David Fuenmayor

David Fuenmayor
Otto-Friedrich-Universität Bamberg · Institut für Angewandte Informatik

Master of Science

About

39
Publications
8,185
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108
Citations
Introduction
Additional affiliations
January 2018 - June 2019
Freie Universität Berlin
Position
  • PhD Student

Publications

Publications (39)
Article
Full-text available
This paper explores the general question of the validity of Gödel's incompleteness theorems by examining the respective arguments from a paraconsistent perspective, while employing combinations of modal logics with Logics of Formal Inconsistency (LFIs). For this purpose, abstract versions of the incompleteness theorems, employing provabil-ity logic...
Preprint
Full-text available
Literature in AI & Law contemplates argumentation in legal cases as an instance of theory construction. The task of a lawyer in a legal case is to construct a theory containing: (a) relevant generic facts about the world, (b) relevant legal rules such as precedents and statutes, and (c) contingent facts describing or interpreting the situation at h...
Preprint
Full-text available
We encode a topological semantics for paraconsistent and paracomplete logics enriched with recovery operators, by drawing upon early works on topological Boolean algebras (by Kuratowski, Zarycki, McKinsey & Tarski, etc.). This work exemplarily illustrates the shallow semantical embedding approach using Isabelle/HOL and shows how we can effectively...
Preprint
Full-text available
An ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is mechanized on the computer. Utilizing Church's type theory as meta-logic to semantically embed a rich combination of expressive non-classical logics as required for the task, our work pushes existing boundaries in knowledge representation and reasoning. We demonstr...
Preprint
Full-text available
It is customary to expect from a logical system that it can be algebraizable, in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa's paraconsistent calculi, algebraic equivalents for such systems have been sought. It is known, however, that these systems are not self-extensional (...
Conference Paper
Full-text available
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 langua...
Preprint
Full-text available
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 la...
Preprint
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...
Preprint
Full-text available
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-theoretic...
Article
It is customary to expect from a logical system that it can be algebraizable , in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa’s paraconsistent calculi, algebraic equivalents for such systems have been sought. It is known, however, that these systems are not self-extensional (...
Conference Paper
Full-text available
Literature in AI & Law contemplates argumentation in legal cases as an instance of theory construction. The task of a lawyer in a legal case is to construct a theory containing: (a) relevant generic facts about the world, (b) relevant legal rules such as precedents and statutes, and (c) contingent facts describing or interpreting the situation at h...
Presentation
Full-text available
Presentation at the AAAI Spring Symposium on Implementing AI Ethics
Preprint
Full-text available
Reductio ad absurdum can easily be avoided in the proof of the surjective Cantor theorem.
Article
Full-text available
The LogiKEy workbench and dataset for ethical and legal reasoning is presented. This workbench simultaneously supports development, experimentation, assessment and deployment of formal logics and ethical and legal theories at different conceptual layers. More concretely, it comprises, in form of a data set (Isabelle/HOL theory files), formal encodi...
Chapter
Computers may help us to better understand (not just verify) arguments. In this chapter we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language argument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the ex...
Preprint
Full-text available
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 formaliz...
Preprint
Full-text available
Enabling machines to legal balancing is a non-trivial task challenged by a multitude of factors some of which are addressed and explored in this work. We propose a holistic approach to formal modeling at different abstraction layers supported by a pluralistic framework in which the encoding of an ethico-legal value and upper ontology is developed i...
Chapter
Climate Engineering (CE) is the intentional large-scale intervention in the Earth’s climate system to counter climate change. CE is highly controversial, spurring global debates about whether and under which conditions it should be considered. We focus on the computer-supported analysis of a small subset of the arguments pro and contra CE intervent...
Conference Paper
Full-text available
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 assis...
Conference Paper
Full-text available
Climate Engineering (CE) is the intentional large-scale intervention in the Earth's climate system to counter climate change. CE is highly controversial, spurring global debates about whether and under what conditions it should be considered. We focus on the computer-supported analysis of a small subset of the arguments pro and contra CE interventi...
Article
Full-text available
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 read...
Chapter
Full-text available
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 logi...
Preprint
Full-text available
Three variants of Kurt Gödel's ontological argument, as proposed byDana 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 r...
Chapter
We present and illustrate an approach to combining logics based on shallow semantical embeddings, a technique that harnesses the high expressive power of classical higher-order logic (HOL) as a meta-language in order to embed the syntax and semantics of some object logic. This approach allows us to reuse existing (higher-order) automated reasoning...
Chapter
Full-text available
The computer-mechanization of an ambitious explicit ethical theory, Gewirth’s Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expre...
Preprint
Full-text available
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 logi...
Preprint
Full-text available
We present and illustrate an approach to combining logics, based on shallow semantical embeddings, which harnesses the high expressive power of classical higher-order logic (HOL) as a metalanguage in order to embed the syntax and semantics of some object logics. This approach allows us to reuse existing (higher-order) automated reasoning infrastruc...
Preprint
Full-text available
An ambitious ethical theory ---Alan Gewirth's "Principle of Generic Consistency"--- is encoded and analysed in Isabelle/HOL. Gewirth's theory has stirred much attention in philosophy and ethics and has been proposed as a potential means to bound the impact of artificial general intelligence.
Presentation
Full-text available
In the past decades, several emendations of Gödel’s (resp.Scott’s) modal ontological argument have been proposed, many of which preserve the intended conclusion (the necessary existence of God), while avoiding a controversial side result of the Gödel/Scott variant called the “modal collapse”, which expresses that there are no contingent truths (eve...
Article
Full-text available
Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language argument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the ex...
Preprint
Full-text available
We motivate and illustrate the utilization of (higher-order) automated deduction technologies for natural language understanding and, in particular, for tackling the problem of finding the most adequate logical formalisation of a natural language argument. Our approach, which we have called computational hermeneutics, is grounded on recent progress...
Preprint
Full-text available
In the past decades, several emendations of Gödel's (resp. Scott's) modal ontological argument have been proposed, many of which preserve the intended conclusion (the necessary existence of God), while avoiding a controversial side result of the Gödel/Scott variant called the "modal collapse", which expresses that there are no contingent truths (ev...
Research
Full-text available
Comparative study between (neo-)confucian philosophy and the concept of flow in modern psychology
Conference Paper
Full-text available
A shallow semantic embedding of an intensional higher-order modal logic (IHOML) in Isabelle/HOL is presented. IHOML draws on Montague/Gallin intensional logics and has been introduced by Melvin Fitting in his textbook Types, Tableaus and Gödel's God in order to discuss his emendation of Gödel's ontological argument for the existence of God. Utilizi...
Article
Full-text available
A computer-formalisation of the essential parts of Fitting’s text- book Types, Tableaus and Gödel’s God in Isabelle/HOL is presented. In particular, Fitting’s (and Anderson’s) variant of the ontological argument is verified and confirmed. This variant avoids the modal collapse, which has been criticised as an undesirable side-effect of Kurt Gödel’s...
Research
Full-text available
Some casual thoughts on the Kantian project of making metaphysics great again (or at least more "scientific")

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Projects

Projects (3)
Project
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. 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.
Project
Project goal is the practical development of computational tools for normative reasoning based on formal methods. Since ethical and legal theories for intelligent systems as well as suitable normative reasoning formalisms are both still under development, we introduce a flexible workbench to support empirical studies with such theories in which the preferred logic formalisms themselves can still be varied, complemented, assessed and compared. In this way we build a bridge between the deduction systems community and the formal ethics community. The deduction systems community is further split into the area of Automated Reasoning and Interactive Theorem Proving. With our work we bridge between all of these communities. The infrastructure we propose draws on both recent developments in universal logical reasoning in classical higher-order logic (HOL) and the coalescence and improvements in interactive and automated theorem proving (ATP) in HOL, as witnessed by systems such as Isabelle/HOL, LEO-II and Leo-III. We are thus linking the historically rich research areas of HOL, automated theorem proving, normative reasoning and formal ethics.