We discuss a `negative' way of defining frame classes in (multi)modal logic, and address the question of whether these classes can be axiomatized by derivation rules, the `non-ξ rules', styled after Gabbay's Irreflexivity Rule. The main result of this paper is a metatheorem on completeness, of the following kind: If Λ is a derivation system having a set of axioms that are special Sahlqvist formulas and Λ+ is the extension of Λ with a set of non-ξ rules, (...) then Λ+ is strongly sound and complete with respect to the class of frames determined by the axioms and the rules. (shrink)

The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state. Unlike Gleason’s theorem, the argument applies even if probabilities are de…ned for only a single resolution of the identity, so it applies to a variety of foundational approaches to quantum mechanics. It also provides a probability rule for state spaces that are not Hilbert spaces.

In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from which (...) they are composed is underpinned, shows moreover that the proof-theoretic analysis of first-order logic can be pursued also beneath the atomic level. (shrink)

In previous articles we presented a simple set of axioms named “Contexts, Systems and Modalities”, where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a quantum system, and the continuum of contexts that are required to define these modalities. In the present article we discuss further how to obtain Born’s rule within this framework. Our approach is compared with other former and recent derivations, and its strong links with (...) Gleason’s theorem are particularly emphasized. (shrink)

If a certain semantic relation (which we call 'local consequence') is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call 'global consequence'), suggested by work of J.W. Garson, turns out to provide a much better - indeed a perfectly accurate - guide to derivability.

In the paper we focus upon the problem of derivability of rulesfrom rule complexes. The notion of a rule complex is the main mathematicalnotion of generalized game theory . Derivability of rules, asdefined here, comprises the concept of an extension from a default theory [9]as well as the classical notion of derivability of rules in logic. The idea oflocalness of reasoning, reasoning with a limited access to rules, is realizedby the concept of relative derivability. Starting with derivability (...) of rules, wenext touch upon the questions of the activation of rules and consistencyof rule complexes. (shrink)

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing experimentally observable properties of probability distributions for the outcome of measurements. Axioms I, II, III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by von Neumann (in Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955) and independently by Turing (Teuscher and Hofstadter, Alan Turing: Life and Legacy of a Great Thinker, Springer, (...) Berlin, 2004), in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for any finite dimension. (shrink)

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or “envariance” [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.

Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs (...) again in its treatment of the structural rules, and has a range of virtues absent from traditional natural deduction systems. (shrink)

It is well established that majority rule is transitive on some restricted domain and that majority rule is the unique social welfare function satisfying some standard axioms on the universal domain. We prove that majority rule is the unique social welfare function satisfying these axioms on a standard restricted domain over which majority rule is transitive. That is, the only profiles which are used to derive majority rule belong to the restricted domain.

We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures (POVMs), as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems (qubits) and even for vector spaces over rational fields—settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a (...) qubit, we investigate similar results for frame functions defined upon various restricted classes of POVMs. For the so-called trine measurements, the standard quantum probability rule is again recovered. (shrink)

The idea that correspondences relating grammatical relations and semantics (argument structure constructions) are needed to account for simple sentence types is reviewed, clarified, updated and compared with two lexicalist alternatives. Traditional lexical rules take one verb as ‘input’ and create (or relate) a different verb as ‘output’. More recently, invisible derivational verb templates have been proposed, which treat argument structure patterns as zero derivational affixes that combine with a root verb to yield a new verb. While the derivational template (...) perspective can address several problems that arise for traditional lexical rules, it still faces problems in accounting for idioms, which often contain specifications that are not appropriately assigned to individual verbs or derivational affixes (regarding adjuncts, modification, and inflection). At the same time, it is clear that verbs play a central role in determining their distribution. The balance between verbs and phrasal argument structure constructions is addressed via the Principles of Semantic Coherence and Correspondence together with a usage-based hierarchy of constructions that contains entries which can include particular verbs and other lexical material. (shrink)

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR + and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.

Pavel Materna proposed valuable explications of concept and conceptual system. After their introduction, we contrast conceptual systems with (a novel notion of) derivation systems. Derivation systems differ from conceptual systems especially in including derivation rules. This enables us to show close connections among the realms of objects, their concepts, and reasoning with concepts.

The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables, upon the basis of the conception of model introduced in :27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models that a rule (...) is derivable in the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant. Finally, we exemplify this application by studying sequent calculi for some of such logics. (shrink)

Animal-derived constituents are frequently used in anaesthesia and surgery, and patients are seldom informed of this. This is problematic for a growing minority of patients who may have religious or secular concerns about their use in their care. It is not currently common practice to inform patients about the use of animal-derived constituents, yet what little empirical data does exist indicates that many patients want the opportunity to give their informed consent. First, we review the nature and scale (...) of the problem by looking at the groups who may have concerns about the use of animal-derived constituents in their care. We then summarise some of the products used in anaesthesia and surgery that can contain such constituents, such as anaesthetic drugs, surgical implants and dressings. Finally, we explore the problem of animal-derived constituents and consent using Beauchamp and Childress’ four principles approach, examining issues of autonomy, beneficence, nonmaleficence and justice. Disclosing the use of animal-derived constituents in anaesthesia and surgery is warranted under Beauchamp and Childress’ four principles approach to the problem. Although there exist systemic and practical challenges to implementing this in practice, the ethical case for doing so is strong. The Montgomery ruling presents additional legal reason for disclosure because it entails that patients must be made aware of risks associated with their treatment that they attach significance to. (shrink)

Utilizing an idea that has its first appearance in Gerhard Gentzen’s unpublished manuscripts, we generate an exhaustive repertoire of all the possible inference rules that are related to the left implication inference rule of the sequent calculus from a ground sequent, that is, a logical axiom. We discuss the similarities and differences of these derived rules as well as their interaction with the implication right rule under cut and the structural axiom. We further consider the question of (...) analyticity of cuts in calculi using one of the new rules instead of the standard left implication rule. (shrink)

What are the principles that ground our moral obligations? One obvious answer is that they are prescriptive rules that govern conduct by imposing obligations much like (certain) legal rules govern conduct by imposing legal obligations. This "rule conception of moral principles" merits our attention for at least three reasons. It's the obvious and most straightforward way to develop the analogy between morality and law, and between moral principles and legal rules. It appears to fit some prominent theories (...) of morality and justice (e.g., Brad Hooker's rule-consequentialism, David Gauthier's contractarianism, and John Rawls's contractualism), and thus to possibly derive support from its fit with them. And it promises to account for the ability of moral principles to do the explanatory, counterfactual-supporting, and necessity-grounding work that they do. Moreover, it seems to be an integral part of some prominent theories (e.g., those of Gauthier, Kant, and Christine Korsgaard). However, I will argue that we should reject it. Moreover, by warranting the rejection of an obvious rival, the arguments presented herein strengthen the case for a dispositional (or powers) conception of moral principles, and perhaps for certain other conceptions, as well. (shrink)

In a quiet London office, a software designer muses on the algorithms that will make possible the risk flags to be visualized on the screens of border guards from Heathrow to St Pancras International. There is, he says, ‘real time decision making’ – to detain, to deport, to secondarily question or search – but there is also the ‘offline team who run the analytics and work out the best set of rules’. Writing the code that will decide the association (...) rules between items of data, prosaic and mundane – flight route, payment type, passport – the analysts derive a novel preemptive security measure. This paper proposes the analytic of the data derivative – a visualized risk flag or score drawn from an amalgam of disaggregated fragments of data, inferred from across the gaps between data and projected onto an array of uncertain futures. In contrast to disciplinary and enclosed techniques of collecting data to govern population, the data derivative functions via ‘differential curves of normality’, imagining a range of potential futures through the association rule, thus ‘opening up to let things happen’ ( Foucault 2007 ). In some senses akin to the risk orientation of the financial derivative, itself indifferent to actual underlying people, places or events by virtue of modulated norms, the contemporary security derivative is not centred on who we are, nor even on what our data say about us, but on what can be imagined and inferred about who we might be – on our very proclivities and potentialities. (shrink)

The rules of the road form part an international willingness to simplify the understanding of road regulations worldwide. There is still an attempt to harmonise all regulations, but some countries are reluctant to do so as they fear a loss of their domestic sovereignty. Indeed, with the increase in car use for private or professional reasons, accidents have become one the central issue in international politics; and one way to curb accidents is said to have a universal visual road (...) semiotics. However as this cultural discernment of road signs in civil society (i.e. visual encoding) has become popular, many other forms of use have derived from it for other purposes than road regulations. (shrink)

The popularity of rule-consequentialism among philosophers has waxed and waned. Waned, mostly; at least lately. The idea that the morality that ought to claim allegiance is the ideal code of rules whose acceptance by everybody would bring about best consequences became the object of careful analysis about half a century ago, in the writings of J. J. C. Smart, John Rawls, David Lyons, Richard Brandt, Richard Hare, and others.1 They considered utilitarian versions of rule consequentialism but discovered flaws in (...) the view that attach to the wider consequentialist doctrine. In the eyes of many, the flaws were decisive. Brad Hooker has produced brilliant work that unsettles this complacent consensus.2 Over a period of several years he has produced a sustained and powerful defense of a version of rule consequentialism that does not obviously succumb to the criticisms that have been thought to render this doctrine a nonstarter. He acknowledges intellectual debts to Richard Brandt. But Hooker avoid certain excrescences in Brandt’s efforts to conceive of morality as an ideal code of rules. Most notably, Hooker eschews Brandt’s misguided attempt to derive some version of rule utilitarianism from an underlying commitment to some form of contractualism. Moreover, Hooker has worked to articulate a version of rule consequentialism in sufficient detail that one can see how the different parts of the doctrine hang together and how the best version of the.. (shrink)

The Kelsen-Weber response, as I will reconstruct it here, is this: to divide legal orders into “rule of law” and non-rule of law legal orders is not to make a legal distinction; it is a matter of imposing a nonlegal distinction, a distinction that is, from the point of view of purely legal considerations, arbitrary. The distinction as formulated by “rule of law” theorists is typically rooted in ideological considerations masquerading as legal distinctions. Defenders of the rule of law conception (...) claim otherwise: they think they are making legal distinctions between legal orders, distinctions that can be based on philosophical considerations rather than ideological preferences for particular types of political orders. Dworkin, for example, argues that what are treated as ideological and non-legal concepts are in fact required by adjudication, and that a proper understanding of the nature of adjudication and of legal interpretation will show that these concepts and considerations play an ineliminable role 5. For these thinkers, as for Kelsen, for the concept of the rule of law to be reduced to a mere political preference is a failure. They thus agree on the terms of the dispute: the concept has to be derived from legal considerations solely. They disagree on what is entailed by legal considerations. This, however, is not the only approach to the topic. A long tradition has been concerned to argue that there is a need (presumably a moral or political need) to distinguish legal orders from oppressive orders, and that there are characteristics of legal systems that allow one to make these distinctions. The large number of lists of criteria for evaluating the degree to which a country is a rule of law regime reflect this basic idea: the criteria are themselves based on features of the legal systems of the countries, but it is not clear that the preference for these features is or can be grounded in legal considerations alone. To the extent that they reflect political or moral preferences for particular kinds of legal systems, the distinction is no longer a legal one. (shrink)

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy (as well as momentum in the relativistic case). Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles (such as compositional principles) that are needed to build up the theoretical edifice. (shrink)

The Prudent Investor Rule creates a potential ethical dilemma for investment advisors selling over-the-counter financial products issued by their firms. The "opportunity" to defraud investors using complex, over-the-counter derivative securities designed for client-specific risk management is much higher than for exchange traded securities. This paper emphasizes the ethical responsibility held by trustees and their organizations to eliminate potential conflict of interests through internal control and monitoring. Independent evaluations of the performance of investment advisors and independent appraisals of complex over-the-counter securities (...) are important in reducing the risks of conflicts of interest. Recent lessons learned from the corporate ethics crisis and requirements of the 2002 Sarbanes Oxley Act would suggest that conflict of interest must be eliminated with third party validation of derivative pricing. By performing due diligence and validation, the trustee is able to satisfy the requirements under the Prudent Investor Rule. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its (...) associated labelled calculus. (shrink)

The standard rule of necessitation in systems of natural deduction for the modal logic S4 concludes □A from A whenever all assumptions A depends on are modal formulas. This condition prevents the composability and normalization of derivations, and therefore modifications of the rule have been suggested. It is shown that both properties hold if, instead of changing the rule of necessitation, all elimination rules are formulated in the manner of disjunction elimination, i.e. with an arbitrary consequence.

A normalization procedure is given for classical natural deduction with the standard rule of indirect proof applied to arbitrary formulas. For normal derivability and the subformula property, it is sufficient to permute down instances of indirect proof whenever they have been used for concluding a major premiss of an elimination rule. The result applies even to natural deduction for classical modal logic.

This chapter contains sections titled: The Idea of an Exceptionless Moral Norm The Role of Exceptionless Precepts in Moral Thinking Exceptionless Rules and Consequentialism The Casuistry of Exceptionless Rule Approaches References.

Logic is traditionally considered to be a purely syntactic discipline, at least in principle. However, prof. David Isles has shown that this ideal is not yet met in traditional logic. Semantic residue is present in the assumption that the domain of a variable should be fixed in advance of a derivation, and also in the notion that a numerical notation must refer to a number rather than be considered a mathematical object in and of itself. Based on his work, the (...) central question of this thesis is what kind of logic, if any, results from removing this semantic residue from traditional logic.We differ from traditional logic in two significant ways. The first is that the assumption that a numerical notation must refer to a number is denied. Numerical notations are considered as mathematical objects in their own right, related to each other by means of rewrite rules. The traditional notion of reference is then replaced by the notion of reduction (by means of the rewrite rules) to a normal form. Two numerical notations that reduce to the same normal form would traditionally be considered identical, as they would refer to the same number, and hence they would be interchangeable salva veritate. In the new system, called Buridan-Volpin (BV), the numerical notations themselves are the elements of the domains of variables, and two numerical notations that reduce to the same normal form need not be interchangeable salva veritate, except when they are syntactically identical (i.e., have the same Gödel number).The second is that we do away with the assumption that the domains of variables need to be fixed in advance of a derivation. Instead we focus on what is needed to guarantee preservation of truth in every step of a derivation. These conditions on the domains of the variables, accumulated in the course of a derivation, are combined in a reference grammar. Whereas traditionally a derivation is considered valid when the conclusion follows from the premisses by way of the derivation rules (and possibly axioms), in the BV system a derivation must meet the extra condition that no inconsistency occurs within the reference grammar. For if the reference grammar were to give rise to inconsistency (i.e., it would be impossible to assign domains to all the variables without breaking at least one of the conditions placed on them in the reference grammar), there is no longer a guarantee that truth has been preserved in every step of the derivation, and hence the truth of the conclusion is not guaranteed by the derivation.In Chapter 2 the BV system is introduced in some formal detail. Chapter 3 gives some examples of derivations, notably totality of addition, multiplication and exponentiation, as well as a lemma needed for the proof of Euclid’s Theorem. These examples, taken from prof. Isles’ First-Order Reasoning and Primitive Recursive Natural Number Notations, show that there is a real proof-theoretical difference between traditional logic and the BV system. Here we also find the first major point of departure between myself and prof. Isles, centered on the notion of inheritance of conditions in the reference grammar by way of lemmata. These different points of view are best illustrated in the sections on the totality of exponentiation and on Euclid’s Lemma: prof. Isles maintains that the proof of totality of exponentiation is not BV valid, while I maintain that it is. But I do agree with him that the traditional proof of Euclid’s Lemma is not BV valid. Chapter 6 also expands the arguments for my choice in this matter.Now that it has been shown that there is a difference between traditional logic and BV, the properties of BV need to be examined. In Chapter 4 we give a proof of Cut-elimination for BV minus induction and the subformula property for BV, which allows us to prove the consistency of BV minus induction. We also expand on the reasons for excluding induction. In Chapter 5 we consider in detail the proof of a finite analog to the Löwenheim–Skolem theorem given by prof. Isles in his article with the same title. He proves that under certain conditions it is always possible, given the existence of a (possibly uncountable) model for a derivation, to give a finite model for this derivation. The system he considers deviates from BV as considered in this thesis in two significant ways: it does not contain the induction rule and the domains contain numbers instead of numerical notations. We then go on to show that it is possible to extend the result to include induction, in the sense that the existence of a possibly uncountable model for a derivation guarantees the existence of a model that is at most countable. We also consider the complications that arise from taking numerical expressions instead of numbers as the elements of domains.Finally, in Chapter 6 we consider the philosophical consequences of the BV system, informed by the formal results from the previous chapters. In particular we discuss the relation between reduction and reference, the status of reference grammars, the notion of induction and its function within BV, and some brief considerations on the consequences of the BV system for the discussion regarding nominalism and realism with regard to mathematical objects. The object of the chapter is twofold. On the one hand applying the formal results to philosophical questions, on the other hand arguing that BV is not just a theoretically acceptable alternative to traditional logic, but is in fact deserving of further development and research into its properties. The latter will probably appeal most to those of a nominalist and/or finitist bent.Abstract prepared by Harrie de Swart and Sven Storms.E-mail:[email protected]:https://research.tilburguniversity.edu/files/6170 1294/Storms_The_Buridan_Volpin_04_05_2022.pdf. (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)

Frank Hindriks has attempted to derive a variant of Timothy Williamson’s knowledge rule for assertion on the basis of a more fundamental belief expression analysis of that speech act. I show that his attempted derivation involves a crucial equivocation between two senses of ‘must,’ and therefore fails. I suggest two possible repairs; but I argue that even if they are successful, we should prefer Williamson’s fully general knowledge rule to Hindriks’s restricted moral norm.

Mainstream historians in recent decades have often treated formal categories and rules as something to be 'used' by individuals, as one might use a stick or stone, and the gains of an earlier legal history are often needlessly set aside. Anthropologists, meanwhile, have treated rules as analytic errors and categories as an imposition by outside powers or by analysts, leaving a very thin notion of 'practice' as the stuff of social life. Philosophy of an older vintage, as well (...) as the work of scholars such as Charles Taylor, provides fresh approaches when applied imaginatively to cases beyond the traditional ground of modern Europe and North America. Not only are different kinds of rules and categories open to examination, but the very notion of a rule can be explored more deeply. This volume approaches rules and categories as constitutive of action and hence of social life, but also as providing means of criticism and imagination. A general theoretical framework is derived from analytical philosophy, from Wittgenstein to his critics and beyond, and from recent legal thinkers such as Schauer and Waldron. Case-studies are presented from a broad range of periods and regions, from Amazonia via northern Chad, Tibet, and medieval Russia to the scholarly worlds of Roman law, Islam, and Classical India. As the third volume in the Legalism series, this collection draws on common themes that run throughout the first two volumes: Legalism: Anthropology and History and Legalism: Community and Justice, consolidating them in a framework that suggests a new approach to rule-bound systems. (shrink)

Logical inferentialists hold that the meaning of logical operators is given by their rules of inference. Arthur Prior cast doubt on this by introducing rules for his tonk operator that would allow for the derivation of any sentence whatsoever from any sentence whatsoever. The obvious inferentialist reply was to require some constraints on the defining rules, such as conservativeness (Belnap) or harmony (Dummett). In this paper, I will defend and investigate a different constraint: rules define a (...) classical logical operator just in case they translate into an explicit definition in pure classical second-order logic. The right-hand side of this criterion will be found (i) to be philosophically principled in taking the idea of rules as definitions perfectly seriously, (ii) to explain how the semantic meaning of the operators can be determined from their rules, (iii) to be local in a similar sense as harmony, (iv) to validate the intuitionistic natural deduction rules and the intuitionistic/classical sequent calculus rules as defining the classical propositional operators while ruling out Prior’s rules for tonk, (v) to make clear why already the intuitionistic natural deduction rules define the classical meaning of logical operators so long as metavariables are interpreted as expressing classical propositions, (vi) to validate the classical natural deduction rules as analytic, (vii) to entail consistency, and, in the case of propositional operators (not quantifiers), (viii) to be decidable and (ix) to determine precisely those operators to be definable by rules that correspond to truth-functions. (shrink)

Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent ‘cut-free’ sequent calculus has recently been shown to fail cut-elimination. We present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. Ensuring completeness is complicated by the interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to future and past modalities in (...) tense logic. Our calculus handles this interaction using derivations and refutations as first class citizens. We employ extended sequents which pass information from premises to conclusions using variables instantiated at the leaves of refutations, and rules which compose certain refutations and derivations to form derivations. Automated deduction using terminating backward search is also possible, although this is not our main purpose. (shrink)

Are norms of inquiry in tension with epistemic norms? I provide a (largely) negative answer, turning to a picture of epistemic practices as rule-governed games. The idea is that, while epistemic norms are correctness standards for the attitudes involved in epistemic games, norms of inquiry derive from the aims of those games. Attitudes that, despite being epistemically correct, are inadvisable regarding the goals of some inquiry are just like bad (but legal) moves in basketball or chess. I further consider cases (...) in which the aims of inquiry recommend breaking epistemic norms. I compare them to strategic infractions, which are common in many coherent games. Finally, I explore the connections between rules and aims in games and in inquiry. I show that in both cases respecting the rules is constitutively required for satisfying the aims of the practice. (shrink)

Mental content normativists hold that the mind’s conceptual contents are essentially normative. Many hold the view because they think that facts of the form “subject S possesses concept c” imply that S is enjoined by rules concerning the application of c in theoretical judgments. Some opponents independently raise an intuitive objection: even if there are such rules, S’s possession of the concept is not the source of the enjoinment. Hence, these rules do not support mental content normativism. (...) Call this the “Source Objection.” This paper refutes the Source Objection, outlining a key strand of the relationship between judgments and their contents in the process. Theoretical judgment and mental conceptual content are equally the source of enjoinment; norms for judging with contents do not derive from one at the expense of the other. (shrink)

This paper attempts to synthesize the Winchian stress on constitutive rules with the Marxian stress on material relationships by developing the concept of emergently material social relations. Such relationships, it is argued, arise from the constitutive rules that constitute a group's way of life. Although such relationships thus are derivative from the conscious rule-following behavior of actors, nevertheless they have an objective existence independent of actors' specific awareness. It is argued that such material relations are an important mechanism (...) beyond the cultural rules through which our behavior is constrained, enabled, and motivated. Yet the Winchian tradition in general and contemporary structuration theory in particular have tended to peripheralize the notion of material relations, treating them largely as epiphenomenal abstractions. This, it is argued, is a mistake and the source of an important lacuna in structuration theory. In particular, because structuration theory decenters the actor, conflates the distinction between regulative and constitutive rules, and peripheralizes social relations, it lacks an adequate explanation of motivation, as symptomized by its inordinate appeal to the unconscious. The concept of emergently material social relations overcomes this problem and offers a reintegration of the Marxian and the Winchian traditions. (shrink)

Stem cell-derived embryo models (SCEMs) are model embryos used in scientific research to gain a better understanding of early embryonic development. The way humans develop from a single-cell zygote to a complex multicellular organism remains poorly understood. However, research looking at embryo development is difficult because of restrictions on the use of human embryos in research. Stem cell embryo models could reduce the need for human embryos, allowing us to both understand early development and improve assisted reproductive technologies. There (...) have been several rapid advances in creating SCEMs in recent years. These advances potentially provide a new avenue to study early human development. The benefits of SCEMs are predicated on the claim that they are different from embryos and should, therefore, be exempt from existing regulations that apply to embryos (such as the 14-day rule). SCEMs are proposed as offering a model that can capture the inner workings of the embryo but lack its moral sensitivities. However, the ethical basis for making this distinction has not been clearly explained. In this current controversy, we focus on the ethical justification for treating SCEMs differently to embryos, based on considerations of moral status. (shrink)

Admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In this paper, a Gentzen-style framework is introduced for analytic proof systems that derive admissible rules of non-classical logics. While Gentzen systems for derivability treat sequents as basic objects, for admissibility, the basic objects are sequent rules. Proof systems are defined here for admissible rules of classes of modal logics, including K4, S4, and GL, and also (...) Intuitionistic Logic IPC. With minor restrictions, proof search in these systems terminates, giving decision procedures for admissibility in the logics. (shrink)

PurposeThe developing academic field of machine ethics seeks to make artificial agents safer as they become more pervasive throughout society. In contrast to computer ethics, machine ethics is concerned with the behavior of machines toward human users and other machines. This study aims to use an action-based ethical theory founded on the combinational aspects of deontological and teleological theories of ethics in the construction of an artificial moral agent (AMA).Design/methodology/approachThe decision results derived by the AMA are acquired via fuzzy (...) logic interpretation of the relative values of the steady-state simulations of the corresponding rule-based fuzzy cognitive map (RBFCM).FindingsThrough the use of RBFCMs, the following paper illustrates the possibility of incorporating ethical components into machines, where latent semantic analysis (LSA) and RBFCMs can be used to model dynamic and complex situations, and to provide abilities in acquiring causal knowledge.Research limitations/implicationsThis approach is especially appropriate for data-poor and uncertain situations common in ethics. Nonetheless, to ensure that a machine with an ethical component can function autonomously in the world, research in artificial intelligence will need to further investigate the representation and determination of ethical principles, the incorporation of these ethical principles into a system’s decision procedure, ethical decision-making with incomplete and uncertain knowledge, the explanation for decisions made using ethical principles and the evaluation of systems that act based upon ethical principles.Practical implicationsTo date, the conducted research has contributed to a theoretical foundation for machine ethics through exploration of the rationale and the feasibility of adding an ethical dimension to machines. Further, the constructed AMA illustrates the possibility of utilizing an action-based ethical theory that provides guidance in ethical decision-making according to the precepts of its respective duties. The use of LSA illustrates their powerful capabilities in understanding text and their potential application as information retrieval systems in AMAs. The use of cognitive maps provides an approach and a decision procedure for resolving conflicts between different duties.Originality/valueThis paper suggests that cognitive maps could be used in AMAs as tools for meta-analysis, where comparisons regarding multiple ethical principles and duties can be examined and considered. With cognitive mapping, complex and abstract variables that cannot easily be measured but are important to decision-making can be modeled. This approach is especially appropriate for data-poor and uncertain situations common in ethics. (shrink)

The integrodifferential equations satisfied by the statistical frequency functions for physical systems undergoing stochastic transitions are derived by application of a causality principle and selection rules to the Markov chain equations. The result equations can be viewed as generalizations of the diffusion equation, but, unlike the latter, they have a direct bearing onactive transport problems in biophysics andcondensation aggregation problems of astrophysics and phase transition theory. Simple specific examples of the effects of severe selection rules, such as (...) the relaxational Boltzmann transport equation and the diffusion equation, are also given. Finally, partial differential equations for the probability amplitudes of quantum mechanics are derived, usingunitarity instead of causality, and a selection rule is applied directly to obtain ageneralization of the Dirac equation in which infinite transitions between states arenot allowed. (shrink)

The author discusses the rational argumentation of the values from a proposal defended by the legal philosopher Robert Alexy. The paper shows that discourse for Alexy is essentially a regulated activity. A model of certain rules ensure the rationality and correctness of practical discourse oriented towards resolving conflicts of value. Firstly, the types of rules responsible for the rationality of practical argumentation are described. Secondly, some open problems relating to the claim to correctness of reasoned practical discourse are (...) posed, namely problems derived from the idea of consensus and that of a single correct answer to certain practical issues that include conflicts of values and raise basic disagreements. (shrink)

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all so-called ‘derivable rules’ can be (...) encoded into the object language using the material conditional. The deduction theorem can be generalized in the sense that one can attempt to encode all types of rules into the object language. When a rule is encoded in this way I say that it is reflected in the object language. What I show, however, is that certain logics which reflect a certain kind of rule must be trivial. Therefore, my generalization of the deduction theorem does fail where the classic deduction theorem didn’t. (shrink)

I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules of (...) Disquotation and of Semantic Ascent cannot be derived for sentences with tonk dominant. These considerations deprive Boghossian's scepticism of its support. (shrink)

In this article, I derive a weak version of Kant's categorical imperative within an informal game-theoretic framework. More specifically, I argue that Hobbesian agents would choose what I call the weak principle of universalization, if they had to decide on a rule of conflict resolution in an idealized but empirically defensible hypothetical decision situation. The discussion clarifies (i) the rationality requirements imposed on agents, (ii) the empirical conditions assumed to warrant the conclusion, and (iii) the political institutions that are necessary (...) to implement the derived principle. The analysis demonstrates the moral significance of the weak principle of universalization and its epistemic advantage over the categorical imperative. (shrink)