In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and (...) Weak Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule. (shrink)

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to (...) dictatorship (resp. oligarchy), either just on the premisses or on the whole agenda. This framework is inspired by the doctrinal paradox of legal theory and arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory. (shrink)

Formalization of reasoning which accepts rules of inference leading to conclusions whose logical values are not smaller than the logical value of the “weakest” premise leads to the concept of consequence operation preserving degrees of truth. Several examples of such consequence operation have already been considered . In the present paper we give a general notion of the consequence operation preserving degrees of truth and its characterization in terms of projective generation and selfextensionality.

The information explosion and digital modes of learning often combine to inform the quest for the best ways of transforming information in digital form for pedagogical purposes. This quest has become more urgent and pervasive with the ‘turn’ to online learning in the context of COVID-19. This can result in linear, asynchronous, transmission-based modes of teaching and learning which commodify, package and deliver knowledge for individual ‘customers’. The primary concerns in such models are often technical and economic – technology (...) as a cost-effective ‘solution’ to educational challenges. In this paper I argue for the importance of dialogic learning space in teaching and learning by means of Information and Communication Technologies, whether in the form of fully online learning, blended learning or face-to-face encounters using ICT affordances. Although the 20th Century theorists Mikhail Bakhtin (1895–1975) and Hans-Georg Gadamer (1900–2002) produced their seminal works before the advent of ICTs, they were both concerned with the quality and authenticity of human engagement with texts and with other persons and contexts. Besides a shared interest in dialogue as an ontological feature of human life and being, they both used spatiotemporal concepts for understanding and interpreting texts. The article draws on Gadamer’s notions of dialogue and horizon, and Bakhtin’s notions of dialogue and chronotope, to conceptualize dialogic possibilities for online education. Its purpose is to provide a framework, grounded in Bakhtin’s and Gadamer’s ideas, for a dialogic approach to online teaching and learning in higher education. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the same generality if (...) after generalizing maximally the rules involved in them they yield the same premises and conclusions up to a renaming of variables. These two proposals proved to be extensionally equivalent only for limited fragments of logic. The normalization proposal stands behind very successful applications of the typed lambda calculus and of category theory in the proof theory of intuitionistic logic. In classical logic, however, it did not fare well. The generality proposal was rather neglected in logic, though related matters were much studied in pure category theory in connection with coherence problems, and there are also links to low-dimensional topology and linear algebra. This proposal seems more promising than the other one for the general proof theory of classical logic. (shrink)

This paper presents a belief revision operator that considers time intervals for modelling norm change in the law. This approach relates techniques from belief revision formalisms and time intervals with temporalised rules for legal systems. Our goal is to formalise a temporalised belief base and corresponding timed derivation, together with a proper revision operator. This operator may remove rules when needed or adapt intervals of time when contradictory norms are added in the system. For the operator, both constructive (...) definition and an axiomatic characterisation by representation theorems are given. (shrink)

Physicalism is usually understood as the claim that every empirical entity is or is determined by physical entities. The claim is however imprecise until it is clarified what are the physical entities in question. A sceptical argument in the form of a dilemma tries to show that this problem of formulation of physicalism cannot be adequately met. If we understand physical entities as the entities introduced by current physics, the resulting claim becomes most probably false. If we instead understand physical (...) entities as those entities introduced by some future ideal physics, the claim then becomes indeterminate in content. Both horns seem equally bad. In the first part of the paper, I survey the strengths and weaknesses of different proposed solutions to this problem of formulation. In the second part, I lay out a new formulation of physicalism, partly based on a mereological principle, which overcomes the dilemma, and argue that it is a correct formulation of physicalism to the extent that it rules out clear antiphysicalist scenarios and is compatible with clear physicalist scenarios. (shrink)

There are frequent claims that the regulation of international law is uncertain, vague, ambiguous, or indeterminate, which does not support the desired stability, transparency, or predictability of international legal relations. This monograph examines the framework of interpretation in international law based on the premise of the effectiveness and determinacy of international legal regulation, which is a necessary pre-requisite for international law to be viewed as law. This study examines this problem for the first time since these questions were (...) introduced and identified as the basic premises of the international legal analysis, in the works of JL Brierly and Sir Hersch Lauterpacht. Addressing different aspects of the effectiveness of legal regulation, this monograph examines the structural limits on, and threshold of, legal regulation, and the relationship between established legal regulation and non-law. Once the limits of legal regulation are ascertained, the analysis proceeds to examine the legal framework of interpretation that serves to maintain and preserve the object and aims of existing legal regulation. The final stage of analysis is the interpretation of those treaty provisions that embody the indeterminate conditions of non-law. Given that the generalist element of international legal doctrine has been virtually silent on the problem and implications of the effectiveness and determinacy of international legal regulation, this study examines the material accumulated in doctrine and practice for the past several decades, including the relevant jurisprudence of all major international tribunals. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to (...) manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

The concept of need is often proposed as providing an additional or alternative criterion to cost-effectiveness in making allocation decisions in health care. If it is to be of practical value it must be sufficiently precisely characterized to be useful to decision makers. This will require both an account of how degree of need for an intervention is to be determined and a prioritization rule that clarifies how degree of need and the cost of the intervention interact in determining the (...) relative priority of the intervention. Three common features of health care interventions must be accommodated in a comprehensive theory of need: the probabilistic nature of prognosis (with and without the intervention); the time course of effects; and the fact that the most effective treatments often combine more than one intervention. These common features are problematic for the concept of need. We outline various approaches to prioritization on the basis of need and argue that some approaches are more promising than others. (shrink)

Every artificial-intelligence research project needs a working definition of "intelligence", on which the deepest goals and assumptions of the research are based. In the project described in the following chapters, "intelligence" is defined as the capacity to adapt under insufficient knowledge and resources. Concretely, an intelligent system should be finite and open, and should work in real time. ;If these criteria are used in the design of a reasoning system, the result is NARS, a non-axiomatic reasoning system. ;NARS uses (...) a term-oriented formal language, characterized by the use of subject-predicate sentences. The language has an experience-grounded semantics, according to which the truth value of a judgment is determined by previous experience, and the meaning of a term is determined by its relations with other terms. Several different types of uncertainty, such as randomness, fuzziness, and ignorance, can be represented in the language in a single way. ;The inference rules of NARS are based on three inheritance relations between terms. With different combinations of premises, revision, deduction, induction, abduction, exemplification, comparison, and analogy can all be carried out in a uniform format, the major difference between these types of inference being that different functions are used to calculate the truth value of the conclusion from the truth values of the premises. ;Since it has insufficient space-time resources, the system needs to distribute them among its tasks very carefully, and to dynamically adjust the distribution as the situation changes. This leads to a "controlled concurrency" control mechanism, and a "bag-based" memory organization. ;A recent implementation of the NARS model, with examples, is discussed. The system has many interesting properties that are shared by human cognition, but are absent from conventional computational models of reasoning. ;This research sheds light on several notions in artificial intelligence and cognitive science, including symbol-grounding, induction, categorization, logic, and computation. These are discussed to show the implications of the new theory of intelligence. ;Finally, the major results of the research are summarized, a preliminary evaluation of the working definition of intelligence is given, and the limitations and future extensions of the research are discussed. (shrink)

In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of the considerations, (...) the problem undertaken in the paper concerns working out fundamental assumptions that refer to building of epistemic logics. They allow establishing the correctness of the discourse defined by rational postulates of protocols of real communication. In the context of the presented problem there are the following two research questions distinguished: 1) How do we determine the rule of building of real dynamic epistemic logics? and 2) How should we define semantics for these logics? Within the framework of considerations relating to the research questions asked, certain epistemic operators, relativized to types of communicating, are introduced. Basic logical relations between using these operators are established for these operators. The relations are presented by a diagram called the square of epis temic operators. On the basis of these logical relations some axioms for real dynamic epistemic logics are presented. The semantics of real dynamic epistem ic logics is extended by the methods of lower and upper approximation of formula evaluating. This allows defining ‘approximation Kripke models’. The results of conceptualization of knowledge on real premises of epistemic argum entation presented in this paper can be applied to rhetoric in real systems of interaction. (shrink)

In this essay I consider the question of whether Elliot D. Cohen has justified sufficiently the metaphysical basis for his Logic-Based Therapy as presented in his paper on “The Metaphysics of Logic-Based Therapy (IJPP, this issue). Although Cohen discusses four different foundations of his cognitive theory, I focus only on one. It is the most important basis of his theory, viz., that human beings logically deduce the cognitive-behavior com­ponents of their emotions from premises. First, I question Cohen’s analysis (...) of the emotion rules we use to deduce evaluations of actions from. Second, I challenge Cohen’s view that we deduce our evaluations from emotion rules. Although I do not think my challenges completely undermine Cohen’s theory, they do raise serious concerns for a theory faced with a preponderance of causal therapies. (shrink)

This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...) and a deductive logic by which the steps of the deduction proceed. Every demonstration produces knowledge of its conclusion for every person who comprehends the demonstration. Aristotle presented a general truth-and-consequence theory of demonstration meant to apply to all demonstrations: a demonstration is an extended argumentation that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining theory of deduction was meant to apply to all deductions: any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. His deductions, both direct and indirect, were rule-based and not tautology-based. The idea of tautology-based deduction, which dominated modern logic in the early years of the 1900s, is nowhere to be found in Analytics. Rule-based deduction was rediscovered by modern logicians. To illustrate his general theory of deduction, Aristotle presented a prototype: an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. With reference only to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained to complete deductions. In his specialized prototype theory, Aristotle explained how to deduce from a given categorical premise set, no matter how large, any categorical conclusion implied by the given set. He did not extend this treatment to non-categorical deductions, thus setting a program for future logicians. The prototype, categorical syllogistic, was seen by Boole as a “first approximation” to a comprehensive logic. Today, however it appears more as the first of the dozens of logics already created and as the first exemplification of a family that continues to expand. (shrink)

We give a characterization of majority voting rules with quorums in the framework of May (Econometrica 20:680–684, 1952)’s seminal article. According to these voting rules, an alternative is socially chosen if and only if it obtains the relative majority of votes and the total number of voters not abstaining reaches the quorum.

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.

Among anti-skeptical arguments based on premises about meaning, Davidson’s is distinctive because of the holistic element in both his semantic starting point and his epistemological conclusion. Davidson takes the primary bearers of meaning to be belief systems, and it is actually-held belief systems whose overall correctness he concludes to be knowable. Critical attention has gravitated toward a part of the argument that claims that any meaningful discourse must be radically interpretable by one who is omniscient except for the meanings (...) of the speaker’s words and thoughts. I argue that there is a reading of this claim on which skeptics have good reason to accept it. But on this reading the argument goes through only if another crucial premise---the necessity for radical interpretation to be done charitably---is construed in a way that leaves skeptics free to reject it. (shrink)

Among anti-skeptical arguments based on premises about meaning, Davidson’s is distinctive because of the holistic element in both his semantic starting point and his epistemological conclusion. Davidson takes the primary bearers of meaning to be belief systems, and it is actually-held belief systems whose overall correctness he concludes to be knowable. Critical attention has gravitated toward a part of the argument that claims that any meaningful discourse must be radically interpretable by one who is omniscient except for the meanings (...) of the speaker’s words and thoughts. I argue that there is a reading of this claim on which skeptics have good reason to accept it. But on this reading the argument goes through only if another crucial premise---the necessity for radical interpretation to be done charitably---is construed in a way that leaves skeptics free to reject it. (shrink)

We introduce two novel frameworks for choice under complete uncertainty. These frameworks employ intervals to represent uncertain utility attaching to outcomes. In the first framework, utility intervals arising from one act with multiple possible outcomes are aggregated via a set-based approach. In the second framework the aggregation of utility intervals employs multi-sets. On the aggregated utility intervals, we then introduce min–max decision rules and lexicographic refinements thereof. The main technical results are axiomatic characterizations of these min–max decision (...) class='Hi'>rules and these refinements. We also briefly touch on the independence of introduced axioms. Furthermore, we show that such characterizations give rise to novel axiomatic characterizations of the well-known min–max decision rule?mnx?mnx in the classical framework of choice under complete uncertainty. (shrink)

This article investigates the properties of multistate top revision, a dichotomous model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies (...) a slightly modified version of the set of basic and supplementary AGM postulates, except the inclusion and success postulates. This result shows that hyperreal probabilities can provide us with efficient tools for overcoming the well known difficulties in combining dichotomous and probabilistic models of belief change. (shrink)

We define a class of formal systems inspired by Prawitz’s theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to epistemically compel to accept the conclusion. Validity is defined in terms of typed objects, called grounds, that reify evidence for given judgments. An inference is valid when a function exists from grounds for the premises to grounds for the conclusion. Grounds are described (...) by formal terms, either directly when the terms are in canonical form, or indirectly when they are in non-canonical form. Non-canonical terms must reduce to canonical form, and two terms may be said to be equal when they converge towards equivalent grounds. In our systems these properties can be proved through rules distinguished according to whether they concern types or logic. Type rules involve type introduction and elimination, equality for application of operational symbols, and re-writing equations for non-canonical terms. The logic amounts to a sort of intuitionistic system in a Gentzen format. To conclude, we show that each system of our class enjoys a normalization property. (shrink)

A central controversy in cognitive science concerns the roles of rules versus similarity. To gain some leverage on this problem, we propose that rule‐ versus similarity‐based processes can be characterized as extremes in a multidimensional space that is composed of at least two dimensions: the number of features (Pothos, 2005) and the physical presence of features. The transition of similarity‐ to rule‐based processing is conceptualized as a transition in this space. To illustrate this, we show how a (...) neural network model uses input features (and in this sense produces similarity‐based responses) when it has a low learning rate or in the early phases of training, but it switches to using self‐generated, more abstract features (and in this sense produces rule‐based responses) when it has a higher learning rate or is in the later phases of training. Relations with categorization and the psychology of learning are pointed out. (shrink)

If the Visser rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of the Visser rules are admissible is not known. In this paper we give a brief overview of results on admissible rules in the context of intermediate logics. We apply these results to some well-known intermediate logics. We provide natural examples of (...) logics for which the Visser rule are derivable, admissible but nonderivable, or not admissible. (shrink)

ABSTRACTThe concept of need is often proposed as providing an additional or alternative criterion to cost‐effectiveness in making allocation decisions in health care. If it is to be of practical value it must be sufficiently precisely characterized to be useful to decision makers. This will require both an account of how degree of need for an intervention is to be determined and a prioritization rule that clarifies how degree of need and the cost of the intervention interact in determining the (...) relative priority of the intervention. Three common features of health care interventions must be accommodated in a comprehensive theory of need: the probabilistic nature of prognosis ; the time course of effects; and the fact that the most effective treatments often combine more than one intervention. These common features are problematic for the concept of need. We outline various approaches to prioritization on the basis of need and argue that some approaches are more promising than others. (shrink)

Empirical results suggest that defocusing attention results in primary process or associative thought, conducive to finding unusual connections, while focusing attention results in secondary process or analytic thought, conducive to rule-based operations. Creativity appears to involve both. It is widely believed that it is possible to escape mental fixation by spontaneously and temporarily engaging in a more divergent or associative mode of thought. The resulting insight may be refined in a more analytic mode of thought. The question addressed here (...) is: how does the architecture of memory support these two modes of thought, and what is happening at the neural level when one shifts between them? Recent advances in neuroscience shed light on this. It was demonstrated that activated cell assemblies are composed of multiple ‘neural cliques’, groups of neurons that respond differentially to general or context-specific aspects of a situation. I refer to neural cliques that would not be included in the assembly if one were in an analytic mode, but would be if one were in an associative mode, as ‘neurds’. It is posited that the shift to a more associative mode of thought conducive to insight is accomplished by recruiting neurds that respond to abstract or atypical subsymbolic microfeatures of the problem or situation. Since memory is distributed and content-addressable this fosters remindings and the forging of creative connections to potentially relevant items previously encoded in those neurons. Thus it is proposed that creative thought involves neither randomness, nor search through a space of predefined alternatives, but emerges naturally through the recruitment of neurds. It is suggested this occurs when there is a need to resolve conceptual gaps in ones’ internal model of the world, and resolution involves context-driven actualization of the potentiality afforded by its fine-grained associative structure. (shrink)

In this work I bring a conception of language and meaning as a shared institution to bear upon rule-following scepticism, i.e., upon the sceptical problem concerning the semantic determinacy of expressions involving infinite or indefinitely large and open extensions. Such scepticism proceeds from the observation that the extensions of expressions of this kind are not uniquely determined by epistemically accessible facts, to conclude that the expressions in question are indeterminate in point of extension, and that their meaning must consist in (...) their use. ;In the first chapter of this work, I argue that rule-following considerations by themselves do not suffice to establish these conclusions, and that additional premises are needed. I consider both internalist and extensionalist schemes to supplement the sceptical argument. I find such schemes lacking in persuasive support. Chapter 2, in particular, concentrates on Kripke's well known exegesis of Wittgenstein's argument, and on the internalist requirements upon which it is based. ;In Chapter 3, I offer an externalist account of the normative aspect in rule following. On the account I give, the rule one is projecting is determined extensionally by one's position in a community in which his projections would be corrected and evaluated by other members, and from which one has acquired the rule in the first place through a chain of communication, rather than by one's own projections, taken in isolation, which constitute only a partial understanding of the rule in question. This account is not designed to refute scepticism; rather its aim is to account for the normativity of rule-following in ways which do not invoke the internalist requirement upon which rule following scepticism is based. (shrink)

Johnson -Laird has argued that spatial reasoning is based on the construction and manipulation of mental models in memory. The present article addresses the question of whether reasoning about time relations is constrained by the same factors as reasoning about spatial relations. An experiment is reported that explored the similarities and the differences in the performance of subjects in comparable spatial and temporal reasoning tasks. The results indicated that, in both the temporal and the spatial content domains, the data (...) were in agreement with the view that subjects solved problems by constructing models in memory rather than with a logical rule conceptualisation of reasoning. An analysis of the premise-reading times on the basis of premise-linking order provided support for an on-line process of mental models construction, and offered an explanation for the finding that spatial problems that did require an inference of transitivity were easier than problems that did not. No essential differences in processing and performance were observed across the two content domains, although in the time domain the correctness data were in agreement with both the mental models theory and the logical rules view. The results are discussed with respect to the mental models theory and the structural characteristics of the problems. (shrink)

The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (the (...) conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

We give necessary and sufficient conditions for a scoring rule to be proper for a quantile if utility is linear, and the distribution is unrestricted. We also give results when the set of distributions is limited, for example, to distributions that have first moments.

The formulation of quantum mechanics as a diffusion process by Nelson provides for an interesting approach on how we may transit from classical mechanics into quantum mechanics. Besides the presence of the real potential function, another type of potential function forms an intrinsic part of this theory. In this paper we attempt to show how both types of potential functions can have a use in a resolutely macroscopic context like financial asset pricing. We are particularly interested in uncovering how the (...) ‘quantum potential’ can add to the economics-based relevant information which is already supplied by the real potential function. (shrink)

The “social-political-hierarchical” qualifications have long been identified as the essential features of the Confucian golden rule. This essay challenges this prevailing characterization by revealing the relation and differences between Confucius’ original shu 恕 and a series of post-Confucius reformulations in ancient Confucianism. Specifically, the premise of equality, which underlies Confucius’ formulation of shu in correlation with ren 仁, rendered shu incompatible with asymmetrical relationships. Besides the advantage of overcoming this limitation by adapting the golden rule structure of shu (...) to specified asymmetrical relationships, the post-Confucius formula, especially “the measuring square” in the Great Learning, was devised to guide one to infer universalizable rules of conduct for various roles in diverse relationships. On this basis, I demonstrate a pivotal shift in the golden rule practice of ancient Confucianism—a shift of focus from its correlation with ren to its conformity with li 禮 as the system of rules of conduct and the principle of “discriminations.”. (shrink)

The implementation of the Wujciak algorithm as a new rule for organ allocation by Eurotransplant is of considerable interest for the theorist of choice making. In the process reformers accepted the status quo in principle but expected that their potential opponents would be willing to make minimal or 'tolerable' concessions. Thereby the consensual introduction of new dimensions of value and reforms of allocation practices based thereupon became viable. The paper characterizes a decision procedure based on ‘almost lexicographically pre-ordering (...) established values and practices’ in a stylized manner, presents a formal reconstruction of it and points out some of its potential implications for rule choices in general. (shrink)

In this paper, we discuss semantical properties of the logic \(\textbf{GL}\) of provability. The logic \(\textbf{GL}\) is a normal modal logic which is axiomatized by the the Löb formula \( \Box (\Box p\supset p)\supset \Box p \), but it is known that \(\textbf{GL}\) can also be axiomatized by an axiom \(\Box p\supset \Box \Box p\) and an \(\omega \) -rule \((\Diamond ^{*})\) which takes countably many premises \(\phi \supset \Diamond ^{n}\top \) \((n\in \omega )\) and returns a conclusion \(\phi \supset (...) \bot \). We show that the class of transitive Kripke frames which validates \((\Diamond ^{*})\) and the class of transitive Kripke frames which strongly validates \((\Diamond ^{*})\) are equal, and that the following three classes of transitive Kripke frames, the class which validates \((\Diamond ^{*})\), the class which weakly validates \((\Diamond ^{*})\), and the class which is defined by the Löb formula, are mutually different, while all of them characterize \(\textbf{GL}\). This gives an example of a proof system _P_ and a class _C_ of Kripke frames such that _P_ is sound and complete with respect to _C_ but the soundness cannot be proved by simple induction on the height of the derivations in _P_. We also show Kripke completeness of the proof system with \((\Diamond ^{*})\) in an algebraic manner. As a corollary, we show that the class of modal algebras which is defined by equations \(\Box x\le \Box \Box x\) and \(\bigwedge _{n\in \omega }\Diamond ^{n}1=0\) is not a variety. (shrink)

Are morphological patterns learned in the form of rules? Some models deny this, attributing all morphology to analogical mechanisms. The dual mechanism model (Pinker, S., & Prince, A. (1998). On language and connectionism: analysis of a parallel distributed processing model of language acquisition. Cognition, 28, 73-193) posits that speakers do internalize rules, but that these rules are few and cover only regular processes; the remaining patterns are attributed to analogy. This article advocates a third approach, which uses (...) multiple stochastic rules and no analogy. We propose a model that employs inductive learning to discover multiple rules, and assigns them confidence scores based on their performance in the lexicon. Our model is supported over the two alternatives by new "wug test" data on English past tenses, which show that participant ratings of novel pasts depend on the phonological shape of the stem, both for irregulars and, surprisingly, also for regulars. The latter observation cannot be explained under the dual mechanism approach, which derives all regulars with a single rule. To evaluate the alternative hypothesis that all morphology is analogical, we implemented a purely analogical model, which evaluates novel pasts based solely on their similarity to existing verbs. Tested against experimental data, this analogical model also failed in key respects: it could not locate patterns that require abstract structural characterizations, and it favored implausible responses based on single, highly similar exemplars. We conclude that speakers extend morphological patterns based on abstract structural properties, of a kind appropriately described with rules. (shrink)

Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions interpreted as expressing high conditional probabilities. In the present article, we investigate four prominent LP systems (namely, systems O, P, Z, and QC) by means of computer simulations. The results reported here extend our previous work in this area, and evaluate the four systems in terms of the expected utility of the dispositions to act that derive from the conclusions that the systems license. In addition to conforming to the dominant (...) paradigm for assessing the rationality of actions and decisions, our present evaluation complements our previous work, since our previous evaluation may have been too severe in its assessment of inferences to false and uninformative conclusions. In the end, our new results provide additional support for the conclusion that (of the four systems considered) inference by system Z offers the best balance of error avoidance and inferential power. Our new results also suggest that improved performance could be achieved by a modest strengthening of system Z. (shrink)

The paper focuses on the application of a particular conception of the rule of law to situations characterized by traditional local justice and legal pluralism. While in the twentieth century international rule‐of‐law programmes were directed almost exclusively at state legal system, they have recently begun to take into account traditional local justice, namely, those institutions which in many world regions represent the main form of effective justice. Starting with a review of the positive and negative aspects of traditional local justice (...) from a rule‐of‐law perspective, the paper underlines the widespread lack of protection of human rights, particularly of women’s rights. Discussing vertical rule‐of‐law functions in contexts of legal pluralism the paper stresses the advantages of an approach to the promotion of the rule of law based on mutual recognition and influence between different legal authorities and sources. It is argued that this “interactive” approach appears best suited to the complex frameworks of relations that characterize present‐day systems of deep legal pluralism. Finally, the paper underlines the correspondence between this approach and a conception of the rule of law as an ideal framework of plural interactions characterized by the limits imposed on the law by the law itself, and it discusses its advantages from the perspective of human rights and women’s rights promotion. (shrink)

Binarizing belief aggregation tackles the problem of aggregating individuals’ probabilistic beliefs on logically connected propositions into the group’s binary beliefs. One common approach to associating probabilistic beliefs with binary beliefs would be applying thresholds to probabilities. This paper aims to introduce and classify a range of threshold-based binarizing belief aggregation rules while characterizing them based on different forms of monotonicity and other properties.

A new property of collective choice rules that we refer to as superset robustness is introduced, and we employ it in several characterization results. The axiom requires that if all individual preference orderings expand weakly (in the sense of set inclusion), then the corresponding social preference relation must also expand weakly. In other words, if a given profile is changed by adding instances of weak preference to some individual relations, then the social weak preference relation for the expanded (...) profile must contain the social weak preference relation for the original—that is, the social relation cannot contract in response to the addition of pairs to the individual relations. We begin by examining social welfare functions (that is, collective choice rules such that the resulting social preferences are orderings) and then move on to rules that generate transitive (but not necessarily complete) social rankings. The remaining results of the paper focus on Suzumura-consistent collective choice rules. In all of these cases, it turns out that the property of superset robustness is closely related to classes of agreement-based collective choice rules. These are rules such that the social relation is determined by collecting the pairs on whose relative rankings the members of the decisive sets agree. (shrink)

The categorical syllogism is the foundation of Aristotelian logic, and Aristotle's logic is the foundation of modern logic. Proper fallacies were rather errors in reasoning based on ambiguities, such as those Aristotle speaks of in Sophistical Refutations and on which Galen comments in De Captionibus (On Fallacies). Each categorical fallacy is a violation of a rule for the formation of valid syllogisms. Formal fallacies, according to Aldrich, include any reasoning that violates the law of identity, law of non‐contradiction, or (...) law of excluded middle. This chapter deals with one of the common fallacies in Western philosophy, the exclusive premises (EP). EP occurs when a syllogism has two negative premises, which are propositions that deny a connection between the subject and predicate. The quality or quantity of the premises of a syllogism can make them exclusive to one another. (shrink)

Most legal theorists, including almost all positivists and many others, take for granted or are implicitly committed to an assumption that is not an official part of positivism. The assumption is that the content of the law is determined by the contents of legally authoritative pronouncements. I call it the Pronouncement View (PV, for short). The kind of determination at issue here is constitutive, not epistemic. That is, PV concerns what makes the content of the law what it is, not (...) how we ascertain the content of the law. PV is more of an organizing principle or core idea, than a precise doctrine. I have introduced PV in an unqualified form, but there are a variety of ways in which its claim could be moderated. For example, a qualified version of PV could hold that the contents of legally authoritative pronouncements play a central or predominant role in determining the content of the law. The debate between positivists and anti-positivists is often framed in a way that takes PV for granted. For example, one typical characterization takes the debate to concern whether laws must pass a moral test in order to be valid. The use of “laws” here betrays an assumption that the starting point is legally authoritative pronouncements. Given this starting point, if morality is relevant it will have to be as a way of screening the content of authoritative pronouncements. I suggest that the issue of whether a PV-based view of law is correct is more fundamental than the issue that divides legal positivists and anti-positivists, at least as the latter issue is commonly understood. For example, one common understanding of the latter issue is that positivists claim, and anti-positivists deny, that the criteria of legal validity – the criteria that determine whether a norm is legally valid – need not include moral facts. As will become clear, however, the picture of law presupposed by this way of framing the debate – according to which candidate norms qualify as legal norms by satisfying criteria of validity – is closely associated with PV and need not be accepted by non-PV-based views of law. PV leads to a characteristic set of concerns and problems, and yields a distinctive way of thinking about how law is supposed to operate. In this paper, I will offer an alternative to PV, which I call the Dependence View (DV, for short). I begin to develop the picture of law that it yields. The discussion throughout is exploratory and tentative. The goal is to sketch the alternative picture and identify problems and possible ways of developing it, not to refute the picture associated with PV. (shrink)

Inflectional morphology has been taken as a paradigmatic example of rule-governed grammatical knowledge (Pinker, 1999). The plausibility of this claim may be related to the fact that it is mainly based on studies of English, which has a very simple inflectional system. We examined the representation of inflectional morphology in Serbian, which encodes number, gender, and case for nouns. Linguists standardly characterize this system as a complex set of rules, with disagreements about their exact form. We present analyses (...) of a large corpus of nouns which showed that, as in English, Serbian inflectional morphology is quasiregular: It exhibits numerous partial regularities creating neighborhoods that vary in size and consistency. We then asked whether a simple connectionist network could encode this statistical information in a manner that also supported generalization. A network trained on 3,244 Serbian nouns learned to produce correctly inflected phonological forms from a specification of a word's lemma, gender, number, and case, and generalized to untrained cases. The model's performance was sensitive to variables that also influence human performance, including surface and lemma frequency. It was also influenced by inflectional neighborhood size, a novel measure of the consistency of meaning to form mapping. A word-naming experiment with native Serbian speakers showed that this measure also affects human performance. The results suggest that, as in English, generating correctly inflected forms involves satisfying a small number of simultaneous probabilistic constraints relating form and meaning. Thus, common computational mechanisms may govern the representation and use of inflectional information across typologically diverse languages. (shrink)

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires that (...) revised beliefs incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (shrink)

Transplantation of vital organs has been premised ethically and legally on "the dead donor rule" (DDR)—the requirement that donors are determined to be dead before these organs are procured. Nevertheless, scholars have argued cogently that donors of vital organs, including those diagnosed as "brain dead" and those declared dead according to cardiopulmonary criteria, are not in fact dead at the time that vital organs are being procured. In this article, we challenge the normative rationale for the DDR by rejecting the (...) underlying premise that it is necessarily wrong for physicians to cause the death of patients and the claim that abandoning this rule would exploit vulnerable patients. We contend that it is ethical to procure vital organs from living patients sustained on life support prior to treatment withdrawal, provided that there is valid consent for both withdrawing treatment and organ donation. However, the conservatism of medical ethics and practical concerns make it doubtful that the DDR will be abandoned in the near future. This leaves the current practice of organ transplantation based on the "moral fiction" that donors are dead when vital organs are procured. (shrink)