No file available
To read the file of this research,
you can request a copy directly from the authors.
Bridging between LegalRuleML and TPTP for Automated Normative Reasoning (extended version)
Preprints and early-stage research may not have been peer reviewed yet.
Abstract
LegalRuleML is a comprehensive XML-based representation framework for modeling and exchanging normative rules. The TPTP input and output formats, on the other hand, are general-purpose standards for the interaction with automated reasoning systems. In this paper we provide a bridge between the two communities by (i) defining a logic-pluralistic normative reasoning language based on the TPTP format, (ii) providing a translation scheme between relevant fragments of LegalRuleML and this language, and (iii) proposing a flexible architecture for automated normative reasoning based on this translation. We exemplarily instantiate and demonstrate the approach with three different normative logics.
ResearchGate has not been able to resolve any citations for this publication.
Non-classical logics are used in a wide spectrum of disciplines, including artificial intelligence, computer science, mathematics, and philosophy. The de-facto standard infrastructure for automated theorem proving, the TPTP World, currently supports only classical logics. This paper describes the latest extension of the TPTP World, providing languages and infrastructure for reasoning in non-classical logics. The extension integrates seamlessly with the existing TPTP World.
A rule based knowledge system consists of three main components: a set of rules, facts to be fed to the reasoning corresponding to the data of a case, and an inference engine. In general, facts are stored in (relational) databases that represent knowledge in a first-order based formalism. However, legal knowledge uses defeasible deontic logic for knowledge representation due to its particular features that cannot be supported by first-order logic. In this work, we present a unified framework that supports efficient legal reasoning. In the framework, a novel inference engine is proposed in which the Semantic Rule Index can identify candidate rules with their corresponding semantic rules if any, and an inference controller is able to guide the executions of queries and reasoning. It can eliminate rules that cannot be fired to avoid unnecessary computations in early stages. The experiments demonstrated the effectiveness and efficiency of the proposed framework.
Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP framework for input formats, reporting results and proofs, and standardized communication between reasoning systems, enabling, e.g., proof reconstruction from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning in polymorphic first-order and higher-order logic, in many quantified normal modal logics, as well as in different deontic logics. Its development had initiated the ongoing extension of the TPTP infrastructure to reasoning within non-classical logics.
A framework and methodology—termed LogiKEy—for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples—all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.
We discuss ongoing work on reusing existing (higher-order) automated reasoning infrastructure for seamlessly combining and reasoning with different non-classical logics (modal, deontic, epistemic, paraconsistent, etc.), particularly suited for normative reasoning. Our work illustrates, in particular, the utilisation of the Is-abelle/HOL proof assistant for the representation and formal assessment of linguistically complex ethical arguments. Our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive, formal encodings of complex ethical theories and their automation on the computer are no longer antipodes.
The DAPRECO knowledge base is the main outcome of the interdisciplinary project bearing the same name (https://www.fnr.lu/projects/data-protection-regulation-compliance). It is a repository of rules written in LegalRuleML, an XML formalism designed to be a standard for representing the semantic and logical content of legal documents. The rules represent the provisions of the General Data Protection Regulation (GDPR), the new Regulation that is significantly affecting the digital market in the European Union and beyond. The DAPRECO knowledge base builds upon the Privacy Ontology (PrOnto) (Palmirani et al in Proceedings of the 7th international conference on electronic government and the information systems perspective: technology-enabled innovation for democracy, government and governance, 2018c), which provides a model for the legal concepts involved in the GDPR, by adding a further layer of constraints in the form of if-then rules, referring either to standard first order logic implications or to deontic statements. If-then rules are formalized in reified Input/Output logic (Robaldo and Sun in J Log Comput 7, 2017) and then codified in LegalRuleML. Reified Input/Output logic is an application of standard Input/Output logic for legal reasoning, in which Input/Output logic is combined with the reification-based approach in Hobbs and Gordon (A formal theory of commonsense psychology, how people think people think. Cambridge University Press, Cambridge, 2017). The DAPRECO knowledge base is then a case study for reified Input/Output logic, and it shows that the formalism indeed appears to be a good candidate to effectively formalize, via uniform and simple (flat) representations, complex linguistic/deontic phenomena that may be found in legal texts. To date, the DAPRECO knowledge base is the biggest knowledge base in LegalRuleML and Input/Output logic freely available online (https://github.com/dapreco/daprecokb/blob/master/gdpr/rioKB_GDPR.xml).
We devise a shallow semantical embedding of Åqvist's dyadic deontic logic E in classical higher-order logic. This embedding is shown to be faithful, viz. sound and complete. This embedding is also encoded in Isabelle/HOL, which turns this system into a proof assistant for deontic logic reasoning. The experiments with this environment provide evidence that this logic implementation fruitfully enables interactive and automated reasoning at the meta-level and the object-level.
A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. This embedding is proven sound and complete, that is, faithful. The work presented here provides the theoretical foundation for the implementation and automation of dyadic deontic logic within o-the-shelf higher-order theorem provers and proof assistants.
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is suitable as a foundation for the development of a universal logical reasoning engine. Such an engine may be employed, as already envisioned by Leibniz, to support the rigorous formalisation and deep logical analysis of rational arguments on the computer. A respective universal logical reasoning framework is described in this article and a range of successful first applications in philosophy, artificial intelligence and mathematics are surveyed.
In order to automate verification process, regulatory rules written in natural language need to be translated into a format that machines can understand. However, none of the existing formalisms can fully represent the elements that appear in legal norms. For instance, most of these formalisms do not provide features to capture the behavior of deontic effects, which is an important aspect in automated compliance checking. This paper presents an approach for transforming legal norms represented using legalruleml to a variant of modal defeasible logic (and vice versa) such that a legal statement represented using LegalRuleML can be transformed into a machine-readable format that can be understood and reasoned about depending upon the client's preferences.
How can computers distinguish the coherent from the unintelligible, recogni
This paper describes the TPTP problem library and associated infrastructure, from its use of Clause Normal Form (CNF), via the First-Order Form (FOF) and Typed First-order Form (TFF), through to the monomorphic Typed Higher-order Form (TH0). TPTP v6.4.0 was the last release prior to the introduction of the polymorphic Typed Higher-order Form, and thus serves as the exemplar. This paper summarizes the aims and history of the TPTP, documents its growth up to v6.4.0, reviews the structure and contents of TPTP problems, and gives an overview of TPTP-related infrastructure.
Defeasible Deontic Logic is a simple and computationally efficient approach for the representation of normative reasoning. Traditionally defeasible logics are defined proof theoretically based on the proof conditions for the logic. While several logic programming, operational and argumentation semantics have been provided for defeasible logics, possible world semantics for (modal) defeasible logics remained elusive. In this paper we address this issue.
Computational semantics is concerned with computing the meanings of linguistic objects such as sentences, text fragments, and dialogue contributions. As such it is the interdisciplinary child of semantics, the study of meaning and its linguistic encoding, and computational linguistics, the discipline that is concerned with computations on linguistic objects.
Domain-specific languages (DSLs) are languages tailored to a specific
application domain. They offer substantial gains in expressiveness
and ease of use compared with general-purpose programming languages
in their domain of application. DSL development is hard, requiring
both domain knowledge and language development expertise. Few people
have both. Not surprisingly, the decision to develop a DSL is often
postponed indefinitely, if considered at all, and most DSLs never
get beyond the application library stage.Although many articles have
been written on the development of particular DSLs, there is very
limited literature on DSL development methodologies and many questions
remain regarding when and how to develop a DSL. To aid the DSL developer,
we identify patterns in the decision, analysis, design, and implementation
phases of DSL development. Our patterns improve and extend earlier
work on DSL design patterns. We also discuss domain analysis tools
and language development systems that may help to speed up DSL development.
Finally, we present a number of open problems.
The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well known and well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The extension of the TPTP from first-order form (FOF) logic to typed higher-order form (THF) logic has provided a basis for new development and application of ATP systems for higher-order logic. Key developments have been the specification of the THF language, the addition of higher-order problems to the TPTP, the development of the TPTP THF infrastructure, several ATP systems for higher-order logic, and the use of higher-order ATP in a range of domains. This paper describes these developments.
This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing “the laws of thought”. In this sense, fundamental logical laws are implicit to our “language games” and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as “inferential landscapes” and logicians as “geographers” who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language.
The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic automated theorem-proving (ATP) systems for classical logic - the world championship for such systems. CASC provides a public evaluation of the relative capabilities of ATP systems, and aims to stimulate ATP research toward the development of more powerful ATP systems. Over the years CASC has been a catalyst for impressive improvements in ATP.
This paper tackles an open problem posed by Aqvist. It is the problem of whether his dyadic deontic systems E and F are complete with respect to their intended Hanssonian preference-based semantics. It is known that there are two different ways of interpreting what it means for a world to be best or top-ranked among alternatives. This can be understood as saying that it is optimal among them, or maximal among them. First, it is established that, under either the maximality rule or the optimality rule, E is sound and complete with respect to the class of all preference models, the class of those in which the betterness relation is reflexive, and the class of those in which it is total. Next, an analogous result is shown to hold for F. That is, it is established that, under either rule, F is sound and complete with respect to the class of preference models in which the betterness relation is limited, the class of those in which it is limited and reflexive, and the class of those in which it is limited and total.
This paper discusses some engineering considerations that should be taken into account when building a knowledge based system, and recommends isomorphism, the well defined correspondence of the knowledge base to the source texts, as a basic principle of system construction in the legal domain. Isomorphism, as it has been used in the field of legal knowledge based systems, is characterised and the benefits which stem from its use are described. Some objections to and limitations of the approach are discussed. The paper concludes with a case study giving a detailed example of the use of the isomorphic approach in a particular application.
- T Athan
- G Governatori
- M Palmirani
- A Paschke
- A Z Wyner
Athan, T., Governatori, G., Palmirani, M., Paschke, A., Wyner, A.Z.: Legal-RuleML: Design Principles and Foundations. In: Reasoning Web. Lecture Notes
in Computer Science, vol. 9203, pp. 151-188. Springer (2015)
Inference and computational semantics
- P Blackburn
- M Kohlhase
Blackburn, P., Kohlhase, M.: Inference and computational semantics. Journal of
Logic, Language, and Information 13(2), 117-120 (2004)
Translating higher-order modal logic from ruleml to TPTP
- H Boley
- C Benzmüller
- M Luan
- Z Sha
Boley, H., Benzmüller, C., Luan, M., Sha, Z.: Translating higher-order modal logic
from ruleml to TPTP. In: RuleML (Supplement). CEUR Workshop Proceedings,
vol. 1620. CEUR-WS.org (2016)
Ruleml 1.0: The overarching specification of web rules
- H Boley
- A Paschke
- M O Shafiq
Boley, H., Paschke, A., Shafiq, M.O.: Ruleml 1.0: The overarching specification of
web rules. In: RuleML. Lecture Notes in Computer Science, vol. 6403, pp. 162-178.
Springer (2010)
Deontic logic and contrary-to-duties. In: Handbook of philosophical logic
- J Carmo
- A J Jones
Carmo, J., Jones, A.J.: Deontic logic and contrary-to-duties. In: Handbook of philosophical logic, pp. 265-343. Springer (2002)
Folding domain-specific languages: deep and shallow embeddings (functional pearl)
- J Gibbons
- N Wu
Gibbons, J., Wu, N.: Folding domain-specific languages: deep and shallow embeddings (functional pearl). In: Jeuring, J., Chakravarty, M.M.T. (eds.) Proceedings
of the 19th ACM SIGPLAN international conference on Functional programming,
Gothenburg, Sweden, September 1-3, 2014. pp. 339-347. ACM (2014)
The MET: the art of flexible reasoning with modalities
- T Gleißner
- A Steen
Gleißner, T., Steen, A.: The MET: the art of flexible reasoning with modalities.
In: RuleML+RR. Lecture Notes in Computer Science, vol. 11092, pp. 274-284.
Springer (2018)
Deontic logic: A historical survey and introduction. Handbook of deontic logic and normative systems
- R Hilpinen
- P Mcnamara
Hilpinen, R., McNamara, P.: Deontic logic: A historical survey and introduction.
Handbook of deontic logic and normative systems 1, 3-136 (2013)
The making of spindle
- H Lam
- G Governatori
Lam, H., Governatori, G.: The making of spindle. In: RuleML. Lecture Notes in
Computer Science, vol. 5858, pp. 315-322. Springer (2009)
Modelling legal knowledge for GDPR compliance checking
- M Palmirani
- G Governatori
Palmirani, M., Governatori, G.: Modelling legal knowledge for GDPR compliance
checking. In: JURIX. Frontiers in Artificial Intelligence and Applications, vol. 313,
pp. 101-110. IOS Press (2018)
Legal-RuleML Core Specification Version 1
- M Palmirani
- G Governatori
- T Athan
- H Boley
- A Paschk
- A Wyner
Palmirani, M., Governatori, G., Athan, T., Boley, H., Paschk, A., Wyner, A.: Legal-RuleML Core Specification Version 1.0. https://docs.oasis-open.org/legalruleml/
legalruleml-core-spec/v1.0/os/legalruleml-core-spec-v1.0-os.html (2021)
An Extensible Logic Embedding Tool for Lightweight Non-Classical Reasoning
- A Steen
Steen, A.: An Extensible Logic Embedding Tool for Lightweight Non-Classical
Reasoning. In: 8th Workshop on Practical Aspects of Automated Reasoning. CEUR
Workshop Proceedings, CEUR-WS.org (2022), accepted for publication.
Supplemental data for submission "Bridging between LegalRuleML and TPTP for Automated Normative Reasoning
- A Steen
- D Fuenmayor
Steen, A., Fuenmayor, D.: Supplemental data for submission "Bridging between
LegalRuleML and TPTP for Automated Normative Reasoning" (Jun 2022).
https://doi.org/10.5281/zenodo.6702576
The TPTP typed first-order form with arithmetic
- G Sutcliffe
- S Schulz
- K Claessen
- P Baumgartner
Sutcliffe, G., Schulz, S., Claessen, K., Baumgartner, P.: The TPTP typed first-order
form with arithmetic. In: LPAR. Lecture Notes in Computer Science, vol. 7180,
pp. 406-419. Springer (2012)