47 Search Results for "Voronkov, Andrei"

Document
Invited Talk
DOI: 10.4230/LIPIcs.SAT.2026.1
SAT in Saturation: A Satisfied Match (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)

Abstract
Saturation is the leading concept behind the proof-search algorithms of state-of-the-art first-order theorem provers [Filip Bártek et al., 2025; Christoph Weidenbach et al., 2009; Stephan Schulz et al., 2019]. The key idea behind saturation-based proof search is to reduce the problem of proving validity of a first-order formula to the problem of establishing unsatisfiability of the respective formula, by using a sound inference system, such as resolution and superposition [Leo Bachmair and Harald Ganzinger, 2001; Robert Nieuwenhuis and Albert Rubio, 2001]. Central to efficient saturation-based proof search is the implementation of redundancy in the form of simplification rules [John Alan Robinson, 1965; Laura Kovács and Andrei Voronkov, 2013]: such rules do not add new formulas to search space, but instead simplify/delete redundant formulas from the search space, while not loosing refutational completeness of superposition. Redundancy in first-order theorem proving is controlled via term/clause ordering and literal selection functions in extension of standard superposition: redundant clauses are logical consequences of smaller clauses with respect to the considered ordering. While redundancy is essential for efficient proof search, establishing whether an arbitrary first-order formula is redundant is as hard as proving whether it is valid. First-order provers therefore implement sufficient conditions towards proving redundancy, so that these conditions can be efficiently checked, ideally using only syntactic arguments over formulas. One such condition comes with the notion of subsumption, yielding one of the most important simplification rules in automated reasoners [Leo Bachmair and Harald Ganzinger, 1994]. It is common that millions of subsumption checks are performed during a single solver run [Jakob Rath et al., 2022]. However, in contrast to propositional subsumption as used by SAT solvers and implemented using sophisticated polynomial algorithms, first-order subsumption in first-order theorem proving involves NP-complete search queries, turning the efficient use of first-order subsumption into a huge practical burden. This talks presents a tailored integration of SAT solving for detecting variants of subsumption in superposition. Key to our approach is retrieving clauses from the search space and checking whether subsumption with retrieved clauses can be applied, using multi-literal matching. A solution to our SAT-based encoding gives a concrete application of (variants of) subsumption, allowing the first-order prover to apply that instance of subsumption as a simplification rule during saturation [Bernhard Gleiss et al., 2020; Jakob Rath et al., 2022; Robin Coutelier et al., 2025]. Our SAT encoding captures subset relations among literals/clauses and formalizes matching of literals between inference premises/conclusions. We show that SAT encodings improve literal matching, and thus subsumption, in first-order theorem proving. In particular, our experimental results using the Vampire prover demonstrate the practical benefits of using SAT solving for variants of first-order subsumption.
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Laura Kovács. SAT in Saturation: A Satisfied Match (Invited Talk). In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kovacs:LIPIcs.SAT.2026.1,
  author =	{Kov\'{a}cs, Laura},
  title =	{{SAT in Saturation: A Satisfied Match}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-431-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{377},
  editor =	{Ignatiev, Alexey and Szeider, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.1},
  URN =		{urn:nbn:de:0030-drops-263076},
  doi =		{10.4230/LIPIcs.SAT.2026.1},
  annote =	{Keywords: Automated Reasoning, First-Order Theorem Proving, Superposition, Subsumption, Redundancy, SAT Solving, Vampire}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2026.2
Saturation-Guided Inductive Synthesis (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract
Proof by induction is common-place in mathematics [Josef Urban and Geoff Sutcliffe, 2010; Martin Desharnais et al., 2022], formal verification [Raven Beutner and Bernd Finkbeiner, 2024; Wolfgang Ahrendt et al., 2000; Pamina Georgiou et al., 2022], cybersecurity [Simon Jeanteur et al., 2024; Evan Laufer et al., 2024], and many more areas. This talk overviews recent progress in automating inductive reasoning in quantified logic, with applications to code synthesis. Key to our work is saturation-based first-order theorem proving [Laura Kovács and Andrei Voronkov, 2013], using variants of the superposition calculus [Robert Nieuwenhuis and Albert Rubio, 2001]. We show that induction and synthesis are better together in saturation, allowing us not only to prove quantified properties F, but also generate a functional implementation of F during proof search. We showcase our results using the first-order theorem prover Vampire [Filip Bártek et al., 2025], a completely automatic push-button theorem prover for first-order logic with theories, including arithmetic, inductively defined datatypes, induction, and higher-order logic. We structure our talk within three inter-connected parts. First, we overview the main ingredients behind saturation provers [Filip Bártek et al., 2025; Stephan Schulz et al., 2019; Christoph Weidenbach et al., 2009] using superposition. Such provers work by negating an input conjecture F, transforming ¬ F into a clausal normal form, and using superposition inferences to derive new clauses from existing ones until a contradiction is reached; when a contradiction is derived, validity of F is established. Many years of development in saturation-based theorem proving have gone into making this process as efficient as possible, while deriving new clauses only when needed in order to tame growth of the search space. Doing so, highly-efficient superposition calculi parametrized by so-called clause selection functions have been proposed, in order to make as few inferences between clauses as possible. Redundancy elimination techniques further prune the search space. Next, we show how to formalize applications of induction in the saturation process [Márton Hajdú et al., 2022], without bringing drastic changes into the overall framework of first-order proving. A natural choice for implementing induction would be by reducing goals to subgoals, in particular by proving a base case and an inductive step case of a valid induction principle. For example, a goal ∀ x. F(x) over natural numbers x can be proven using structural induction: we prove F[0] (base case) and ∀ x. F(x) ⇒ F(x+1) (step case). However, saturation theorem proving is not about reducing goals to subgoals: in principle, each clause in the search space can be chosen during any step of saturation. We therefore automate induction in saturation as follows. When a clause F(x) is chosen and inductive reasoning over F should be applied (for example, because F uses inductively defined data types x, such as natural numbers), we combine the application of a valid induction schema over F(x) with resolution. Put it simply, induction and resolution are combined in one step of saturation, allowing us to use parts of F(x) as subgoals of F(x). Interestingly with this approach is that clauses generated during saturation may be stronger than the induction schema and, most importantly, are friendly to saturation provers: they are mostly quantifier-free Horn clauses and their (at most one) positive equality cannot be used in many inferences during saturation. Thus, applying many induction inferences during proof search would hardly affect the performance of a saturation prover. Figure 1 lists a property over natural numbers: every natural number x is the half of another natural number y. Proving this property in saturation, and in particular using Vampire, can be achieved by (structural) induction over x. Finally, we extend saturation proof search with code synthesis [Petra Hozzová et al., 2024]. While proving formula F, we track the constructive parts of the proof of F using so-called answer literals [Cordell Green, 1969]. We use these parts to synthesize a program satisfying F and use the applications of induction in saturation to construct recursive programs satisfying F. In a nutshell, the base case and inductive case steps of induction in saturation express how to construct the desired program for the next recursive step using the program for the previous recursive step; we capture this information via answer literals. When we apply induction in saturation, we introduce a special term into the answer literal and record the program corresponding to the induction step. As we prove induction steps, we capture their corresponding programs in the answer literal. Finally, we convert the special tracker terms from the answer literals into recursive functions, and obtain a program satisfying property F. For example, from the proof of property of Figure 1, our approach implemented in Vampire infers the following functional implementation of a recursive function r, while using only the signature of Figure 1: 𝗋(0) & := 0 𝗋(s(x)) & := s(s(𝗋(x))) The above inferred function r satisfies the property of Figure 1 and, for each input natural number x, computes a natural number 𝗋(x) such that x is half of 𝗋(x). In summary, induction and synthesis are better together in saturation-based theorem proving using the superposition calculus. Soundness and practical use of our work has been addressed and experimented using the Vampire theorem prover, both in the case of automating induction [Márton Hajdú et al., 2022; Márton Hajdú et al., 2024] and program synthesis [Petra Hozzová et al., 2023; Petra Hozzová et al., 2024]. Interesting questions regarding completeness arise: if a program satisfying a given property exists, can we derive it from saturation-based proof search? Our recent results [Hajdu et al., 2026] answer this question for recursion-free program using additional assumptions of realizability. A natural direction for future work is to identify realizability assumptions for recursive program synthesis and induction.
Cite as

Laura Kovács. Saturation-Guided Inductive Synthesis (Invited Talk). In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 2:1-2:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kovacs:LIPIcs.FSCD.2026.2,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Saturation-Guided Inductive Synthesis}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{2:1--2:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.2},
  URN =		{urn:nbn:de:0030-drops-263521},
  doi =		{10.4230/LIPIcs.FSCD.2026.2},
  annote =	{Keywords: automated reasoning, first-order theorem proving, saturation, induction, program synthesis}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2026.12
The Complexity of Finding Missing Answer Repairs

Authors: Jesse Comer and Val Tannen

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
We investigate the problem of identifying database repairs for missing tuples in query answers. We show that when the query is part of the input - the combined complexity setting - determining whether or not a repair exists is polynomial-time equivalent to the satisfiability problem for classes of queries admitting a weak form of projection and selection. We then identify the sub-classes of unions of conjunctive queries with negated atoms, defined by the relational algebra operations permitted to appear in the query, for which the minimal repair problem can be solved in polynomial time. In contrast, we show that the problem is NP-hard, as well as set cover-hard to approximate via strict reductions, whenever both projection and join are permitted in the input query. Additionally, we show that finding the size of a minimal repair for unions of conjunctive queries (with negated atoms permitted) is OptP[log(n)]-complete, while computing a minimal repair is possible with O(n²) queries to an NP oracle. With recursion permitted, the combined complexity of all of these variants increases significantly, with an EXP lower bound. However, from the data complexity perspective, we show that minimal repairs can be identified in polynomial time for all queries expressible as semi-positive datalog programs.
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Jesse Comer and Val Tannen. The Complexity of Finding Missing Answer Repairs. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{comer_et_al:LIPIcs.ICDT.2026.12,
  author =	{Comer, Jesse and Tannen, Val},
  title =	{{The Complexity of Finding Missing Answer Repairs}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.12},
  URN =		{urn:nbn:de:0030-drops-256265},
  doi =		{10.4230/LIPIcs.ICDT.2026.12},
  annote =	{Keywords: Missing answers, database repairs, datalog, computational complexity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.17
A Uniform Cut-Elimination Theorem for Linear Logics with Fixed Points and Super Exponentials

Authors: Alexis Saurin and Esaïe Bauer

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
In the realm of light logics deriving from linear logic, a number of variants of exponential rules have been investigated. The profusion of such proof systems induces the need for cut-elimination theorems for each logic, the proofs of which may be redundant. A number of approaches in proof theory have been adopted to cope with this need. In the present paper, we consider this issue from the point of view of enhancing linear logic with least and greatest fixed-points and considering such a variety of exponential connectives. Our main contribution is to provide a uniform cut-elimination theorem for a parametrized system with fixed-points by combining two approaches: cut-elimination proofs by reduction (or translation) to another system and the identification of sufficient conditions for cut-elimination. More precisely, we examine a broad range of systems, taking inspiration from Nigam and Miller’s subexponentials and from the first author and Laurent’s super exponentials. Our work is motivated, on the one hand, by Baillot’s work on light logics with recursive types and on the other hand by our recent work on the proof theory of the modal μ-calculus.
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Alexis Saurin and Esaïe Bauer. A Uniform Cut-Elimination Theorem for Linear Logics with Fixed Points and Super Exponentials. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 17:1-17:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{saurin_et_al:LIPIcs.CSL.2026.17,
  author =	{Saurin, Alexis and Bauer, Esa\"{i}e},
  title =	{{A Uniform Cut-Elimination Theorem for Linear Logics with Fixed Points and Super Exponentials}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{17:1--17:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.17},
  URN =		{urn:nbn:de:0030-drops-254418},
  doi =		{10.4230/LIPIcs.CSL.2026.17},
  annote =	{Keywords: cut elimination, exponential modalities, fixed-points, linear logic, light logics, mu-calculus, non-wellfounded proofs, proof theory, sequent calculus, subexponentials, super exponentials}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.7
Modern Datalog: Concepts, Methods, Applications (Invited Paper)

Authors: Markus Krötzsch

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Pure Datalog is arguably the most fundamental rule language, elegant and simple, but also often too limited to be useful in practice. This has motivated the introduction of many new expressive features, ranging from datatypes and related functions, over aggregates and semi-ring generalisations, to existential quantifiers and complex terms. In spite of their variety, all these approaches remain true to the nature of Datalog as a direct, pattern-based way of computing on structured data. We therefore find that a modern notion of Datalog is emerging, distinctly different from other approaches of logic programming and with its own set of related methods and applications. In this course, we introduce Datalog and its most common extensions, and explain when and how these features can be used together (which is often, but not always, safe to do). We further look at modern Datalog systems and some of their primary use cases. Hands-on work with Datalog and its extensions is done with the free Datalog engine https://knowsys.github.io/nemo-doc/. The course is accessible to all audiences and does not assume specific prior knowledge.
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Markus Krötzsch. Modern Datalog: Concepts, Methods, Applications (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 7:1-7:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{krotzsch:OASIcs.RW.2024/2025.7,
  author =	{Kr\"{o}tzsch, Markus},
  title =	{{Modern Datalog: Concepts, Methods, Applications}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{7:1--7:41},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.7},
  URN =		{urn:nbn:de:0030-drops-250524},
  doi =		{10.4230/OASIcs.RW.2024/2025.7},
  annote =	{Keywords: Datalog, query language, knowlegde representation and reasoning, logic programming, Horn logic, SPARQL, datatypes and aggregation, lecture notes, tutorial}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.8
ASP Essentials: Modelling and Efficient Solving (Invited Paper)

Authors: Giuseppe Mazzotta and Francesco Ricca

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Answer Set Programming (ASP) is a logic-based Knowledge Representation and Reasoning (KRR) paradigm that facilitates rapid prototyping of solutions for complex problems. It is particularly effective for tackling Deep Reasoning tasks involving exponentially large search spaces, such as combinatorial search and optimization. While getting started with ASP is relatively easy, mastering its advanced constructs and scaling solutions to real-world problem sizes can be challenging. This paper provides an introduction to ASP, guiding the reader from the fundamentals of the language to the application of programming methodologies and the computation of answer sets. Beyond the core framework, the paper also examines selected extensions of ASP that enable the modeling of complex problems, as well as compilation techniques designed to enhance solving efficiency. Furthermore, it mentions some recent tools that combine ASP with LLMs.
Cite as

Giuseppe Mazzotta and Francesco Ricca. ASP Essentials: Modelling and Efficient Solving (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mazzotta_et_al:OASIcs.RW.2024/2025.8,
  author =	{Mazzotta, Giuseppe and Ricca, Francesco},
  title =	{{ASP Essentials: Modelling and Efficient Solving}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{8:1--8:21},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.8},
  URN =		{urn:nbn:de:0030-drops-250539},
  doi =		{10.4230/OASIcs.RW.2024/2025.8},
  annote =	{Keywords: Answer Set Programming, ASP with Quantifiers, Grounding Bottleneck, Compilation-based ASP solving, Neurosymbolic AI, LLMs}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.5
Inconsistency-Tolerant Semantics Based on (Preferred) Repairs (Invited Paper)

Authors: Camille Bourgaux

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Real-world datasets are plagued by data quality issues which may render the data inconsistent w.r.t. a set of constraints, be they given by database integrity constraints or ontologies. A prominent way to handle such inconsistent data is to use inconsistency-tolerant semantics to obtain meaningful answers to queries. Most of these semantics are based on some notion of repairs, which represent ways of restoring the data consistency. The most basic kind of repairs is that of subset repairs, which are maximal consistent subsets of the dataset. However, in many scenarios, one can define preferred repairs based on some preference information. These lecture notes present inconsistency-tolerant semantics, focusing on the repair-based ones, then review different kinds of preferred repairs that have been considered in the literature. We present in particular the relationships between different kinds of preferred repairs and other notions related to inconsistency handling, the computational complexity of reasoning with (preferred) repairs, and some implementations.
Cite as

Camille Bourgaux. Inconsistency-Tolerant Semantics Based on (Preferred) Repairs (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 5:1-5:67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bourgaux:OASIcs.RW.2024/2025.5,
  author =	{Bourgaux, Camille},
  title =	{{Inconsistency-Tolerant Semantics Based on (Preferred) Repairs}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{5:1--5:67},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.5},
  URN =		{urn:nbn:de:0030-drops-250504},
  doi =		{10.4230/OASIcs.RW.2024/2025.5},
  annote =	{Keywords: Knowledge bases, databases, inconsistency handling, repairs, preferences}
}
Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.9
Reasoning About Time in DatalogMTL: Course Notes (Invited Paper)

Authors: Przemysław Andrzej Wałęga

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
Many real-world applications, such as those in healthcare, finance, and logistics, require reasoning over temporal data. Standard rule-based languages like Datalog, however, lack explicit mechanisms for handling time and temporal dependencies. In this chapter, we discussDatalogMTL, an extension of Datalog with operators frommetric temporal logic that allow to express complex temporal properties. We focus on reasoning algorithms for DatalogMTL, discussing bothmaterialisation, based on fixpoint applications of the immediate consequence operator, and anovel saturation-based extensionthat detects and halts infinite derivations, ensuring both completeness and termination of reasoning.
Cite as

Przemysław Andrzej Wałęga. Reasoning About Time in DatalogMTL: Course Notes (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{walega:OASIcs.RW.2024/2025.9,
  author =	{Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  title =	{{Reasoning About Time in DatalogMTL: Course Notes}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{9:1--9:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.9},
  URN =		{urn:nbn:de:0030-drops-250546},
  doi =		{10.4230/OASIcs.RW.2024/2025.9},
  annote =	{Keywords: DatalogMTL, Logic Programming, Temporal Reasoning}
}
Document
DOI: 10.4230/OASIcs.DX.2025.1
Beyond Static Diagnosis: A Temporal ASP Framework for HVAC Fault Detection

Authors: Roxane Koitz-Hristov, Liliana Marie Prikler, and Franz Wotawa

Published in: OASIcs, Volume 136, 36th International Conference on Principles of Diagnosis and Resilient Systems (DX 2025)

Abstract
Improving sustainability in the building sector requires more efficient operation of energy-intensive systems such as Heating, Ventilation, and Air Conditioning (HVAC). We present a novel diagnostic framework for HVAC systems that integrates Answer Set Programming (ASP) with Functional Event Calculus (FEC). Our approach exploits the declarative nature of ASP for modeling and incorporates FEC to capture temporal system dynamics. We demonstrate the feasibility of our approach through a case study on a real-world heating system, where we model key components and system constraints. Our evaluation on nominal and faulty traces shows that exploiting ASP in combination with FEC can identify plausible diagnoses. Moreover, we explore the difference between static and rolling-window strategies and provide insights into runtime versus soundness on those variants. Our work provides a step toward the practical application of ASP-based temporal reasoning in building diagnostics.
Cite as

Roxane Koitz-Hristov, Liliana Marie Prikler, and Franz Wotawa. Beyond Static Diagnosis: A Temporal ASP Framework for HVAC Fault Detection. In 36th International Conference on Principles of Diagnosis and Resilient Systems (DX 2025). Open Access Series in Informatics (OASIcs), Volume 136, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koitzhristov_et_al:OASIcs.DX.2025.1,
  author =	{Koitz-Hristov, Roxane and Prikler, Liliana Marie and Wotawa, Franz},
  title =	{{Beyond Static Diagnosis: A Temporal ASP Framework for HVAC Fault Detection}},
  booktitle =	{36th International Conference on Principles of Diagnosis and Resilient Systems (DX 2025)},
  pages =	{1:1--1:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-394-2},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{136},
  editor =	{Quinones-Grueiro, Marcos and Biswas, Gautam and Pill, Ingo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.DX.2025.1},
  URN =		{urn:nbn:de:0030-drops-247901},
  doi =		{10.4230/OASIcs.DX.2025.1},
  annote =	{Keywords: Model-based diagnosis, Answer set programming, HVAC, Modeling for diagnosis, Experimental evaluation}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.25
The Exchange Problem

Authors: Mohit Garg and Suneel Sarswat

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the matching are maximizing volume with dynamic pricing and maximizing volume at a uniform price. In this work, we study the algorithmic complexity of the problems arising from these matching tasks. For dynamic-price matching, we establish a lower bound of Ω(n log n) on the running time, thereby proving that the currently best-known O(n log n) algorithm is time-optimal. In contrast, for uniform-price matching, we present a linear-time algorithm, improving upon previous methods that require O(n log n) time to match n requests.
Cite as

Mohit Garg and Suneel Sarswat. The Exchange Problem. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garg_et_al:LIPIcs.AFT.2025.25,
  author =	{Garg, Mohit and Sarswat, Suneel},
  title =	{{The Exchange Problem}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.25},
  URN =		{urn:nbn:de:0030-drops-247449},
  doi =		{10.4230/LIPIcs.AFT.2025.25},
  annote =	{Keywords: Exchanges, Double Auctions, Matching Algorithms, Element Distinctness, Time Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.8
Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness à la Fitting

Authors: Asta Halkjær From and Anders Schlichtkrull

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Smullyan and Fitting have used abstract consistency properties to great effect in unifying meta-theoretical results in logic. In this paper, we generalize these developments with the help of Isabelle/HOL. We use locales to decompose abstract consistency into general parts, and provide the textbook variants as special cases. Users can assemble their own consistency property for a given logic. The compositionality alleviates the absence of dependent types in Isabelle/HOL. We use our development to mechanize completeness of calculi for three logics: (1) first-order logic where we only instantiate universal quantifiers with already occurring terms, (2) second-order logic over general models, and (3) a recently developed strong hybrid logic with propositional quantification.
Cite as

Asta Halkjær From and Anders Schlichtkrull. Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness à la Fitting. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{from_et_al:LIPIcs.ITP.2025.8,
  author =	{From, Asta Halkj{\ae}r and Schlichtkrull, Anders},
  title =	{{Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness \`{a} la Fitting}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.8},
  URN =		{urn:nbn:de:0030-drops-246406},
  doi =		{10.4230/LIPIcs.ITP.2025.8},
  annote =	{Keywords: Logic, completeness, abstract consistency property, Isabelle/HOL, locales}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.5
A Mechanized First-Order Theory of Algebraic Data Types with Pattern Matching

Authors: Joshua M. Cohen

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Algebraic data types (ADTs) and pattern matching are widely used to write elegant functional programs and to specify program behavior. These constructs are critical to most general-purpose interactive theorem provers (e.g. Lean, Rocq/Coq), first-order SMT-based deductive verifiers (e.g. Dafny, VeriFast), and intermediate verification languages (e.g. Why3). Such features require layers of compilation - in Rocq, pattern matches are compiled to remove nesting, while SMT-based tools further axiomatize ADTs with a first-order specification. However, these critical steps have been omitted from prior formalizations of such toolchains (e.g. MetaRocq). We give the first proved-sound sophisticated pattern matching compiler (based on Maranget’s compilation to decision trees) and first-order axiomatization of ADTs, both based on Why3 implementations. We prove the soundness of exhaustiveness checking, extending pen-and-paper proofs from the literature, and formulate a robustness property with which we find an exhaustiveness-related bug in Why3. We show that many of our proofs could be useful for reasoning about any first-order program verifier supporting ADTs.
Cite as

Joshua M. Cohen. A Mechanized First-Order Theory of Algebraic Data Types with Pattern Matching. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cohen:LIPIcs.ITP.2025.5,
  author =	{Cohen, Joshua M.},
  title =	{{A Mechanized First-Order Theory of Algebraic Data Types with Pattern Matching}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.5},
  URN =		{urn:nbn:de:0030-drops-246046},
  doi =		{10.4230/LIPIcs.ITP.2025.5},
  annote =	{Keywords: Pattern Matching Compilation, Algebraic Data Types, First-Order Logic}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.13
Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized

Authors: Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Barendregt’s book on the untyped λ-calculus refines the inconsistent view of β-divergence as representation of the undefined via the key concept of head reduction. In this paper, we put together recent revisitations of some key theorems laid out in Barendregt’s book, and we formalize them in the Abella proof assistant. Our work provides a compact and refreshed presentation of the core of the book. The formalization faithfully mimics pen-and-paper proofs. Two interesting aspects are the manipulation of contexts for the study of contextual equivalence and a formal alternative to the informal trick at work in Takahashi’s proof of the genericity lemma. As a by-product, we obtain an alternative definition of contextual equivalence that does not mention contexts.
Cite as

Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs. Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lancelot_et_al:LIPIcs.ITP.2025.13,
  author =	{Lancelot, Adrienne and Accattoli, Beniamino and Vemclefs, Maxime},
  title =	{{Barendregt’s Theory of the \lambda-Calculus, Refreshed and Formalized}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.13},
  URN =		{urn:nbn:de:0030-drops-246114},
  doi =		{10.4230/LIPIcs.ITP.2025.13},
  annote =	{Keywords: lambda-calculus, head reduction, equational theory}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.11
Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL

Authors: Jan van Brügge, Andrei Popescu, and Dmitriy Traytel

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Nominal Isabelle provides powerful tools for meta-theoretic reasoning about syntax of logics or programming languages, in which variables are bound. It has been instrumental to major verification successes, such as Gödel’s incompleteness theorems. However, the existing tooling is not compositional. In particular, it does not support nested recursion, linear binding patterns, or infinitely branching syntax. These limitations are fundamental in the way nominal datatypes and functions on them are constructed within Nominal Isabelle. Taking advantage of recent theoretical advancements that overcome these limitations through a modular approach using the concept of map-restricted bounded natural functor (MRBNF), we develop and implement a new definitional package for binding-aware datatypes in Isabelle/HOL, called MrBNF. We describe the journey from the user specification to the end-product types, constants and theorems the tool generates. We validate MrBNF in two formalization case studies that so far were out of reach of nominal approaches: (1) Mazza’s isomorphism between the finitary and the infinitary affine λ-calculus, and (2) the POPLmark 2B challenge, which involves non-free binders for linear pattern matching.
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Jan van Brügge, Andrei Popescu, and Dmitriy Traytel. Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanbrugge_et_al:LIPIcs.ITP.2025.11,
  author =	{van Br\"{u}gge, Jan and Popescu, Andrei and Traytel, Dmitriy},
  title =	{{Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.11},
  URN =		{urn:nbn:de:0030-drops-246091},
  doi =		{10.4230/LIPIcs.ITP.2025.11},
  annote =	{Keywords: syntax with bindings, datatypes, inductive predicates, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
Cite as

Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
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