Dyadic Deontic Logic in HOL: Faithful Embedding and Meta-Theoretical Experiments

Benzmüller, Christoph; Farjami, Ali; Parent, Xavier

doi:10.1007/978-3-030-70084-3_14

Cited by 3 publications

(5 citation statements)

References 21 publications

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“…A key feature of LogiKEy is that these pen-and-paper faithfulness studies can be supported and complemented by experimentation and verification. This is illustrated in Figure 1.2 of Benzmüller et al [84], where it is shown that both the standard inference rules and the axioms of the embedded dyadic deontic logic can be proven valid in our approach. For further related experiments and a discussion of the current limitations of the embedding approach, we refer the reader to Benzmüller and Reiche [85] and in particular to §4.5 of Parent and Benzmüller [86], which briefly discusses in this context the distinction between validity on frame structures versus validity on model structures for a frame.…”

Section: Data Availability Statementmentioning

confidence: 72%

“…12 In HOL (with Henkin semantics), sets are associated with their characteristic functions. 13 For many logics, our embedding technique allows such faithfulness results, and an example for a non-trivial dyadic deontic logic has been worked out in detail by Benzmüller et al [84]. A key feature of LogiKEy is that these pen-and-paper faithfulness studies can be supported and complemented by experimentation and verification.…”

Section: Data Availability Statementmentioning

confidence: 99%

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Modelling Value-Oriented Legal Reasoning in LogiKEy

Benzmüller,

Fuenmayor,

Lomfeld

2024

Logics

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The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing, in which legal knowledge (cases and laws) is encoded by utilising context-dependent value preferences. The theory obtained is then used to formalise, automatically evaluate, and reconstruct illustrative property law cases (involving the appropriation of wild animals) within the Isabelle/HOL proof assistant system, illustrating how LogiKEy can harness interactive and automated theorem-proving technology to provide a testbed for the development and formal verification of legal domain-specific languages and theories. Modelling value-oriented legal reasoning in that framework, we establish novel bridges between the latest research in knowledge representation and reasoning in non-classical logics, automated theorem proving, and applications in legal reasoning.

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Section: Data Availability Statementmentioning

confidence: 72%

Section: Data Availability Statementmentioning

confidence: 99%

Modelling Value-Oriented Legal Reasoning in LogiKEy

Benzmüller,

Fuenmayor,

Lomfeld

2024

Logics

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show abstract

“…The dyadic deontic operator is represented by {$$obl} (short for obligatory). An embedding of the above DDL is studied in [7,5] Note that the name $modal of modal logics and that of its connective names are given by TPTP defined names (starting with a single dollar sign) since it is the first non-classical logic standardized by the TPTP [21,36]. All further logics are LET-specific logic representations that have not (yet) been included in the collection of TPTP curated NCLs; following the TPTP naming convention, their identifiers hence start with two dollar signs (system defined names).…”

Section: Overview Of Supported Nclsmentioning

confidence: 99%

An Extensible Logic Embedding Tool for Lightweight Non-Classical Reasoning

Steen¹

2022

Preprint

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The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets. When used as a pre-processor or library for higher-order theorem provers, the tool admits off-the-shelf automation for logics for which otherwise few to none provers are currently available.

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“…al. [12,10] implements DDL in Isabelle. I add the Formula of Universal Law as an axiom to their library.…”

Section: Automated Kantian Ethicsmentioning

confidence: 99%

“…The implementation of this paper was inspired by and builds on Benzmüller, Parent, and Farjami's foundational work with the LogiKEy framework for machine ethics, which includes their implementation of DDL in Isabelle [10,12]. The LogiKEy project has been used to study metaphysics [11,32], law [56], and ethics [25], but not Kant's categorical imperative.…”

Section: Related Workmentioning

confidence: 99%

Automated Kantian Ethics: A Faithful Implementation

Singh¹

2022

Preprint

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As we grant artificial intelligence increasing power and independence in contexts like healthcare, policing, and driving, AI faces moral dilemmas but lacks the tools to solve them. Warnings from regulators, philosophers, and computer scientists about the dangers of unethical artificial intelligence have spurred interest in automated ethics-i.e., the development of machines that can perform ethical reasoning. However, prior work in automated ethics rarely engages with philosophical literature. Philosophers have spent centuries debating moral dilemmas so automated ethics will be most nuanced, consistent, and reliable when it draws on philosophical literature. In this paper, I present an implementation of automated Kantian ethics that is faithful to the Kantian philosophical tradition. I formalize Kant's categorical imperative in Dyadic Deontic Logic, implement this formalization in the Isabelle/HOL theorem prover, and develop a testing framework to evaluate how well my implementation coheres with expected properties of Kantian ethic. My system is an early step towards philosophically mature ethical AI agents and it can make nuanced judgements in complex ethical dilemmas because it is grounded in philosophical literature. Because I use an interactive theorem prover, my system's judgements are explainable.

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Dyadic Deontic Logic in HOL: Faithful Embedding and Meta-Theoretical Experiments

Cited by 3 publications

References 21 publications

Modelling Value-Oriented Legal Reasoning in LogiKEy

Modelling Value-Oriented Legal Reasoning in LogiKEy

An Extensible Logic Embedding Tool for Lightweight Non-Classical Reasoning

Automated Kantian Ethics: A Faithful Implementation

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