This paper examines the exercise of individual or group rights within the game form approach. It focuses in particular on what it means for a strategy or action to be feasible and admissible. Admissibility is best discussed in relation to two basic distinctions among rights, passive and active rights on the one hand and negative and positive rights on the other. It is argued that while there are quite a few cases in which the outcomes of mutual rights exercising are (...) to the fore, there are many situations where the uninhibited exercise of individual or group rights and not particular outcomes are what society is primarily interested in. (shrink)

The?-admissibility is one of the most important problems in the realm of relevant logics. To prove the 7-admissibility, either the method of normal models or the method using metavaluations may be employed. The?-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the?-admissibility based on metavaluations has not hitherto been fully considered. Sahlqvist axioms are well known as a means of expressing generalized forms of formulas with modal operators. This (...) paper shows that? is admissible for relevant modal logics with restricted Sahlqvist axioms in terms of the method using metavaluations. (shrink)

This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.

Which objects and properties are represented in perceptual experience, and how are we able to determine this? The papers in this collection address these questions together with other fundamental questions about the nature of perceptual content. The book draws together papers by leading international philosophers of mind, including Alex Byrne (MIT), Alva Noë (University of California, Berkeley), Tim Bayne (St Catherine’s College, Oxford), Michael Tye (University of Texas, Austin), Richard Price (All Souls College, Oxford) and Susanna Siegel (Harvard University) Essays (...) address the central questions surrounding the content of perceptual experience Investigates how are we able to determine the admissible contents of experience Published in association with the journal Philosophical Quarterly . (shrink)

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...) attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

This paper examines the impact of education reforms on school admissions policies and practices. It discusses the changes that are needed to improve the current system, especially in areas where the market is highly developed. It is concluded that the new legislation to be enacted by the current Labour Government should be beneficial, but that more far-reaching changes are needed for the admissions process to be equitable, transparent and accountable.

The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds are admissible as propositions, and an interpretation of propositional quantification that makes ∀ pA true when there is some true admissible proposition that entails all p -instantiations of A . It is also shown that without the admissibility qualification many of the systems considered are (...) semantically incomplete, including all those that are sub-logics of the quantified version of Anderson and Belnap’s system E of entailment, extended by the mingle axiom and the Ackermann constant t . The incompleteness proof involves an algebraic semantics based on atomless complete Boolean algebras. (shrink)

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.

It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties.

The admissibility of Ackermann’s rule γ is one of the most important problems in relevant logic. While the γ-admissibility of normal modal logics based on the relevant logic R has been previously discussed, the case for weaker relevant modal logics has not yet been considered. The method of normal models has often been used to prove the γ-admissibility. This paper discusses which relevant modal logics admit γ from the viewpoint of the method of normal models.

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.

With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$, providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is admissible. We prove that (...) any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. (shrink)

Self‐admission to inpatient treatment is a novel approach that aims to increase agency and autonomy for patients with severe psychiatric illness and a history of high utilization of inpatient care. By focusing on brief, preventive hospital admissions in times of increased risk of relapse, self‐admission seeks to reduce the need for prolonged episodes of inpatient treatment. Participants are generally satisfied with the model, which is not surprising given that self‐admission programs allocate a scarce resource—hospital beds—to a select (...) group. However, the patients targeted by these programs are not necessarily those in most need of hospital admission, which may compromise the commonly accepted ‘principle of need’ in allocation of public healthcare resources. In light of the current lack of consistent evidence of the usefulness and cost‐effectiveness of the model, several aspects need to be further studied in order to guide any large‐scale implementation of self‐admission in psychiatry. (shrink)

This paper raises two objections to the freedom of movement argument from the perspective of nonideal philosophy: the argument cannot provide a means for establishing admissions priorities when all prospective immigrants cannot be admitted and it ignores alternative grounds for moral claims to admission in the context of histories of injustice. I develop an alternative admissions-guiding principle that assigns strong moral claims to admission to certain prospective immigrants based on a global extension of the no-harm principle. It claims (...) that a society must admit prospective immigrants if admission is necessary either to prevent that society from harming those immigrants or to compensate immigrants whom it has already harmed. States must fulfill these duties before they may legitimately use immigrant admissions policy in service of other national goals, including the advancement of economic interests. (shrink)

The main goal in this paper is to present the legal rules connected with medical experiment on human beings in emergency medicine and to explain the scope, significance, and meaning of these rules, especially with regard to their interpretation. As the provisions about medical experiments truly make sense only if they can be observed by the whole “civilised” international community, they are presented in the context of international law with reference to Polish law. By considering the appropriate regulations of research (...) contained in legal documents, it is possible to formulate a catalogue of doctors’ duties and patients’ rights. This general catalogue refers to all kinds of medical research involving human beings. In the field of emergency medicine, general provisions are sometimes involved, and they are sometimes limited. The main and most important conclusion is that a medical experiment in emergency medicine is admissible only if previously indicated conditions based on general rules of conducting research are fulfilled. (shrink)

My purpose is to take a close look at the nature of visual content. I discuss the view that visual experiences have only existential contents, the view that visual experiences have either singular or gappy contents, and the view that visual experiences have multiple contents. I also consider a proposal about visual content inspired by Kaplan's well known theory of indexicals. I draw out some consequences of my discussion for the thesis of intentionalism with respect to the phenomenal character of (...) visual experience. (shrink)

The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterize the existence of covers in certain models by means of formulae. Through this characterization, we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation, coupled with a description of a generalization of the disjunction property, to provide a basis of admissibility for the intermediate logics BD2 and GSc.

In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type-2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical representation (...) is admissible with respect to the weak topology on Borel probability measures. Moreover, we prove that for countably-based topological spaces the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology. (shrink)

Suicide is considered a global public health issue and compulsory admission is a commonly used measure to prevent suicide. However, the practice has been criticised since several studies indicate that the measure lacks empirical support and may even increase suicide risk. This paper investigates whether the practice has enough empirical support to be considered proportionate. To that end, arguments supporting compulsory admission as a suicide-preventive measure for most suicidal patients are scrutinized. The ethical point of departure is that (...) the expected benefits of compulsory admission should outweigh the potential harms of the measure to be proportionate and defensible. It is concluded that, for most suicidal patients, suicide-preventive compulsory admission cannot be presumed to be a proportionate measure. To be so, the expected medical benefits of the measure should be greater than the potential increase in suicide risk and other harms that compulsory admission could entail. Instead of using compulsory admission as a suicide-preventive measure, extra safety measures may be needed during and after compulsory admission to prevent the risk of hospitalisation-induced suicide. (shrink)

Epistemic logics for subjects of bounded rationality are in effect nonnormal modal logics. Admissible rules are of interest in such logics. However, the usual methods for establishing admissibility employ Kripke models and are therefore inappropriate for nonnormal logics. This paper extends syntactic methods for a variety of rules and nonnormal logics. In doing so it answers a question asked by Chellas and Segerberg.

This article compares the moral significance of two types of immigration, that which is based on the unification of citizens and non-citizens and that which is based on the skilled labor needs of the receiving society. I assess the interests of both citizens and non-citizens affected by each of these types of inflows and argue that unification admissions should be given priority over skilled workers but states retain a qualified moral permission to incentivize skilled worker migration.

My purpose is to take a close look at the nature of visual content. I discuss the view that visual experiences have only existential contents, the view that visual experiences have either singular or gappy contents, and the view that visual experiences have multiple contents. I also consider a proposal about visual content inspired by Kaplan's well known theory of indexicals. I draw out some consequences of my discussion for the thesis of intentionalism with respect to the phenomenal character of (...) visual experience. (shrink)

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which (...) these challenges may be addressed. (shrink)

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with (...) proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. (shrink)

A collective choice mechanism can be viewed as a game in normal form; in this article it is shown, for very attractive rules and for sets with any number of alternatives, how individuals involved in a collective decision problem can construct the preferences they choose to express. An example is given with a version of plurality rule. Manipulability results are deduced from such a characterization.

Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics (...) in terms of their admissible rules. To illustrate the technique, we also provide a refutation system for Medvedev’s logic. (shrink)

We propose two admissible closures $${\mathbb{A}({\sf PTCA})}$$ and $${\mathbb{A}({\sf PHCA})}$$ of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) $${\mathbb{A}({\sf PTCA})}$$ is conservative over PTCA with respect to $${\forall\exists\Sigma^b_1}$$ sentences, and (ii) $${\mathbb{A}({\sf PHCA})}$$ is conservative over full bounded arithmetic PHCA for $${\forall\exists\Sigma^b_{\infty}}$$ sentences. This yields that (i) the $${\Sigma^b_1}$$ definable functions of $${\mathbb{A}({\sf PTCA})}$$ are the polytime functions, and (ii) the $${\Sigma^b_{\infty}}$$ definable (...) functions of $${\mathbb{A}({\sf PHCA})}$$ are the functions in the polynomial time hierarchy. (shrink)

In a recent contribution in this journal, Sascia Pavan proposed a new game theoretic approach to explain generalized conversational implicatures in terms of general principles of rational behavior. His approach is based on refining Nash equilibrium by a procedure called iterated admissibility. I would like to strengthen Pavan’s case by sketching an epistemic interpretation of iterated admissibility, so as to further our understanding of why iterated admissibility might be a good approximation of pragmatic reasoning. But the explicit epistemic view taken (...) here also points to some shortcomings of his approach in comparison to rivaling accounts. (shrink)

Iterated admissibility embodies a minimal criterion of rationality in interactions. The epistemic characterization of this solution has been actively investigated in recent times: it has been shown that strategies surviving \ rounds of iterated admissibility may be identified as those that are obtained under a condition called rationality and m assumption of rationality in complete lexicographic type structures. On the other hand, it has been shown that its limit condition, with an infinity assumption of rationality ), might not be satisfied (...) by any state in the epistemic structure, if the class of types is complete and the types are continuous. In this paper we analyze the problem in a different framework. We redefine the notion of type as well as the epistemic notion of assumption. These new definitions are sufficient for the characterization of iterated admissibility as the class of strategies that indeed satisfy \. One of the key methodological innovations in our approach involves defining a new notion of generic types and employing these in conjunction with Cohen’s technique of forcing. (shrink)

Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded extension. As such, strongly admissible sets and labellings can be used as an explanation of membership of the grounded extension, as is for instance done in some of the proof procedures for grounded semantics. In the current paper, we present two polynomial algorithms for constructing relatively small (...) strongly admissible labellings, with associated min–max numberings, for a particular argument. These labellings can be used as relatively small explanations for the argument’s membership of the grounded extension. Although our algorithms are not guaranteed to yield an absolute minimal strongly admissible labelling for the argument (as doing so would have implied an exponential complexity), our best performing algorithm yields results that are only marginally larger. Moreover, the runtime of this algorithm is an order of magnitude smaller than that of the existing approach for computing an absolute minimal strongly admissible labelling for a particular argument. As such, we believe that our algorithms can be of practical value in situations where the aim is to construct a minimal or near-minimal strongly admissible labelling in a time-efficient way. (shrink)

The increasing unethical practices of graduates’ admissions have heightened concerns about the integrity of the academy. This article informs this important subject that affects the students, admission systems, and the entire scientific community, thus, representing an approach against scholarly black market activities including falsified documents and unethical practices by consultants and students’ recruitment agencies.

We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.

Lewis' concept of admissibility was introduced as an integral part of his famous Principal Principle; the principle that initial rational/reasonable belief should conform to objective chance unless there is evidence to the contrary. At that time Lewis offered only the rough and ready characterisation that evidence not to the contrary of such dependence is admissible. This, together with some sufficiency conditions, served well enough until it became clear that admissibility was central to debates on the viability of Humean Supervenience and (...) the analysis of objective chance. In response, Thau and Lewis refined the concept of admissibility in various ways. Since the mid 90's those who have employed the concept have, with minor variations and additions, followed the Thau/Lewis line. Yet, in the 30 years since its introduction what has been all too conspicuous by its absence is a full formal definition of admissibility and its degrees. Herein a family of definitions—all in terms of screening off by chance—that capture much that has been agreed about admissibility are proposed and evaluated; one of which is ultimately found to be serviceable as a definition schema for relative admissibility and its degrees. (shrink)

The involuntary admission or treatment of a mentally ill individual is highly controversial, as it may be argued that such intervention infringes on individual autonomy and the right to choose a particular treatment. However, this argument must be balanced with the need to provide immediate healthcare services to a vulnerable person who cannot or will not make a choice in his or her own best interests at a particular time. A study carried out in Gauteng Province, South Africa, highlighted (...) the fact that the annual rate of involuntary admissions increased by almost double from 2007 to 2008. This could indicate that healthcare providers are not treating patients without their consent only when this is absolutely necessary. Alternatively, it could indicate that healthcare professionals are more aware of the provisions of the Mental Health Care Act and relevant national policy guidelines. Or it could suggest that more patients are presenting with mental illnesses or disorders that require their involuntary admission. It remains for strategies to be developed that change negative perceptions and inequities for individuals with mental illness. Above all, the strategies should be underpinned by inalienable respect for mentally ill individuals – a concept that was blatantly disregarded in the Life Esidimeni case. In this article, we highlight the functions of mental health review boards and their accountability where involuntary admissions are concerned, while emphasising the protections for mentally ill persons as a vulnerable population group, as set out in the SA Constitution. (shrink)

The paper studies the admissibility of some cancellation rules in normal modal systems with the Brouwerian axiom. For example, KDB and KTB are proved to admit the following rule: if ⊢ ¬ and ⊢ ⋄α ≡ ⋄β then ⊢ ¬. Two notions of the preservation of validity by a rule on a frame are defined; on both, the preservation of validity by the preceding rule is shown not to be a first-order condition. A speculative connection is suggested with logics of (...) vagueness. (shrink)

This paper contains a detailed account of the notion of admissibility in the setting of consequence relations. It is proved that the two notions of admissibility used in the literature coincide, and it provides an extension to multi–conclusion consequence relations that is more general than the one usually encountered in the literature on admissibility. The notion of a rule scheme is introduced to capture rules with side conditions, and it is shown that what is generally understood under the extension of (...) a consequence relation by a rule can be extended naturally to rule schemes, and that such extensions capture the intuitive idea of extending a logic by a rule. (shrink)

The paper studies admissibility of multiple-conclusion rules in positive logics. Using modification of a method employed by M. Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility of multiple-conclusion rules in the positive logics is equivalent to the problem of admissibility in intermediate logics defined by positive additional axioms. Moreover, a multiple-conclusion rule \ follows from a set of multiple-conclusion rules \ over a positive logic \ if and only if \ follows from (...) \ over \. (shrink)

Forthcoming (2011) in K. Hawley and F. Macpherson (eds.) The Admissible Contents of Experience, Wiley‐Blackwell. The Admissible Contents of Experience Fiona Macpherson This essay provides an overview of the debate concerning the admissible contents of experience, together with an introduction to the papers in this volume. The debate is one that takes place among advocates of a certain way of thinking of perceptual experiences: that they are states that represent the world. For to say that a state has content is (...) to say that it represents; and its content is usually taken to be that which is represented. One should not be tempted to think that the debate is therefore marginal or esoteric, for this view of perceptual experience has been by far the dominant view of perceptual experience in recent years in philosophy (and in psychology and neuroscience). The debate is about what answer to give to a fundamental question about the nature of perceptual experience, namely: what objects and properties can it represent? (shrink)

We present a detailed proof of the admissibility of cut in sequent calculus for some congruent modal logics. The result was announced much earlier during the Trends in Logic Conference, Toruń 2006 and the proof for monotonic modal logics was provided already in Indrzejczak [5]. Also some tableau and natural deduction formalizations presented in Indrzejczak [6] and Indrzejczak [7] were based on this result but the proof itself was not published so far. In this paper we are going to fill (...) this gap. The delay was partly due to the fact that the author from time to time was trying to improve the result and extend it to some additional logics by testing other methods of proving cut elimination. Unfortunately all these attempts failed and cut elimination holds only for these logics which were proved to satisfy this property already in 2005. (shrink)

The paper investigates admissible inference rules for the multi-modal logic LTK, which describes a combination of linear time and knowledge. This logic is semantically defined as the set of all ℒ.

In this paper we discuss the ``admissibility troubles'' for Bayesian accounts of direct inference proposed in, which concern the existence of surprising, unintuitive defeaters even for mundane cases of direct inference. We first show that one could reasonably suspect that the source of these troubles was informal talk about higher-order probabilities: for cardinality-related reasons, classical probability spaces abound in defeaters for direct inference. We proceed to discuss the issues in the context of the rigorous framework of Higher Probability Spaces. However, (...) we show that the issues persist; we prove a few facts which pertain both to classical probability spaces and to HOPs, in our opinion capturing the essence of the problem. In effect we strengthen the message from the admissibility troubles: they arise not only for approaches using classical probability spaces---which are thus necessarily informal about metaprobabilistic phenomena like agents having credences in propositions about chances---but also for at least one respectable framework specifically tailored for rigorous discussion of higher-order probabilities. (shrink)

Aczel's theory of hypersets provides an interesting alternative to the standard view of sets as inductively constructed, well-founded objects, thus providing a convienent formalism in which to consider non-well-founded versions of classically well-founded constructions, such as the "circular logic" of [3]. This theory and ZFC are mutually interpretable; in particular, any model of ZFC has a canonical "extension" to a non-well-founded universe. The construction of this model does not immediately generalize to weaker set theories such as the theory of admissible (...) sets. In this paper, we formulate a version of Aczel's antifoundation axiom suitable for the theory of admissible sets. We investigate the properties of models of the axiom system KPU - , that is, KPU with foundation replaced by an appropriate strengthening of the extensionality axiom. Finally, we forge connections between "non-wellfounded sets over the admissible set A" and the fragment L A of the modal language L ∞. (shrink)