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Invited Talk

DOI: 10.4230/LIPIcs.FSCD.2024.1

Meaningfulness and Genericity in a Subsuming Framework (Invited Talk)

Authors: Delia Kesner, Victor Arrial, and Giulio Guerrieri

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

This paper studies the notion of meaningfulness for a unifying framework called dBang-calculus, which subsumes both call-by-name (dCBN) and call-by-value (dCBV). We first define meaningfulness in dBang and then characterize it by means of typability and inhabitation in an associated non-idempotent intersection type system previously appearing in the literature. We validate the proposed notion of meaningfulness by showing two properties: (1) consistency of the smallest theory, called ℋ, equating all meaningless terms, and (2) genericity, stating that meaningless subterms have no bearing on the significance of meaningful terms. The theory ℋ is also shown to have a unique consistent and maximal extension ℋ*, which coincides with a well-known notion of observational equivalence. Last but not least, we show that the notions of meaningfulness and genericity in the literature for dCBN and dCBV are subsumed by the corresponding ones proposed here for the dBang-calculus.

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Delia Kesner, Victor Arrial, and Giulio Guerrieri. Meaningfulness and Genericity in a Subsuming Framework (Invited Talk). In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kesner_et_al:LIPIcs.FSCD.2024.1,
  author =	{Kesner, Delia and Arrial, Victor and Guerrieri, Giulio},
  title =	{{Meaningfulness and Genericity in a Subsuming Framework}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.1},
  URN =		{urn:nbn:de:0030-drops-203305},
  doi =		{10.4230/LIPIcs.FSCD.2024.1},
  annote =	{Keywords: Lambda calculus, Solvability, Meaningfulness, Inhabitation, Genericity}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.32

Termination of Generalized Term Rewriting Systems

Authors: Salvador Lucas

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

We investigate termination of Generalized Term Rewriting Systems (GTRS), which extend Conditional Term Rewriting Systems by considering replacement restrictions on selected arguments of function symbols, as in Context-Sensitive Rewriting, and conditional rewriting rules whose conditional part may include not only a mix of the usual (reachability, joinability,...) conditions, but also atoms defined by a set of definite Horn clauses. GTRS can be used to prove confluence and termination of Generalized Rewrite Theories and Maude programs. We have characterized confluence of terminating GTRS as the joinability of a finite set of conditional pairs. Since termination of GTRS is underexplored to date, this paper introduces a Dependency Pair Framework which is well-suited to automatically (dis)prove termination of GTRS.

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Salvador Lucas. Termination of Generalized Term Rewriting Systems. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lucas:LIPIcs.FSCD.2024.32,
  author =	{Lucas, Salvador},
  title =	{{Termination of Generalized Term Rewriting Systems}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.32},
  URN =		{urn:nbn:de:0030-drops-203616},
  doi =		{10.4230/LIPIcs.FSCD.2024.32},
  annote =	{Keywords: Program Analysis, Reduction-Based Systems, Termination}
}

Document

DOI: 10.4230/DagMan.10.1.1

Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.

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James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}

Document

DOI: 10.4230/DagRep.11.8.35

Integrated Deduction (Dagstuhl Seminar 21371)

Authors: Maria Paola Bonacina, Philipp Rümmer, and Renate A. Schmidt

Published in: Dagstuhl Reports, Volume 11, Issue 8 (2022)

Abstract

Logical reasoning plays a key role in fields as diverse as verification and synthesis, programming language foundations, knowledge engineering, and computer mathematics. Logical reasoning is increasingly important in intelligent systems, such as decision support systems, agent programming environments, and data processing systems, where deduction may provide explanation, course of action, and the capability of learning from missing information. Problem formalization in these domains typically involves multiple mathematical theories, knowledge bases, and ontologies, all of which may be very large. Problem solving requires both efficient automation and sophisticated human-machine interaction. The thrust of this seminar was that the key to unleash the power of computerized logical reasoning is integration, at different abstraction levels. This seminar offered a forum to discuss the issues related to integration of deduction in a diverse range of applications. In terms of reasoning procedures, the presence of both theories and quantifiers in problems from many contexts calls for methodologies to integrate state-of-the-art SMT solvers and automated theorem provers. This leads to investigate techniques such as model-based reasoning and semantic guidance, that were presented and discussed at the seminar. Similarly, the integration of inference rules for higher-order reasoning in inference systems that were born for first-order reasoning, such as superposition, was prominent among the topics debated at the seminar. At the architectural level, the sheer difficulty of the problems calls for the integration of provers and solvers into interactive reasoning environments. These range from higher-order proof assistants with background reasoners as hammers, to interactive program verifiers, both widely covered at the seminar in talks and discussions. The seminar showed how the application of deduction to intelligent systems necessitates the integration of deduction with other paradigms, such as probabilistic reasoning and statistical inferences. In fact, it emerged from the seminar that even systems that are not natively deductive, such as agent programming environments and industrial tools for ontology-based processing, benefit significantly from the integration of deduction. A clear and shared uptake from the seminar was that scalability and usability are crucial challenges at all levels of integration. The seminar fully succeded in promoting the exchange of new ideas and suggestions for future research.

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Maria Paola Bonacina, Philipp Rümmer, and Renate A. Schmidt. Integrated Deduction (Dagstuhl Seminar 21371). In Dagstuhl Reports, Volume 11, Issue 8, pp. 35-51, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{bonacina_et_al:DagRep.11.8.35,
  author =	{Bonacina, Maria Paola and R\"{u}mmer, Philipp and Schmidt, Renate A.},
  title =	{{Integrated Deduction (Dagstuhl Seminar 21371)}},
  pages =	{35--51},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{11},
  number =	{8},
  editor =	{Bonacina, Maria Paola and R\"{u}mmer, Philipp and Schmidt, Renate A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.8.35},
  URN =		{urn:nbn:de:0030-drops-157685},
  doi =		{10.4230/DagRep.11.8.35},
  annote =	{Keywords: Automated theorem proving, deduction, logic, reasoning, SMT solving}
}

Document

DOI: 10.4230/DagRep.9.9.23

Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)

Authors: Carsten Fuhs, Philipp Rümmer, Renate Schmidt, and Cesare Tinelli

Published in: Dagstuhl Reports, Volume 9, Issue 9 (2020)

Abstract

Research in automated deduction is traditionally focused on the problem of determining the satisfiability of formulas or, more generally, on solving logical problems with yes/no answers. Thanks to recent advances that have dramatically increased the power of automated deduction tools, there is now a growing interest in extending deduction techniques to attack logical problems with more complex answers. These include both problems with a long history, such as quantifier elimination, which are now being revisited in light of the new methods, as well as newer problems such as minimal unsatisfiable cores computation, model counting for propositional or first-order formulas, Boolean or SMT constraint optimization, generation of interpolants, abductive reasoning, and syntax-guided synthesis. Such problems arise in a variety of applications including the analysis of probabilistic systems (where properties like safety or liveness can be established only probabilistically), network verification (with relies on model counting), the computation of tight complexity bounds for programs, program synthesis, model checking (where interpolation or abductive reasoning can be used to achieve scale), and ontology-based information processing. The seminar brought together researchers and practitioners from many of the often disjoint sub-communities interested in the problems above. The unifying theme of the seminar was how to harness and extend the power of automated deduction methods to solve problems with more complex answers than binary ones.

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Carsten Fuhs, Philipp Rümmer, Renate Schmidt, and Cesare Tinelli. Deduction Beyond Satisfiability (Dagstuhl Seminar 19371). In Dagstuhl Reports, Volume 9, Issue 9, pp. 23-44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{fuhs_et_al:DagRep.9.9.23,
  author =	{Fuhs, Carsten and R\"{u}mmer, Philipp and Schmidt, Renate and Tinelli, Cesare},
  title =	{{Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)}},
  pages =	{23--44},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{9},
  number =	{9},
  editor =	{Fuhs, Carsten and R\"{u}mmer, Philipp and Schmidt, Renate and Tinelli, Cesare},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.9.23},
  URN =		{urn:nbn:de:0030-drops-118432},
  doi =		{10.4230/DagRep.9.9.23},
  annote =	{Keywords: abduction, automated deduction, interpolation, quantifier elimination, synthesis}
}

5 Search Results for "Schmidt, Renate A."

Meaningfulness and Genericity in a Subsuming Framework (Invited Talk)

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Termination of Generalized Term Rewriting Systems

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Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

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Integrated Deduction (Dagstuhl Seminar 21371)

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Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)

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