We provide a general framework for constructing natural consequence relations for paraconsistent and plausible nonmonotonic reasoning. The framework is based on preferential systems whose preferences are based on the satisfaction of formulas in models. We show that these natural preferential In the research on paraconsistency, preferential systems systems that were originally designed for for paraconsistent reasoning fulfill a key condition (stopperedness or smoothness) from the theoretical research of nonmonotonic reasoning. Consequently, the nonmonotonic consequence relations (...) that they induce fulfill the desired conditions of plausible consequence relations. Hence our framework encompasses different types of preferential systems that were developed from different motivations of paraconsistent reasoning and non-monotonic reasoning, and reveals an important link between them. (shrink)

Multiarm bandit problems have been used to model the selection of competing scientific theories by boundedly rational agents. In this paper, I define a variable-arm bandit problem, which allows the set of scientific theories to vary over time. I show that Roth-Erev reinforcement learning, which solves multiarm bandit problems in the limit, cannot solve this problem in a reasonable time. However, social learning via preferential attachment combined with individual reinforcement learning which discounts the past, does.

Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, (...) the revisited logic does not change the expressive power of our previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Reasoners based on the previous semantics therefore also suffice for reasoning over the new semantics. We complete the picture by investigating different notions of defeasible conditionals in modal logic that can also be captured within our framework. (shrink)

Handling exceptions in a knowledge-based system is an important issue in many application domains, such as medical domain. Recently, there is an increasing interest in nonmonotonic extension of description logics to handle exceptions in ontologies. In this paper, we propose three preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases. Our preferential semantics are defined in the framework of possibility theory, which is an uncertainty theory devoted to handling incomplete information. We consider the (...) properties of these semantics and their relationships. We also discuss the relationship between two of our preferential semantics and two existing preferential semantics. We extend a description logic-based knowledge base by adding preferential subsumptions. Entailment of plausible subsumptions relative to an extended knowledge base is defined. Properties of the preferential subsumption relations relative to an extended description logic-based knowledge base are discussed. Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic. Thus, the problem of plausible subsumption checking under our semantics can be reduced to the problem of subsumption checking under the classical semantics. (shrink)

We introduce and explore the notion of duality for entailment relations induced by preference orderings on states. We discuss the relationship between these preferential entailment relations from the perspectives of Boolean algebra, inference rules, and modal axiomatisation. Interpreting the preference relations as accessibility relations establishes modular Gödel-Löb logic as a suitable modal framework for rational preferential reasoning.

Suppose a person lives in a sub-Saharan country that has won its independence from colonial powers in the last 50 years or so. Suppose also that that person has become a high-ranking government official who makes decisions on how to allocate goods, such as civil service jobs and contracts with private firms. Should such a person refrain from considering any particulars about potential recipients or might it be appropriate to consider, for example, family membership, party affiliation, race or revolutionary stature (...) as reasons to benefit certain individuals at some cost to the general public? Which of these factors should be considered unjust, or even corrupt, as a basis on which to allocate state goods and which should not? This chapter outlines an attractive moral theory with African content that forbids both impartialism and a strong form of partialism that would permit government officials to favour members of their families or political parties. Between these two extremes, a moderate partialism is prescribed. This permits government agents to occasionally favour veterans and victims of state injustices at some cost to the general public. This chapter seeks to provide a new, unified explanation of why sub-Saharan values permit some forms of partiality, such as the preferential hiring of those who struggled against colonialism, but prohibit other nepotistic forms of partiality. (shrink)

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: 1339-1368, 2010) (...) to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases. (shrink)

We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels, and that reasoning with these logics can be simulated by algorithms for processing circumscriptive theories, such as DLS and SCAN.

A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical (...) test? One way to do so is to isolate a number of key principles of the system, and design experiments to gauge the extent to which participants do or do not follow them in reasoning tasks. Another way is to take relevant existing results and check whether a particular formal model predicts these results. The present investigation provides an illustration of the second kind of empirical testing by comparing two formal models for reasoning – namely the non-monotonic logic known as preferential logic; and a particular version of belief revision theories, screened belief revision – against the reasoning phenomenon known as belief bias in the psychology of reasoning literature: human reasoners typically seek to maintain the beliefs they already hold, and conversely to reject contradicting incoming information. The conclusion of our analysis will be that screened belief revision is more empirically adequate with respect to belief bias than preferential logic and non-monotonic logics in general, as what participants seem to be doing is above all a form of belief management on the basis of background knowledge. The upshot is thus that, while it may offer valuable insights into the nature of human reasoning, preferential logic is ultimately inadequate as a formal model of the phenomena in question. (shrink)

Shortened and mildly revised version of an essay that initially appeared in Murove (ed.) African Ethics (2009). This chapter is a work of applied ethics that aims to provide a convincing comprehensive account of how a government official in a post-independence sub-Saharan country should make decisions about how to allocate goods such as civil service jobs and contracts with private firms. Should such a person refrain from considering any particulars about potential recipients, or might it be appropriate to consider, for (...) example, family membership, party affiliation, race, or revolutionary stature as reasons to benefit certain individuals at some cost to the public? Which of these factors should be considered an unjust or corrupt basis on which to allocate state goods and which should not? Drawing on an African ethic, this chapter answers these questions with what it calls a “moderate partialism,” according to which a government agent may rightly favor at some cost to the public veterans and victims of state injustices, but not those in her family or party. This chapter seeks to provide a new, unified explanation of why characteristically sub-Saharan values permit some forms of partiality, such as the preferential hiring of those who suffered from or struggled against colonialism, but forbid other, nepotist or prebendalist forms of partiality. (shrink)

A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical (...) test? One way to do so is to isolate a number of key principles of the system, and design experiments to gauge the extent to which participants do or do not follow them in reasoning tasks. Another way is to take relevant existing results and check whether a particular formal model predicts these results. The present investigation provides an illustration of the second kind of empirical testing by comparing two formal models for reasoning – namely the non-monotonic logic known as preferential logic; and a particular version of belief revision theories, screened belief revision – against the reasoning phenomenon known as belief bias in the psychology of reasoning literature: human reasoners typically seek to maintain the beliefs they already hold, and conversely to reject contradicting incoming information. The conclusion of our analysis will be that screened belief revision is more empirically adequate with respect to belief bias than preferential logic and non-monotonic logics in general, as what participants seem to be doing is above all a form of belief management on the basis of background knowledge. The upshot is thus that, while it may offer valuable insights into the nature of human reasoning, preferential logic is ultimately inadequate as a formal model of the phenomena in question. (shrink)

Nonmonotonic reasoning is a theory of the rational use of assumptions. We describe the relations between NMR and Logic, and two main paradigms of NMR, preferential and explanatory one.

The traditional problems of epistemology have often been thought to be properly solved only by the provision of an argument, with premises justified by rational intuition and introspection, for the probable truth of our beliefs in the problematic domains. Following the lead of Thomas Reid, a sizable number of contemporary epistemologists, including many proponents of so-called "Reformed epistemology" regarding religious belief, reject as arbitrary the preferential treatment of reason and introspection implicit in the traditional view of the problems. These (...) "Reidians" insist that the traditional problems cannot be solved in the expected manner, but they go on to suggest that this result is of little significance because similar skeptical questions can be raised regarding a priori and introspective justification. After making clear the significance of the Reidian objection, I endeavor to defend the traditional preference for rational intuition over our other sources of belief by demonstrating that the usual skeptical worries cannot be equally raised against a priori justification. Then, after a brief consideration of some unduly neglected passages in Reid's writings in which he appears to concede that the traditional partiality to reason and introspection is not, in fact, arbitrary, I argue that it is the Reidians who are guilty of arbitrary partiality. (shrink)

This paper has two goals. First, we develop frameworks for logical systems which are able to reflect not only non-monotonic patterns of reasoning, but also paraconsistent reasoning. Our second goal is to have a better understanding of the conditions that a useful relation for nonmonotonic reasoning should satisfy. For this we consider a sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson. These generalizations allow the use of monotonic nonclassical logics as the (...) underlying logic upon which nonmonotonic reasoning may be based. Our sequence of frameworks culminates in what we call plausible, nonmonotonic, multiple-conclusion consequences relations . Our study yields intuitive justifications for conditions that have been proposed in previous frameworks and also clarifies the connections among some of these systems. In addition, we present a general method for constructing plausible nonmonotonic relations. This method is based on a multiple-valued semantics, and on Shoham's idea of preferential models. (shrink)

Ethics education has become a priority at many business schools. A common pedagogical strategy in business ethics education has been to encourage students to deliberate and reason about cases and dilemmas. However, relatively little is known about how students actually reason, by default, about business ethics cases and dilemmas. In a large-scale study with undergraduate management students, we investigate how students reason about ethical dilemmas in business. Our results suggest that, after making an initial decision in a dilemma, students rarely (...) changed their minds after deliberating over an extensive set of reasons for both sides of the dilemma. Students evaluated reasons in a way that preferentially supported their initial decisions. This post-hoc evaluation of reasons to preferentially support initial decisions also had implications for decision entrenchment: students actually tended to become more confident in the superiority of their initial decisions after deliberating over the reasons for both sides. We discuss the challenges that our findings pose for teaching business ethics. (shrink)

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are “syntax- based” or “semantic-based”, “foundational” or “coherentist”, “consistence-restoring” or “inconsistency-tolerant”. Our contribution towards clarifying the connections between these various approaches is threefold: •We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to (...) revision and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. •We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches [BDP95]. •As a direct application of the above, we show that Poole's (syntax-based) system of default reasoning and Shoham's preferential semantic for non monotonic reasoning are also expressively equivalent, in that they can represent the same set of non monotonic consequence relations. (shrink)

The paper presents a non-monotonic inference relation on a language containing a conditional that satisfies the Ramsey Test. The logic is a weakening of classical logic and preserves many of the ‘paradoxes of implication’ associated with the material implication. It is argued, however, that once one makes the proper distinction between supposing that something is the case and accepting that it is the case, these ‘paradoxes’ cease to be counterintuitive. A representation theorem is provided where conditionals are given a non-bivalent (...) semantics and epistemic states are represented via preferential models. (shrink)

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are ?syntax- based? or ?semantic-based?, ?foundational? or ?coherentist?, ?consistence-restoring? or ?inconsistency-tolerant?. Our contribution towards clarifying the connections between these various approaches is threefold: ?We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to (...) revision and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. ?We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches [BDP95]. ?As a direct application of the above, we show that Poole's (syntax-based) system of default reasoning and Shoham's preferential semantic for non monotonic reasoning are also expressively equivalent, in that they can represent the same set of non monotonic consequence relations. (shrink)

This article is about conditionalized modal statements whose antecedents concern a preferential attitude of an agent. The focus is on anankastic conditionals or, as they are known in the philosophical literature, hypothetical imperatives. We present a linguistically-motivated analysis of anankastic and related conditionals and use it to address challenges for semantic theories of natural language conditionals motivated by certain philosophical concerns about practical reasoning and the requirements of rationality.

In this work, we propose a meaningful extension of description logics for non-monotonic reasoning. We introduce \, a logic allowing for the representation of and reasoning about both typical class-membership and typical instances of a relation. We propose a preferential semantics for \ in terms of partially-ordered DL interpretations which intuitively captures the notions of typicality we are interested in. We define a tableau-based algorithm for checking \ knowledge-base consistency that always terminates and we show that it (...) is sound and complete w.r.t. our preferential semantics. The general framework we here propose can serve as the foundation for further exploration of non-monotonic reasoning in description logics and similarly structured logics. (shrink)

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. (...) A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (shrink)

As Kant claimed in the Groundwork, and as the idea has been developed by Korsgaard 1997, Bratman 1987, and Broome 2002. This formulation is agnostic on whether reasons for ends derive from our desiring those ends, or from the relation of those ends to things of independent value. However, desire-based theorists may deny, against Hubin 1999, that their theory is a combination of a principle of instrumental transmission and the principle that reasons for ends are provided by desires. Instead, they (...) may say, there is just one principle, a principle of, if you will, instrumental transmutation: if one desires the end, then one has reason to take the means. See the discussion of General Production, in section 8, for a doubt about this. (shrink)

The 'no-supervenience' theorem (Reason, 2019; Reason and Shah, 2021) is a proof that no fully self-aware system can entirely supervene on any objectively observable system. I here present a simple, non-technical summary of the proof and demonstrate its implications for four separate theories of consciousness: the 'property dualism' theory of David Chalmers; the 'reflexive monism' of Max Velmans; Galen Strawson's 'realistic monism'; and the 'illusionism' of Keith Frankish. It is shown that all are ruled out in their current form by (...) the no-supervenience theorem, except for Chalmers' theory, which I show requires humans to behave irrationally. (shrink)

We offer a model of moral reform and regeneration that involves a wrong-doer making two movements: on the one hand, he identifies with himself as the one who did the act, while he also intentionally moves away from that self (or set of desires and intentions) and moves toward a transformed identity. We see this model at work in the formal practice of contrition and reform in Christian and Buddhist rites. This paper is part of a broader project we are (...) undertaking on the philosophy of forgiveness. (shrink)

This chapter contains sections titled: Reincarnation/Rebirth Karma Causality Problem of Evil Determinism, Freedom, and Moral Responsibility Karma and Release Transfer of Merit Recent Developments Works cited.

Conscious macrostates are usually assumed to be emergent from the underlying physical microstates comprising the brain and nervous system of biological organisms. However, a major problem with this assumption is that consciousness is essentially nonmeasurable unlike all other proven emergent properties of physical systems. In an earlier paper, using a no-go theorem, it was shown that conscious states cannot be comprised of processes that are physical in nature (Reason, 2019). Combining this result with another unrelated work on causal emergence in (...) physical systems (Hoel, Albantakis and Tononi, 2013), we show in this paper that conscious macrostates are not emergent from physical systems and they also do not supervene on physical microstates. An important implication of our work is that there must be some form of violation of energy conservation in biological systems that are conscious. (shrink)