Selmer Bringsjord's research while affiliated with Rensselaer Polytechnic Institute and other places

Publications (228)

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After introductory remarks, we share our two-part theoretical position, viz. that: (P1) The best overarching approach to suitably defining GI, and obtaining AGI, is via formal logic, including specifically via logic-based learning that is academic in nature; and (P2) AI/AGI is best pursued by seeking artificial agents that pass determinate cognitiv...
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As we work toward artificial general intelligence, it is clear that we must try to imbue agents with faculties which ensure they are trustworthy. We firmly believe that an AGI agent must be able to explain its decision-making in order for it to be considered trustworthy. More specifically, agents must be able to explain themselves in a way that is...
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This chapter attempts to give an answer to the following question: Given an obligation and a set of potentially-inconsistent, ethically-charged beliefs, how can an artificially-intelligent agent ensure that its actions maximize the likelihood that the obligation is satisfied? Our approach to answering this question is in the intersection of several...
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The year is 2030. A two-young-child, two-parent household, the Rubensteins, owns and employs a state-of-the-art household robot, Rodney. With the parents out, the children ask Rodney to perform some action α that violates a Rubensteinian ethical principle PR. Rodney replies: (s1) “Doing that would be (morally) wrong, kids.” The argument the childre...
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Qualitative mechanical problem-solving (QMPS) is central to human-level intelligence. Human agents use their capacity for such problem-solving to succeed in tasks as routine as opening the tap to drink or hanging a picture on the wall, as well as for more sophisticated tasks in demanding jobs in today’s economy (e.g., emergency medicine, plumbing,...
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Machine learning is incapable of generating the kind of subterfuge that a human mind can. It is the human mind that can harness this new technology to nefarious ends that should be feared.
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Suppose an artificial agent aadj, as time unfolds, (i) receives from multiple artificial agents (which may, in turn, themselves have received from yet other such agents…) propositional content, and (ii) must solve an ethical problem on the basis of what it has received. How should aadj adjudicate what it has received in order to produce such a solu...
Preprint
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We propose to build directly upon our longstanding, prior r&d in AI/machine ethics in order to attempt to make real the blue-sky idea of AI that can thwart mass shootings, by bringing to bear its ethical reasoning. The r&d in question is overtly and avowedly logicist in form, and since we are hardly the only ones who have established a firm foundat...
Chapter
After taking note of the conceptual fact that robots may well carry humans inside them, and more specifically that modern AI-infused cars, jets, spaceships, etc. can be viewed as such robots, we present a case study in which inconsistent attitude measurements resulted in the tragic crash in Sweden of such a jet and the death of both pilots. After s...
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Khemlani et al. (2018) mischaracterize logic in the course of seeking to show that mental model theory (MMT) can accommodate a form of inference (, let us label it) they find in a high percentage of their subjects. We reveal their mischaracterization and, in so doing, lay a landscape for future modeling by cognitive scientists who may wonder whethe...
Article
We provide an overview of the theory of cognitive consciousness (TCC), and of [Formula: see text]; the latter provides a means of measuring the amount of cognitive consciousness present in a given cognizer, whether natural or artificial, at a given time, along a number of different dimensions. TCC and [Formula: see text] stand in stark contrast to...
Article
Fundamental Proof Methods in Computer Science: A Computer-Based Approach, by Musser Arkoudas, The MIT Press, Cambridge, USA, ISBN 978-0-262-03553-8 - SELMER BRINGSJORD, NAVEEN SUNDAR GOVINDARAJULU
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I critically review Raymond Turner’s Computational Artifacts – Towards a Philosophy of Computer Science by placing beside his position a rather different one, according to which computer science is a branch of, and is therefore subsumed by, immaterial formal logic.
Conference Paper
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This paper introduces, philosophically and to a degree formally, the novel concept of learning ex nihilo, intended (obviously) to be analogous to the concept of creation ex nihilo. Learning ex nihilo is an agent's learning "from nothing", by the suitable employment of inference schemata for deductive and inductive reasoning. This reasoning must be...
Conference Paper
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This paper discusses the tragic accident in which the first pedestrian was killed by an autonomous car: due to several grave errors in its design, it failed to recognize the pedestrian and stop in time to avoid a collision. We start by discussing the accident in some detail, enlightened by the recent publication of a report from the National Transp...
Preprint
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In the last decade, formal logics have been used to model a wide range of ethical theories and principles with the goal of using these models within autonomous systems. Logics for modeling ethical theories, and their automated reasoners, have requirements that are different from modal logics used for other purposes, e.g. for temporal reasoning. Mee...
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In the last decade, formal logics have been used to model a wide range of ethical theories and principles with the goal of using these models within autonomous systems. Logics for modeling ethical theories, and their automated reasoners, have requirements that are different from modal logics used for other purposes, e.g. for temporal reasoning. Mee...
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Núñez et al.'s (2019) negative assessment of the field of cognitive science derives from evaluation criteria that fail to reflect the true nature of the field. In reality, the field is thriving on both the research and educational fronts, and it shows great promise for the future.
Book
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Hybrid worlds is the proceedings book of ICRES 2018 - the third edition of International Conference series on Robot Ethics and Standards, organized by CLAWAR Association in collaboration with the Rensselaer Polytechnic Institute (RPI) within the premises of RPI in Troy, New York, USA during 20 – 21 August 2018. ICRES 2018 brings new developments an...
Chapter
The doctrine of double effect ($$\mathcal {{DDE}}$$) is an ethical principle that can account for human judgment in moral dilemmas: situations in which all available options have large good and bad consequences. We have previously formalized $$\mathcal {{DDE}}$$ in a computational logic that can be implemented in robots. $$\mathcal {{DDE}}$$, as an...
Preprint
Full-text available
This paper introduces, philosophically and to a degree formally, the novel concept of learning $\textit{ex nihilo}$, intended (obviously) to be analogous to the concept of creation $\textit{ex nihilo}$. Learning $\textit{ex nihilo}$ is an agent's learning "from nothing," by the suitable employment of schemata for deductive and inductive reasoning....
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Conference Paper
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While various traditions under the 'virtue ethics' umbrella have been studied extensively and advocated by ethicists, it has not been clear that there exists a version of virtue ethics rigorous enough to be a target for machine ethics (which we take to include the engineering of an ethical sensibility in a machine or robot itself, not only the stud...
Preprint
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While various traditions under the 'virtue ethics' umbrella have been studied extensively and advocated by ethicists, it has not been clear that there exists a version of virtue ethics rigorous enough to be a target for machine ethics (which we take to include the engineering of an ethical sensibility in a machine or robot itself, not only the stud...
Preprint
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We briefly introduce herein a new form of distributed, multi-agent artificial intelligence, which we refer to as "tentacular." Tentacular AI is distinguished by six attributes, which among other things entail a capacity for reasoning and planning based in highly expressive calculi (logics), and which enlists subsidiary agents across distances circu...
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We answer the present paper’s title in the negative. We begin by introducing and characterizing “real learning” ($$\mathcal {RL}$$) in the formal sciences, a phenomenon that has been firmly in place in homes and schools since at least Euclid. The defense of our negative answer pivots on an integration of reductio and proof by cases, and constitutes...
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Our paradigm for the use of artificial agents to teach requires among other things that they persist through time in their interaction with human students, in such a way that they "teleport" or "migrate" from an embodiment at one time t to a different embodiment at later time t'. In this short paper, we report on initial steps toward the formalizat...
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Given what has been discovered in the case of human cognition, this principle seems plausible: An artificial agent that is both autonomous (A) and creative (C) will tend to be, from the viewpoint of a rational, fully informed agent, (U) untrustworthy . After briefly explaining the intuitive, internal structure of this disturbing (in the context of...
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Epistemology includes in large part investigation of the conditions by which rational human knowledge and belief, of the propositional variety, can be secured. Our particular instance of this investigation arises from the stipulation that a human (a) receives a partial or complete formal argument/proof ($$\mathcal {A}$$) for/of a conclusion ϕ, wher...
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A well-ingrained and recommended engineering practice in safety-critical software systems is to separate safety concerns from other aspects of the system. Along these lines, there have been calls for operating systems (or computing substrates, termed ethical operating systems) that implement ethical controls in an ethical layer separate from, and n...
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In this chapter, we describe an intelligent music system approach that utilizes a joint bottom-up/top-down structure. The bottom-up structure is purely signal driven and calculates pitch, loudness, and information rate among other parameters using auditory models that simulate the functions of different parts of the brain. The top-down structure bu...
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I articulate a novel modal argument for P=NP.
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Akl has claimed that universal computation is a myth, and has offered a number of ingenious arguments in support of this claim, one of which features the challenge of tracking the locations of multiple, ever-moving robots on Mars. I provide what I see as a refutation of this argument; my counter-argument is based on a thesis that is less informal a...
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This is an essay on the Singularity business. Contrary to what many might expect upon parsing our title, we don’t use ‘the Singularity business’ to refer to the general and multi-faceted discussion and debate surrounding the Singularity, that mythical future point in time when AI exceeds today’s technology beyond what we can see from the present. R...
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We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more generally, theory-of-mind reasoning systems) should be at least as expressive as first-order (quantified) modal logic (...
Article
As computational power has continued to increase, and sensors have become more accurate, the corresponding advent of systems that are cognitive-and-immersive (CAI) has come to pass. CAI systems fall squarely into the intersection of AI with HCI/HRI: such systems interact with and assist the human agents that enter them, in no small part because suc...
Conference Paper
The doctrine of double effect (DDE) is a long-studied ethical principle that governs when actions that have both positive and negative effects are to be allowed. The goal in this paper is to automate DDE. We briefly present DDE, and use a first-order modal logic, the deontic cognitive event calculus, as our framework to formalize the doctrine. We p...
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We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize Chisholm's system by grounding his undefined and primitive (i.e. foundational) concept of reasonablenes in probab...
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The doctrine of double effect ($\mathcal{DDE}$) is a long-studied ethical principle that governs when actions that have both positive and negative effects are to be allowed. The goal in this paper is to automate $\mathcal{DDE}$. We briefly present $\mathcal{DDE}$, and use a first-order modal logic, the deontic cognitive event calculus, as our frame...
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The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for conventional proof systems such as first-order logic with a standard proof calculus such as natural deduction or...
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I introduce and propose the ethical hierarchy ($$\mathscr {E \! H}$$) into which can be placed robots and humans in general. This hierarchy is catalyzed by the question: Can robots be more moral than humans? The light shed by $$\mathscr {E \! H}$$ reveals why an emphasis on legal obligation for robots, while not unwise at the moment, is inadequate,...
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There can be no denying that it is entirely possible for a car-manufacturing company like Daimler to build and the deploy self-driving cars without hiring a single computational logician. However, for reasons we explain herein, a logician-less approach to engineering self-driving automobiles (and, for that matter, self-moving vehicles of any conseq...
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When IBM’s Deep Blue beat Kasparov in 1997, Bringsjord (Technol Rev 101(2):23–28, 1998) complained that despite the impressive engineering that made this victory possible, chess is simply too easy a challenge for AI, given the full range of what the rational side of the human mind can muster. However, arguably everything changed in 2011. For in tha...
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The Association for the Advancement of Artificial Intelligence presented the 2015 Fall Symposium Series, on Thursday through Saturday, November 12-14, at the Westin Arlington Gateway in Arlington, Virginia. The titles of the six symposia were as follows: AI for Human-Robot Interaction, Cognitive Assistance in Government and Public Sector Applicatio...
Book
Cognitive architectures represent an umbrella term to describe ways in which the flow of thought can be engineered towards cerebral and behavioral outcomes. Cognitive Architectures are meant to provide top-down guidance, a knowledge base, interactive heuristics and concrete or fuzzy policies for which the virtual character can utilize for intellige...
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Conditional reasoning is an important part of sophisticated cognition. Such reasoning is systematically studied in the sub-discipline of conditional logic, where the focus has been on the objects over which conditional reasoning operates (formulae, and the internals thereof). We introduce herein a new approach: one marked by a focus on the mental a...
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What does the contemporary craft of character design (by human authors), which is beyond the reach of foreseeable AI, and which isn't powered by any stunning, speculative, AI-infused technology (immersive or otherwise), but is instead aided by tried-and-true “AI-less” software tools and immemorial techniques that are still routinely taught today, i...
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Fetzer famously claims that program verification is not even a theoretical possibility, and offers a certain argument for this far-reaching claim. Unfortunately for Fetzer, and like-minded thinkers, this position-argument pair, while based on a seminal insight that program verification, despite its Platonic proof-theoretic airs, is plagued by the i...
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We provide an underlying theory of argument by disanalogy, in order to employ it to show that cyberwarfare is fundamentally new (relative to traditional kinetic warfare, and espionage). Once this general case is made, the battle is won: we are well on our way to establishing our main thesis: that Just War Theory itself must be modernized. Augustine...
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Taddeo and Floridi [2007. A praxical solution of the symbol grounding problem. Minds and Machines, 17, 369–389. (This paper is reprinted in Floridi, L. (2011). The philosophy of information. Oxford: Oxford University Press)] propose a solution to the symbol grounding problem (SGP). Unfortunately, their proposal, while certainly innovative, interest...
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The authors argue that unless computational deontic logics (or, for that matter, any other class of systems for mechanizing moral and/or legal principles) or achieving ethical control of future AIs and robots are woven into the operatingsystem level of such artifacts, such control will be at best dangerously brittle.
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Analogy is a major component of human creativity. Tasks from the ability to generate new stories to the ability to create new and insightful mathematical theorems can be shown to at least partially be explainable in terms of analogical processes. Artificial creativity and AGI systems, then, require powerful analogical subsystems—or so we will soon...
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We embrace a “middle-standard” view of creativity in AI, according to which the driving goal is to engineer computational systems able to “trick” humans into regarding them to be human-level creative. We then report upon three versions of our system of this type in the realm of music: Handle. One of the important hallmarks of our engineering is a c...
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There appears to be considerable evidence against the claim that general intelligence entails creativity. For example, with this claim unpacked as the proposition that any general-intelligent agent must be creative, the field of AI declares the claim to be false. To see this, we need but note that the dominant and encyclopedic AI textbook [16] defi...
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People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cogni...
Conference Paper
How tough is a given question-answering problem? Answers to this question differ greatly among different researchers and groups. To begin rectifying this, we start by giving a quick, simple, propaedeutic formalization of a question-answering problem class. This formalization is just a starting point and should let us answer, at least roughly, this...
Conference Paper
Psychologically and neurobiologically plausible models of knowledge often must make a difficult choice between distributed and localist representation. Distributed representation can be flexible and hold up well to noisy data, but localist models allow for structured knowledge to be represented unambiguously and reasoned over in rigorous, transpare...
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In order to employ and exhibit our Simon-inspired approach to computational economics, and specifically defend our version of the view that even logically untrained humans are rational, albeit no more than “boundedly” so, we provide two models, both rooted in computational logic, of how it is that logically untrained humans perform in a seemingly i...
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Alas, there are akratic persons. We know this from the human case, and our knowledge is nothing new, since for instance Plato analyzed rather long ago a phenomenon all human persons, at one point or another, experience: (1) Jones knows that he ought not to - say - drink to the point of passing out, (2) earnestly desires that he not imbibe to this p...
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The vision of machines autonomously carrying out substantive conjecture generation, theorem discovery, proof discovery, and proof verification in mathematics and the natural sciences has a long history that reaches back before the development of automatic systems designed for such processes. While there has been considerable progress in proof verif...
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Knowledge Representation and Reasoning (KR&R) is based on the idea that propositional content can be rigorously represented in formal languages long the province of logic, in such a way that these representations can be productively reasoned over by humans and machines; and that this reasoning can be used to produce knowledge-based systems (KBSs)....
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Herein we make a plea to machine ethicists for the inclusion of constraints on their theories consistent with empirical data on human moral cognition. As philosophers, we clearly lack widely accepted solutions to issues regarding the existence of free will, the nature of persons and firm conditions on moral agency/patienthood; all of which are indi...
Conference Paper
After setting a context based on two general points (that humans appear to reason in infinitary fashion, and two, that actual hypercomputers aren’t currently available to directly model and replicate such infinitary reasoning), we set a humble engineering goal of taking initial steps toward a computing machine that can reason in infinitary fashion....
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We herein report on a project devoted to charting some of the most salient points in a modern “geography” of minds, machines, and mathematics; the project is funded by the John Templeton Foundation, and is being carried out in Bringsjord’s AI and Reasoning Laboratory.
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What does Wolfram’s new kind of science (nksw ) imply about the decidedly non-new topic of free will versus determinism? I answer this question herein. More specifically, I point out that Wolfram’s nksw -based position on free will is centered on the nature of physical laws, rather than formal logic; briefly rehearse the longstanding ontology of ma...
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Although the computational modeling of “mindreading” (e.g., believing that you believe that there’s a deadly boa in the box, Smith mindreadingly predicts that you will refrain from removing the top) is well-established, this success has been achieved primarily in connection with scenarios that, relatively speaking, are both simple and common. Herei...
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Blue-pill robots are engineered to deceive (perhaps in an attempt to secure desirable ends). Red-pill robots, on the other hand, are built to do no violence to truth. While “taking the blue pill” is an option some select, this path, in the context of present and future robotics, is an exceedingly bad one by our lights, and we herein defend this pos...
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A myth has unfortunately arisen in connection with Martin Davis’s rather aggressively titled paper [“The myth of hypercomputation”, in C. Teuscher (ed.), Alan Turing: life and legacy of a great thinker. Berlin: Springer. 195–211 (2004; Zbl 1058.68001)]. The myth is that Davis is profoundly and decisively right therein, and that hypercomputation is...
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Psychometric AGI (PAGI) is the brand of AGI that anchors AGI science and engineering to explicit tests, by insisting that for an information-processing (i-p) artifact to be rationally judged generally intelligent, creative, wise, and so on, it must pass a suitable, well-defined test of such mental power(s). Under the tent of PAGI, and inspired by p...
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This article argues that existing systems on the Web cannot approach human-level intelligence, as envisioned by Descartes, without being able to achieve genuine problem solving on unseen problems. The article argues that this entails committing to a strong intensional logic. In addition to revising extant arguments in favor of intensional systems,...
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We deploy a framework for classifying the bases for belief in a category of events marked by being at once weighty, unseen, and temporally removed (wutr, for short). While the primary source of wutr events in Occidental philosophy is the list of miracle claims of credal Christianity, we apply the framework to belief in The Singularity, surely—wheth...
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We show that hypercomputation might be needed to rigorously model a scientist trying to study economic phenomena. In this situation, super-Turing hardness manifests in both the modeling process performed by the scientist and the models produced. We start with an introduction to the conventional formal "science-of-sciences" paradigm and present modi...
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After providing some context via (i) earlier work on literary creativity carried out by Bringsjord et al., and (ii) an account of creativity espoused by Cope, which stands in rather direct opposition to Bringsjord’s account, we summarize our nascent attempt to engineer an artificial conductor: Handle. Handle is a microcosmic version of part of a la...
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The concept of psychometric artificial intelligence (PAI) is presented. Psychometric AI is the field devoted to building information-processing entities capable of at least solid performance on all established, validated tests of intelligence and mental ability. One of the experts, Newell, cites his work based on production systems, but makes it cl...
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Psychometric AI is a type of AI distinguished by the pursuit of intelligent systems able to excel on psychometrically validated human-level tests of cognitive abilities. We seek to build a system that solves a specific sub-test within Psychometric AI: the story arrangment test. Items in this test confront the test-taker with a set of jumbed snapsho...
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This paper reports on the architecture and performance of the Creative Artificially-Intuitive and Reasoning Agent Caira as a conductor for improvised avant-garde music. Caira's listening skills are based on a music recognition system that simulates the human auditory periphery to perform an Auditory Scene Analysis (ASA). Its simulation of cognitive...
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This paper introduces an approach to, rather than the final results of, sustained research and development in the area of roboethics described herein. Encapsulated, the approach is to engineer ethically correct robots by giving them the capacity to reason over, rather than merely in, logical systems (where logical systems are used to formalize such...
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Purpose It is widely known that when Turing first introduced his “imitation‐game” test for ascertaining whether a computing machine can think, he considered, and found wanting, a series of objections to his position. It seems safe to say that one of these objections, the “theological objection” (TO), is regarded by Turing to be positively anemic, a...
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In the course of seeking an answer to the question “How do you know you are not a zombie?”Floridi (2005) issues an ingenious, philosophically rich challenge to artificial intelligence (AI) in the form of an extremely demanding version of the so-called knowledge game (or “wise-man puzzle,” or “muddy-children puzzle”)—one that purportedly ensures tha...
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We describe provability-based semantic interoperability (PBSI), a framework transcending syntactic translation that enables robust, meaningful, knowledge exchange across diverse information systems. PBSI is achieved through translation graphs that capture complex ontological relationships, and through provability-based queries. We work through an e...

Citations

... Perhaps the most critical of all commentaries upon my work is that provided by Bringsjord (2021). Although critical, I do not sense that we are too far apart in persuasion or ambition. ...
... In such conditions, the agents may be required to adjudicate such inconsistent information to derive meaningful operational or ethical conclusions [22]. Our analysis does not consider such possibilities in which the information propagated for coordination may include beliefs of the individual agents instead of only consistent facts about reality. ...
... For the particular case of UMM, there are different recent papers challenging it. For example, it has been said that its conjunctions of possibilities reflect cases in truth tables (e.g., Baratgin, Douven, Evans, Oaksford, Over, Politzer, & Thompson, 2015), that the proponents of the theory tend to speak about logic as if logic were just one system, and there were not diverse kinds of logics (e.g., Bringsjord & Govindarajulu, 2020), or that the assumption of certain theses of UMM can lead to absurd conclusions form the logical point of view (e.g., Oaksford, Over, & Cruz, 2019). However, regarding this, two points can be made. ...
... Fourth, risks may arise at the system level that are not apparent or relevant to the decisionmaking of individual AGIs. For example, if Hanson (2001) and Bringsjord and Johnson's (2012) analyses are correct, then ubiquitous AGIs could lead to a decline in human wages that is not necessarily intended by any particular AGI or human. Also, unintended systemic effects may arise due to ubiquitous ethical actions carried out by previously amoral artefacts being used by self-interested humans, akin to the unintended effects that can arise from ubiquitous defecting behaviour by humans (i.e. ...
Citing article
... Automated reasoning in the tradition of higher-order logic (HOL) as descended from Frege, and most prominently from Church, which is masterfully chronicled in ref. [61], is obviously related to cognitive calculi; this is especially true since HOL is now very much on the scene in twenty-first-century AI (e.g., ref. [62]). In contrast, cognitive calculi, and the automation thereof, are based on commitments guided by the study of human cognition; and as we see it, that cognition for matters formal and extensional is for the most part circumscribed by natural deduction in thirdorder logic in the complete absence of formal semantics (e.g., consider the raw material in the practice of mathematics that gives rise to the argument and analysis in ref. [63]) and in matters literary circumscribed by modal operators mixed with third-order logic (e.g., ref. [64]). Traditionally, in terms of the Frege-to-Church-to… history that HOL has, HOL is extensional; in contrast, cognitive calculi by definition cannot fail to have operators that cover human cognition. ...
... In this case, social robots as autonomous agents could exhibit behavior that can be considered "ethical" [84]. There are several case studies that discuss and study the direct implementation of ethics in this sense as a part of autonomous agents' behavior [85][86][87][88]. Other useful studies in this realm analyze human norms themselves and the way autonomous agents can engage in norm-conforming ways of interacting [89]. ...
... A physicist like Einstein may in a real sense feel what simultaneity is, but that doesn't mean that relativity can't be captured in formal logic.¹⁹ As a matter of fact, we expect that our own axiomatization of (cognitive) consciousness [45], combined with our theory, Λ, for the measurement of levels of cognitive consciousness [46], will in subsequent work be married to the formalisms and techniques we present in the present paper for machineethics in multi-agent environments. ...
... to known traffic aircraft. In such situations, the recipient agent must adjudicate these arguments to derive a conclusion [64] for the purpose of coordination. One interesting direction of work is, therefore, the investigation of provably correct decentralized coordination algorithms that can be used when agents must adjudicate inconsistent and uncertain information received from other agents to derive some conclusion for safety-critical applications. ...
... 13 In fact, the automated reasoner ShadowProver we use for our implementation (see Appendix A2) makes crucial use, during its processing, of multiple formal languages. This is true for technical reasons pertaining to the core algorithms of ShadowProver; for more details, see ref. [78]. ...