David Fuenmayor

Otto-Friedrich-Universität Bamberg · Institut für Angewandte Informatik

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...

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 (...

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...

We present a formalisation of basic topology in simple type theory encoded using the Isabelle/HOL proof assistant. In contrast to related formalisation work, which follows more ‘traditional’ approaches, our work builds upon closure algebras, encoded as Boolean algebras of (characteristic functions of) sets featuring an axiomatised closure operator...

We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical logic in a controlled manner. These structures are known as topological Boolean algebras, which are Boolean a...

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...

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 observa...

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 nor...

Boolos' Curious Inference is automated in Isabelle/HOL after interactive speculation of a suitable shorthand notation (one or two definitions).

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 nor...

This paper reports on an exploration of variants of Boolos' curious inference, using higher-order automated theorem provers (ATPs). Surprisingly, only a single shorthand notation had to be provided by hand. All higher-order lemmas required for obtaining short proof are automatically discovered by the ATPs. Given the observations and suggestions in...

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...

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...

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...

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 (...

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 at the AAAI Spring Symposium on Implementing AI Ethics

Reductio ad absurdum can easily be avoided in the proof of the surjective Cantor theorem.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

Comparative study between (neo-)confucian philosophy and the concept of flow in modern psychology

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...

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...

We understand logic education as an interdisciplinary challenge, which we want to tackle with the support of modern computer technologies. Thus, we have been researching and experimenting with an uniform approach towards teaching logic at undergraduate level for mixed groups of computer science, mathematics and philosophy students, with the support...

Some casual thoughts on the Kantian project of making metaphysics great again (or at least more "scientific")