming language for dynamic domains. Journal of Logic Programming, 31 0 (1-3): 0 59--83, 1997. doi:10.1016/S0743-1066(96)00121-5

    work page doi:10.1016/s0743-1066(96)00121-5 1997

  24. [24]

    Lifschitz

    V. Lifschitz. Answer Set Programming. Springer-Verlag, 2019. doi:10.1007/978-3-030-24658-7

    work page doi:10.1007/978-3-030-24658-7 2019

  25. [25]

    A. Nemes. Implementing a temporal answer set solver using metaprogramming techniques. Master's thesis, University of Potsdam, 2024

    2024

  26. [26]

    D. Pearce. Equilibrium logic. Annals of Mathematics and Artificial Intelligence, 47 0 (1-2): 0 3--41, 2006. doi:10.1007/s10472-006-9028-z

    work page doi:10.1007/s10472-006-9028-z 2006

  27. [27]

    A. Pnueli. The temporal logic of programs. In Proceedings of the Eighteenth Symposium on Foundations of Computer Science (FOCS'77), pages 46--57. IEEE Computer Society Press, 1977. doi:10.1109/SFCS.1977.32

    work page doi:10.1109/sfcs.1977.32 1977

  28. [28]

    V. Pratt. Semantical consideration on floyd-hoare logic. In Proceedings of the Seventeenth Annual Symposium on Foundations of Computer Science (SFCS'76), pages 109--121. IEEE Computer Society Press, 1976

    1976