David Fuenmayor

Alexander Steen, David Fuenmayor

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.

Christoph Benzmüller, David Fuenmayor, Alexander Steen et al.

This paper reports on an exploration of Boolos' Curious Inference, using higher-order automated theorem provers (ATPs). Surprisingly, only suitable shorthand notations had to be provided by hand for ATPs to find a short proof. The higher-order lemmas required for constructing a short proof are automatically discovered by the ATPs. Given the observations and suggestions in this paper, full proof automation of Boolos' and related examples now seems to be within reach of higher-order ATPs.

Alexander Steen, David Fuenmayor, Tobias Gleißner et al.

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. Similar standards for non-classical logic reasoning do not exist (yet). This hampers practical development of reasoning systems, and limits their interoperability and application. This paper describes the latest extension of the TPTP World, which provides languages and infrastructure for reasoning in non-classical logics. The extensions integrate seamlessly with the existing TPTP World.

Alexander Steen, David Fuenmayor

We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using interactive and automated reasoning tools. This enables the formal analysis and verification of meta-theoretical properties as well as the flexible generation of extensions and labellings with respect to well-known argumentation semantics.

David Fuenmayor, Christoph Benzmüller

We present an approach towards the deep, pluralistic logical analysis of argumentative discourse that benefits from the application of state-of-the-art automated reasoning technology for classical higher-order logic. Thanks to its expressivity this logic can adopt the status of a uniform \textit{lingua franca} allowing the encoding of both formalized arguments (their deep logical structure) and dialectical interactions (their attack and support relations). We illustrate this by analyzing an excerpt from an argumentative debate on climate engineering. Another, novel contribution concerns the definition of abstract, language-theoretical foundations for the characterization and assessment of shallow semantical embeddings (SSEs) of non-classical logics in classical higher-order logic, which constitute a pillar stone of our approach. The novel perspective we draw enables more concise and more elegant characterizations of semantical embeddings of logics and logic combinations, which is demonstrated with several examples.

Christoph Benzmüller, David Fuenmayor, Bertram Lomfeld

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 appropriation of wild animals) within the Isabelle 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 latest research in knowledge representation and reasoning in non-classical logics, automated theorem proving, and applications in legal reasoning.

Christoph Benzmüller, David Fuenmayor

Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the utilization of suitably adapted notions of (modal) ultrafilters, and a careful distinction between extensions and intensions of positive properties.

David Fuenmayor, Christoph Benzmüller

We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at formalizing natural-language argumentative discourse using flexible combinations of expressive non-classical logics. In doing so, it allows us to render explicit the tacit conceptualizations implicit in argumentative discursive practices. Our approach operates on networks of structured arguments and is iterative and two-layered. At one layer we search for logically correct formalizations for each of the individual arguments. At the next layer we select among those correct formalizations the ones which honor the argument's dialectic role, i.e. attacking or supporting other arguments as intended. We operate at these two layers in parallel and continuously rate sentences' formalizations by using, primarily, inferential adequacy criteria. An interpretive, logical theory will thus gradually evolve. This theory is composed of meaning postulates serving as explications for concepts playing a role in the analyzed arguments. Such a recursive, iterative approach to interpretation does justice to the inherent circularity of understanding: the whole is understood compositionally on the basis of its parts, while each part is understood only in the context of the whole (hermeneutic circle). We summarily discuss previous work on exemplary applications of human-in-the-loop computational hermeneutics in metaphysical discourse. We also discuss some of the main challenges involved in fully-automating our approach. By sketching some design ideas and reviewing relevant technologies, we argue for the technological feasibility of a highly-automated computational hermeneutics.