Toward the Engineering of Virtuous Machines

12/07/2018 ∙ by Naveen Sundar Govindarajulu, et al. ∙ 0

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 study of ethics in the humans who might create artificial agents). We begin to address this by presenting an embryonic formalization of a key part of any virtue-ethics theory: namely, the learning of virtue by a focus on exemplars of moral virtue. Our work is based in part on a computational formal logic previously used to formally model other ethical theories and principles therein, and to implement these models in artificial agents.



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What is virtue ethics? One way of summarizing virtue ethics is to contrast it with the two main families of ethical theories: deontological ethics () and consequentialism (). Ethical theories in the family  that are utilitarian in nature hold that actions are morally evaluated based on their total utility (or total disutility) to everyone involved. The best action is the action that has the highest total utility. In stark contrast, ethical theories in  emphasize inviolable principles, and reasoning from those principles to whether actions are obligatory, permissible, neutral, etc.111Both the families  and  are crisply explained as being in conformity with what we say here in e.g. [Feldman1978]. In a departure from both  and , ethical theories in the virtue-ethics family  are overall distinguished by the principle that the best action in a situation, morally speaking, is the one that a virtuous person would perform [Annas2011]. A virtuous person is defined as a person who has learned and internalized a set of habits or traits termed virtuous. For a virtuous person, virtuous acts become second-nature, and hence are performed in many different situations, through time.

While there has been extensive formal and rigorous modeling done in  and , there has been little such work devoted to formalizing and mechanizing . Note that unlike  and , it is not entirely straightforward how one could translate the concepts and principles in  into a form that is precise enough to be realized in machines. Proponents of  might claim that it is not feasible to do so given ’s emphasis on persons and traits, rather than individual actions or consequences. From the perspective of machine ethics, this is not satisfactory. If  is to be on equal footing with  and  for the purpose of building morally competent machines, AI researchers need to start formalizing parts of virtue ethics, and to then implement such formalization in computation.

We present one such formalization herein; one that uses learning and is based on a virtue-ethics theory presented by Zagzebski [Zagzebski2010]. The formalization is presented courtesy of an expressive computational logic that has been used to model principles in both  and  [e.g. [Govindarajulu and Bringsjord2017a, Govindarajulu et al.2017]].222See [sb_etal_ieee_robots] for an introduction to the logicist methodology for building ethical machines. The formalization answers, abstractly, the following two questions: [linecolor=white, frametitle=Questions, frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]

  1. When can we say an agent is virtuous?

  2. What is a virtue?

The plan for the paper is as follows. First, we briefly look at why virtuous machines might be useful, and then we briefly cover related work that can be considered as formalizations of virtue ethics. Next, we present an overview of virtue ethics itself, and specifically show that an emphasis on moral exemplars makes good sense for any attempt to engineer a virtuous machine. We next present one version of virtue ethics, (Zagzebski’s version of virtue ethics), that we seek to formalize fully. Then, our calculus and the formalization itself () are presented. We conclude by discussing future work and remaining challenges.

Why Virtuous Robots?

Note that we do not advocate that machine ethicists pursue virtue ethics over other familiies of ethical theories. Our goal in the present paper is merely to formalize one version of virtue ethics within the family . That said, why might virtue ethics be considered over consequentialism or deontological ethics for building morally competent machines? To partially answer this question, we take a short digression into a a series of conditions laid out by alfano2013identifying, and characterized as identifying the core of virtue ethics:

[linecolor=white, frametitle= Hard Core of Virtue Ethics (quoting [Alfano2013]), frametitlebackgroundcolor=gray!08, backgroundcolor=gray!05, roundcorner=8pt]

  1. acquirability It is possible for a non-virtuous person to acquire some of the virtues.

  2. stability If someone possesses a virtue at time , then ceteris paribus she will possess that virtue at a later time .

  3. consistency If someone possesses a virtue sensitive to reason , then ceteris paribus she will respond to in most contexts.

  4. access It is possible to determine what the virtues are.

  5. normativity Ceteris paribus, it is better to possess a virtue than not, and better to possess more virtues than fewer.

  6. real saints There is a non-negligible cohort of saints in the human population.

  7. explanatory power If someone possesses a virtue, then reference to that virtue will sometimes help to explain her behavior.

  8. predictive power If someone possesses a high-fidelity virtue, then reference to that virtue will enable nearly certain predictions of her behavior; if someone possesses a low-fidelity virtue, then reference to that virtue will enable weak predictions of her behavior.

  9. egalitarianism Almost anyone can reliably act in accordance with virtue.

Particularly, we feel that if the conditions of stability, consistency, explanatory power, and predictive power hold, then virtuous agents or robots might be easier for humans to understand and interact with (compared to consequentialist or deontological agents or robots). This is but our initial motivation; we now present an overview of virtue ethics, in order to show that our focus specifically on learning of virtuous behavior from moral exemplars is advisable.

Surveying Virtue Ethics

See [scheutzmallemoral] for a general introduction to the field of moral robots. We begin our survey by reporting that Hurka [Hurka2000] presents an ingenious formal account involving a recursive notion of goodness and badness. The account starts with a given set of primitive good and bad states-of-affairs. Virtues are then defined as love of good states-of-affairs or hatred of bad states-of-affairs. Vice is defined as love of bad states-of-affairs or hatred of good states-of-affairs. Virtues and vices are then themselves taken to be good and bad states-of-affairs, resulting in a recursive definition (see Figure 2) that is attractive to AI researchers and computer scientists. But despite this, and despite our sense that the main problems with Hurka’s account are rectifiable [Hiller2011], we feel that Hurka’s definition might not capture central aspects of virtue [Miles2013]. More problematic is that it must be shown that Hurka’s account is different from rigorous and formal accounts of , which after all are themselves invariably based upon good and bad states-of-affairs. Moreover, it is not clear to us how Hurka’s account is amenable to automation. Therefore, we now proceed to step back and survey the overarching family  of virtue ethics, to specifically pave a more promising AI road: a focus on moral exemplars.

Figure 1: Hurka’s Account Virtues (vices) are defined recursively as love of good (bad) states-of-affairs or hate (love) of bad states of affairs.

Virtue Ethics: Overview to Exemplarism

The core concepts of consequentialist ethical theories (i.e. of members of ), at least certainly in the particular such theory known as utilitarianism, are doubtless at minimum relatively familiar to most of our readers. For instance, most in our audience will know that utilitarianism’s core tenet is that actions are obligatory just in case they have the consequence of maximizing happiness, and are forbidden exactly when they fail to so maximize. A parallel state-of-affairs holds for at least basic knowledge of deontological ethical theories (= family ): most readers have for instance some familiarity with Kant’s moral system in family , and specifically with his famous “categorical imperative,” which, paraphrasing, says that, unconditionally, one must always act in such a way that this behavior could be universalized.333This imperative is first set out in — as it’s known in abbreviation — Groundwork; see [Kant19971785]. It’s generally thought by ethicists, and this may be convenient for machine/AI ethics, that Kant had in mind essentially a decision procedure to follow in the attempt to behave in an ethically correct manner. For a lucid and laconic overview of this point, see [Johnson20042016]; and cf. [Powers2006]. In addition, generally people are familiar with the core tenet of divine-command ethical theories (i.e. of members of ), which is (approximately) that actions are obligatory for humans if and only if God commands that these actions be performed (a particular member of is specified in [Quinn1978]). However, in our experience the epistemic situation is radically different when it comes to the family of ethical theories virtue ethics (= ). For while it’s true that generally educated people can be assumed to be acquainted with the concept of virtue, and with many things long deemed to be virtues (e.g. bravery), an understanding of virtue ethics at the level of ethical theory cannot be assumed. We therefore now provide a rapid (and admittedly cursory) synopsis of , by drawing from [Vallor2016], and to some degree from [Annas2011]. It will be seen that  makes central use of exemplars, and of learning and development that revolves around them. Hence we shall arrive at a convenient entry point for our AI work devoted to trying to design and build a virtuous machine.

Obviously we cannot in the span of the space we have at hand do full justice to the book-length treatment of  that is [Vallor2016]. But we can quickly establish that our technical work, in its focus on the cultivation of virtue for a machine via learning from exemplars, is not merely based on a single, idiosyncratic member of , and on one peripheral aspect of this member. On the contrary, study of the work of Vallor and other scholars concerned with a characterization of the family  confirms that our exploitation specifically of Zagzebski’s [Zagzebski2010] focus, from the standpoint of the field of ethics itself, is a worthy point of entry for AI researchers.

To begin, Vallor, drawing on and slightly adapting Van Norden’s [Van Norden2007] sets out a quartet of commonalities that at least seem to be true of all members of , and the second one is: “A conception of moral virtues as cultivated states of character, manifested by those exemplary persons who have come closest to achieving the highest human good” (¶5, §2.2).444In her book, Vallor gives her own more detailed and technologically relevant list of seven core elements that can be viewed as common to all members of  (or two what she refers to as “traditions” within virtue ethics). We do not have the space to discuss this list, and show that it fits nicely with our technical work’s emphasis on exemplars and learning therefrom. But given our specific efforts toward engineering a virtuous machine, it is important to note that Vallor specifically informs us about the key concepts of exemplars in the particular members of the family; to pick just one of many available places, she writes:

Buddhism’s resonances with other classical virtue traditions do not end here. As with the central role granted by Confucian and Aristotelian ethics to ‘exemplary persons’ (the junzi and phronimoi respectively), bodhisattvas (persons actively seeking enlightenment) generally receive direction to or assistance on the path of self-cultivation from the community of exemplary persons to which they have access. In Buddhism this is the monastic community and lay members of the Sangha [¶5, §2.1.3, [Vallor2016]]

We said above that we would also draw, albeit briefly, from a second treatment of , viz. [Annas2011], in order to pave the way into our AI-specific, exemplar-based technical work. About this second treatment we report only that it is one based squarely on a “range of development” (¶3, §Right Action in Ch. 3), where the agent (a human in her case) gradually develops into a truly virtuous person, beginning with unreflective adoption of direct instruction, through a final phase in which “actions are based on understanding gained through experience and reflection” (ibid.). Moreover, Annas explicitly welcomes the analogy between an agent’s becoming virtuous, and an agent’s becoming, say, an excellent tennis-player or pianist. The idea behind the similarity is that “two things are united: the need to learn and the drive to aspire (emphasis hers; ¶4 Ch. 3). In addition, following Aristotle on  (e.g. see [Aristotle2000] 1103), no one can become a master tennis-player or pianist without, specifically, playing tennis/the piano with an eye to the mastery of great exemplars in these two domains.

In order to now turn to specific AI work devoted to engineering a virtuous machine, we move from completed consideration of the general foundation of , and its now-confirmed essential use of moral exemplars, to a specific use of such exemplars that appears ripe for mechanization.

Exemplarist Virtue Theory

Exemplarist virtue theory () builds on the direct reference theory (DRT) of semantics. Briefly, in DRT, given a word or term , its meaning is determined by what the word points out, say , and not by some definition . For example, for a person to use the word “water,” in a correct manner, that person neither needs to possess a definition of water nor needs to understand all the physical properties of water. The person simply needs to know which entity the word “water” picks out in common usage.

In , persons understand moral terms, such as “honesty,”, in a similar manner. That is, moral terms are understood by persons through direct references instantiated in exemplars. Persons identify moral examplars through the emotion of admiration. The emotions of admiration and contempt play a foundational role in this theory.  posits a process very similar to scientific or empirical investigation. Exemplars are first identified and their traits are studied; then they are continously further studied to better understand their traits, qualities, etc. The status of an individual as an exemplar can change over time. Below is an informal version that we seek to formalize:

[frametitle= Informal Version ,linewidth=0,backgroundcolor=gray!05,frametitlebackgroundcolor=gray!10]

  1. Agent or person perceives a person perform an action . This observation causes the emotion of admiration in .

  2. then studies and seeks to learn what traits (habits/dispositions) has.

The Goal

From the above presentation of , we can glean the following distilled requirements that should be present in any formalization.

[frametitle= Formalization Components,linewidth=0,backgroundcolor=gray!05,frametitlebackgroundcolor=gray!10]

  1. A formalization of emotions, particularly admiration.

  2. A representation of traits.

  3. A process of learning traits (and not just simple individual actions) from a small number of observations.

Building the Formalization

For fleshing out the above requirements and formalizing , we will use the deontic cognitive event calculus (), a computational formal logic. This logic was used previously in [Govindarajulu and Bringsjord2017a, Govindarajulu et al.2017] to automate versions of the Doctrine of Double Effect (), an ethical principle with deontological and consequentialist components.  has also been used to formalize akrasia (the process of succumbing to temptation to violate moral principles) [Bringsjord et al.2014]. Fragments of  have been used to model highly intensional reasoning processes, such as the false-belief task [Arkoudas and Bringsjord2008].555 is both intensional and intentional. There is a difference between intensional and intentional systems. Broadly speaking, extensional systems are formal systems in which the references and meanings of terms are independent of any context. Intensional systems are formal systems in which meanings of terms are dependent on context, such as the cognitive states of agents, time, etc. Modal logics used for modeling beliefs, desires, and intentions are considered intensional systems. Please see the appendix in [Govindarajulu and Bringsjord2017a] for a more detailed discussion.

Overview of

 is a quantified multi-operator666The full catalogue of available operators exceeds those for belief, desire, and intention, and a fortiori exceeds the available operators in any standard modal logic designed to formalize e.g. only either alethic, epistemic, or deontic phenomena. modal logic (also known as sorted first-order multi-operator modal logic) that includes the event calculus, a first-order calculus used for commonsense reasoning over time and change [Mueller2014]. This calculus has a well-defined syntax and proof calculus; see Appendix A of [Govindarajulu and Bringsjord2017a]. The proof calculus is based on natural deduction [Gentzen1935], and includes all the introduction and elimination rules for first-order logic, as well as inference schemata for the modal operators and related structures. As a sorted calculus,  can be regarded analogous to a typed programming language. We show below some of the important sorts used in . Among these, the Agent, Action, and ActionType sorts are not native to the event calculus.

Sort Description
Agent Human and non-human actors.
Time The Time type stands for time in the domain; e.g. simple, such as , or complex, such as .
Event Used for events in the domain.
ActionType Action types are abstract actions. They are instantiated at particular times by actors. Example: eating.
Action A subtype of Event for events that occur as actions by agents.
Fluent Used for representing states of the world in the event calculus.

Note: actions are events that are carried out by an agent. For any action type and agent , the event corresponding to carrying out is given by . For instance, if is “running” and is “Jack” , denotes “Jack is running”.


The syntax has two components: a first-order core and a modal system that builds upon this core. The figures below show the formal language and inference schemata of . Commonly used function and relation symbols of the event calculus are included. Any formally defined calculi (e.g. the venerable situation calculus) for modeling commonsense and physical reasoning can be easily switched out in-place of the event calculus.

The modal operators present in the calculus include the standard operators for knowledge , belief , desire , intention , obligation etc. For example, consider , which says that agent believes at time the proposition . Here can in turn be any arbitrary formula.

[linecolor=white, frametitle=Syntax (fragment), frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]

Inference Schemata

The figure below shows a fragment of inference schemata for . is an inference schema that let us model idealized agents that have their knowledge and belief closed under the  proof theory. While normal humans are not deductively closed, this lets us model more closely how deliberative agents such as organizations and more strategic actors reason. (Some dialects of cognitive calculi restrict the number of iterations on intensional operators.) states that if an agent communicates a proposition to , then believes that believes . dictates how obligations propagate to intentions.

[linecolor=white, frametitle=Inference Schemata (fragment), frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]

We also define the following inference-schemata-based relationships between expressions in our calculus.

Generalization of Formulae. The generalization of a set of formulae , is a set of formulae from which any element of can be inferred: . This is denoted by .

Generalization of Terms: A term is a generalization of a term if given any first-order predicate , from we can derive : . This is denoted by .


 uses proof-theoretic semantics [Gentzen1935, Francez and Dyckhoff2010], an approach commonly associated with natural deduction inference systems. Briefly, in this approach, meanings of modal operators are defined via functions over proofs. Specifying semantics then reduces to specifying inference schemata.

Events, Fluents, and Utilities

In the event calculus, fluents represent states of the world. Our formalization of admiration requires a notion of utility for states of the world. Therefore, we assign utilities to fluents through a utility function: . An event can initiate one or more fluents. Therefore, events can also have a utility associated with them. For an event at time , let be the set of fluents initiated by the event, and let be the set of fluents terminated by the event. If we are looking up till horizon , then , the total utility of event at time , is:

With the calculus given above, we now move on to specifying parts of the formalization , that is, , , and .

With the calculus given above, we now move on to specifying parts of the formalization , that is, , , and .

Defining Admiration

We start with and formalize admiration in . To acheive this, we build upon the OCC model. There are many models of emotion from psychology and cognitive science. Among these, the OCC model [Ortony, Collins, and Clore1988] has found wide adoption among computer scientists. Note that the model presented by [Ortony, Collins, and Clore1988] is informal in nature and one formalization of the model has been presented in [Adam, Herzig, and Longin2009]. This formalization is based on propositional modal logic, and while comprehensive and elaborate, is not expressive enough for our modelling, which requires at the least quantification over objects.

In OCC, emotions are short-lived entities that arise in response to events. Different emotions arise based on: (i) whether the consequences to events are positive (desirable) or negative (undesirable); (ii) whether the event has occured; and (iii) whether the event has consequences for the agent or for another agent. OCC assumes an undefined primitive notion of an agent being pleased or displeased in response to an event. We represent this notion by a predicate in our formalization. In OCC, admiration is defined as “(approving of) someone else’s praiseworthy action.” We translate this definition into  as follows. An agent is said to admire another agent ’s action , if agent believes the action is a good action. An action is a considered a good action if . In OCC, agents can admire only other agents and not themselves. This is captured by the inequality

[linecolor=white,nobreak, frametitle=() Admiration in , backgroundcolor=gray!05, frametitlebackgroundcolor=gray!10, roundcorner=8pt]

Defining Traits

To satisfy , we need to define traits. We define a situation as simply a collection of formulae that describe what fluents hold at a time , along with other event-calculus constraints and descriptions (sometimes we use to represent the conjunction of all the formulae in .)

[linecolor=white, frametitle= () Trait, frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt] An agent has a situation and action type as an -trait if there are at least situations in which instantiations of are performed, and is the generalization of the situations.

A trait can be represented as single formula:

We introduce a new modal operator that can then be applied to the collection of formulae denoting a trait. says that agent has trait . The following inference schema then applies to :

[linecolor=white, frametitle= () Inference Schema for , frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]

Defining Learning of Traits

To address we need a definition of what it means for an agent to learn a trait. We start with a learning agent . An agent is identified as an exemplar by iff the emotion of admiration is triggered times or more by in . This is written down in  as follows (note that admiration can be triggered by different actions):

[linecolor=white, frametitle=Exemplar Defninition, frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]

Once is identified as an exemplar, the learner then identifies one or more traits of by observing over an extended period of time. Let believe that has a trait ; then incorporates as its own trait:

[linecolor=white, frametitle=() Learning a Trait, frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]


For instance, if the action type “being truthful” is triggered in situations: “talking with alice,”, “talking with bob”, “talking with charlie”; then the trait learned is that “talking with an agent” situation should trigger the “being truthful” action type.

A Note on Learning Methods

When we look at humans learning virtues by observing others or by reading from texts or other sources, it is not entirely clear how models of learning that have been successful in perception and language processing (e.g. the recent successes of deep learning and statistical learning) can be applied. Learning in

-relevant situations is from one or few instances or in some cases through instruction, and such learning may not be readily amenable to models of learning which require a large number of examples.

The abstract learning method that we will use is generalization, defined previously. See one simple example immediately below:

[linecolor=white, frametitle=Example 1, frametitlebackgroundcolor=white, backgroundcolor=white, roundcorner=8pt]

One particularly efficient and well-studied mechanism to realize generalization is anti-unification, which has been applied successfully in learning programs from few examples.777This discipline, known as inductive programming, seeks to build precise computer programs from examples [Nienhuys-Cheng and De Wolf1997]. See [Muggleton et al.2018] for an application in generating human comprehensible programs. In anti-unification, we are given a set of expressions and need to compute an expression that when substituted with an appropriate term gives us . For example, if we are given and , the anti-unification of those terms would be .

In higher-order anti-unification, we can substitute function symbols and predicate symbols. Here is a higher-order variable.

Defining Virtuous Person and Virtues

With the formal machinery in place we finally present formalizations that answer and posed at the outset. An -virtuous person or agent is an agent that is considered as an exemplar by agents:

[linecolor=white, frametitle=() Virtuous Person, frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]

An -virtue is a trait possesed by at least virtuous agents: [linecolor=white, frametitle=() Virtue, frametitlebackgroundcolor=gray!10, backgroundcolor=gray!05, roundcorner=8pt]

Implementation & Simulation

We have extended ShadowProver, a quantified modal logic prover for  used in [Govindarajulu and Bringsjord2017a] to handle the new inference schemata and definitional axioms given above. We now show a small simulation in which an agent learns a trait and uses that trait to perform an action. Assume that we have a marketplace where things that are either old or new can be bought and sold. A seller can either honestly state the condition of an item or falsely report the state of the item. Agent has two items and . is new and is old. is asked about the state of the items, and responds accurately. We have an agent that observes agent correctly report the state of the items. also has beliefs about ’s state of mind. We also have that the agent considers to be an exemplar. When all this information is fed into the prover along with the definitions above, learns a trait representing a form of honesty, shown below:

[linecolor=white, frametitlebackgroundcolor=white, backgroundcolor=white, roundcorner=8pt]

When is queried about the state of an item , responds accurately (input and output shown in Figure  2). The prover responds with the required output in seconds.888A notebook for running this simulation can be found here: anonymized.

Figure 2: Simulation Input and Output Formulae

Conclusion & Future Work

We have presented an initial formalization of a virtue ethics theory in a calculus that has been used in automating other ethical principles in deontological and consequentialist ethics. Many important questions have to be addressed in future research. Among them are questions about the nature and source of the utility functions that are used in the definitions of emotions. Lacking in our above model is an account of uncertainties and how they interact with virtues. We plan to leverage an account of uncertainty for a fragment of  presented in [Govindarajulu and Bringsjord2017b]. In future work, we will compare learning traits with work on learning norms [sarathy2017learning]. The notion of learning we have presented here is quite abstract. In order to handle more complex traits, more sophisticated learning frameworks may have to be considered. Finally, we need to apply this model to more realistic examples and case studies. The way forward to the production of virtuous machines is thus challenging, but we are confident that the foundation is now in place for their eventual arrival.


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