‘First. That on October 23, in the city of New York, your relator was arrested by divers persons claiming to be acting by authority of the government of the United States, and was by said persons conveyed to the United States immigration station at Ellis island, in the harbor of New York, and is now there imprisoned by the commissioner of immigration of the port of New York.

Common-sense folk psychology and mainstream philosophy of action agree about decisions: these are under an agent's direct control, and are thus intentional actions for which agents can be held responsible. I begin this paper by presenting a problem for this view. In short, since the content of the motivational attitudes that drive deliberation and decision remains open-ended until the moment of decision, it is unclear how agents can be thought to exercise control over what they decide at the moment of (...) deciding. I note that this problem might motivate a non-actional view of deciding?a view that decisions are not actions, but are instead passive events of intention acquisition. For without an understanding of how an agent might exercise control over what is decided at the moment of deciding, we lack a good reason for maintaining commitment to an actional view of deciding. However, I then offer the required account of how agents exercise control over decisions at the moment of deciding. Crucial to this account is an understanding of the relation of practical deliberation to deciding, an understanding of skilled deliberative activity, and the role of attention in the mental action of deciding. (shrink)

To decide to A, as I conceive of it, is to perform a momentary mental action of forming an intention to A. I argue that ordinary instances of practical deciding, so conceived, falsify the following...

Can we decide to trust? Sometimes, yes. And when we do, we need not believe that our trust will be vindicated. This paper is motivated by the need to incorporate these facts into an account of trust. Trust involves reliance; and in addition it requires the taking of a reactive attitude to that reliance. I explain how the states involved here differ from belief. And I explore the limits of our ability to trust. I then turn to the idea of (...) trusting what others say. I suggest that we sometimes decide to trust people to be sincere and knowledgeable; and that having taken this attitude towards them, we come to believe what they say. I spell out some consequences that this has for an account of testimony, and for van Fraassen's decision theoretic principle of Reflection. (shrink)

This book is the most comprehensive treatment available of one of the most urgent - and yet in some respects most neglected - problems in bioethics: decision-making for incompetents. Part I develops a general theory for making treatment and care decisions for patients who are not competent to decide for themselves. It provides an in-depth analysis of competence, articulates and defends a coherent set of principles to specify suitable surrogate decisionmakers and to guide their choices, examines the value of advance (...) directives, and investigates the role that considerations of cost ought to play in decisions concerning incompetents. Part II applies this theoretical framework to the distinctive problems of three important classes of individuals, many of whom are incompetent: minors, the elderly and psychiatric patients. The authors' approach combines a probing analysis of fundamental issues in ethical theory with a sensitive awareness of the concrete realities of health care institutions and the highly personal and individual character of difficult practical problems. Its broad scope will appeal to health professionals, moral philosophers and lawyers alike. (shrink)

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers ∀p, ∃p, where the propositional variables range over upward-closed subsets of the set of worlds in a Kripke structure. If the permitted accessibility relations are arbitrary partial orders, the resulting logic is known to be recursively isomorphic to full second-order logic (Kremer, 1997). It is shown that if the Kripke structures are restricted to trees of at height and width at most ω, the resulting logics are decidable. (...) This provides a partial answer to a question by Kremer. The result also transfers to modal S4 and some Gödel-Dummett logics with quantifiers over propositions. (shrink)

This chapter's aim is threefold: to articulate and defend an account of what it is to decide to do something; to defend the thesis that there are genuine instances of deciding so understood; and to shed light on how decisions are to be explained. This chapter defends the idea that to decide to do something is to perform a momentary mental action of forming an intention to do it. Actively forming an intention is distinguished from passively acquiring one, and the (...) bearing of reasons and motivational strength on deciding is discussed. (shrink)

Mereological theories are theories based on a binary predicate ‘being a part of’. It is believed that such a predicate must at least define a partial ordering. A mereological theory can be obtained by adding on top of the basic axioms of partial orderings some of the other axioms posited based on pertinent philosophical insights. Though mereological theories have aroused quite a few philosophers’ interest recently, not much has been said about their meta-logical properties. In this paper, I will look (...) into whether those theories are decidable or not. Besides, since theories of Boolean algebras are in some sense upper bounds of mereological theories which can be found in the literature, I shall also make some observations about the possibility of getting mereological theories beyond Boolean algebras. (shrink)

This paper presents two general results of decidability concerning logics based on an indeterministic metric tense logic, which can be applied to, among others, logics combining knowledge, time and agency. We provide a general Kripke semantics based on a variation of the notion of synchronized Ockhamist frames. Our proof of the decidability is by way of the finite frame property, applying subframe transformations and a variant of the filtration technique.

We study concepts of decidability for subsets of Euclidean spaces ℝk within the framework of approximate computability . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff's concept of resolvable sets, and it modifies and generalizes notions of recursivity known from computable analysis, formerly used for open or closed sets only, to more general types of sets. Approximate decidability of sets can equivalently be expressed by (...) computability of the characteristic functions by means of appropriately working oracle Turing machines. The notion fulfills some natural requirements and is hereditary under canonical embeddings of sets into spaces of higher dimensions. However, it is not closed under binary union or intersection of sets. We also show how the framework of resolvability and approximate decidability can be applied to investigate concepts of reducibility for subsets of Euclidean spaces. (shrink)

The signature of the formal language of mereology contains only one binary predicate P which stands for the relation “being a part of”. Traditionally, P must be a partial ordering, that is, ${\forall{x}Pxx, \forall{x}\forall{y}((Pxy\land Pyx)\to x=y)}$ and ${\forall{x}\forall{y}\forall{z}((Pxy\land Pyz)\to Pxz))}$ are three basic mereological axioms. The best-known mereological theory is “general extensional mereology”, which is axiomatized by the three basic axioms plus the following axiom and axiom schema: (Strong Supplementation) ${\forall{x}\forall{y}(\neg Pyx\to \exists z(Pzy\land \neg Ozx))}$ , where Oxy means ${\exists (...) z(Pzx\land Pzy)}$ , and (Fusion) ${\exists x\alpha \to \exists z\forall y(Oyz\leftrightarrow \exists x(\alpha \land Oyx))}$ , for any formula α where z and y do not occur free. In this paper, I will show that general extensional mereology is decidable, and will also point out that the decidability of the first-order approximation of the theory of complete Boolean algebras can be shown in the same way. (shrink)

A sequent calculus S for the variety tqBa of all topological quasi-Boolean algebras is established. Using a construction of syntactic finite algebraic model, the finite model property of S is shown, and thus the decidability of S is obtained. We also introduce two non-distributive variants of topological quasi-Boolean algebras. For the variety TDM5 of all topological De Morgan lattices with the axiom 5, we establish a sequent calculus S5 and prove that the cut elimination holds for it. Consequently the (...) decidability of S5 is established. Furthermore, this proof-theoretic method is applied to some subvarieties of TDM5. (shrink)

Policy-makers must sometimes choose between an alternative which has somewhat lower expected value for each person, but which will substantially improve the outcomes of the worst off, or an alternative which has somewhat higher expected value for each person, but which will leave those who end up worst off substantially less well off. The popular ex ante Pareto principle requires the choice of the alternative with higher expected utility for each. We argue that ex ante Pareto ought to be rejected (...) because it conflicts with the requirement that, when possible, one ought to decide as one would with full information. We apply our argument in an analysis of US policy on screening for breast cancer. -/- . (shrink)

As this passage from a recent book on the psychology of decision-making indicates, deciding seems to be part of our daily lives. But what is it to decide to do something? It may be true, as some philosophers have claimed, that to decide to A is to perform a mental action of a certain kind – specifically, an action of forming an intention to A. (Henceforth, the verb ‘form’ in this context is to be understood as an action verb.) Even (...) if this is so, we are faced with pressing questions. Do we form all of our intentions? If not, how does forming an intention differ from other ways of acquiring one? Do we ever, in fact, form intentions, or do we rather merely acquire them in something like the way we acquire beliefs or desires? These are some of the questions that will occupy me here. My aim is to clarify the nature of deciding to act and to make a case for the occurrence of genuine acts of intention formation. (shrink)

In this paper we show that the usual intuitionistic characterization of the decidability of the propositional function B prop [x : A], i. e. to require that the predicate ∨ ¬ B) is provable, is equivalent, when working within the framework of Martin-Löf's Intuitionistic Type Theory, to require that there exists a decision function ψ: A → Boole such that = Booletrue) ↔ B). Since we will also show that the proposition x = Booletrue [x: Boole] is decidable, we (...) can alternatively say that the main result of this paper is a proof that the decidability of the predicate Bprop [x : A] can be effectively reduced by a function ψ A → Boole to the decidability of the predicate ψ = Booletrue [x : A]. All the proofs are carried out within the Intuitionistic Type Theory and hence the decision function ψ, together with a proof of its correctness, is effectively constructed as a function of the proof of ∨ ¬ B). (shrink)

The paper considers the set $\mathscr{M}\mathscr{L}_1$ of first-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using a mosaic technique, we prove a general satisfiability criterion for formulas in $\mathscr{M}\mathscr{L}_1$, which reduces the modal satisfiability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragments of various modal predicate logics.

A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema about intuitionistic decidability that asserts “there exists an intuitionistic enumerable set (...) that is not intuitionistic decidable” and show that the existence of a Specker sequence is equivalent to ED. We show that ED is consistent with some certain well known axioms of intuitionistic analysis as Weak Continuity Principle, bar induction, and Kripke Schema. Thus, the assumption of the existence of a Specker sequence is conceivable in intuitionistic analysis. We will also introduce the notion of double Specker sequence and study the existence of them. (shrink)

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

In this paper, we introduce a new fragment of the first-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator have at most one free variable. We show that the satisfiability problem for monodic formulas in various linear time structures can be reduced to the satisfiability problem for a certain fragment of classical first-order logic. This reduction is then used to single out a number of decidable fragments of first-order temporal logics and of two-sorted (...) first-order logics in which one sort is intended for temporal reasoning. Besides standard first-order time structures, we consider also those that have only finite first-order domains, and extend the results mentioned above to temporal logics of finite domains. We prove decidability in three different ways: using decidability of monadic second-order logic over the intended flows of time, by an explicit analysis of structures with natural numbers time, and by a composition method that builds a model from pieces in finitely many steps. (shrink)

We prove that if an n-element algebra generates the variety \ which is actively structurally complete, then the cardinality of the carrier of each subdirectly irreducible algebra in \ is at most \\cdot n^{2\cdot n}}\). As a consequence, with the use of known results, we show that there exist algorithms deciding whether a given finite algebra \ generates the structurally complete variety \\) in the cases when \\) is congruence modular or \\) is congruence meet-semidistributive or \ is a semigroup.

This paper presents proofs of completeness and decidability of a non-temporal fragment of an Xstit logic. This shows a distinction between the non-temporal fragments of Xstit logic and regular stit logic since the latter is undecidable. The proof of decidability is via the finite model property. The finite model property is shown to hold by constructing a filtration. However, the set that is used to filter the models isn’t simply closed under subformulas, it has more complex closure conditions. (...) The filtration set is akin to the Fischer–Ladner closure of a set used to show completeness and decidability of propositional dynamic logic. (shrink)

Presented here is a new result concerning the computational power of so-called SADn computers, a class of Turing-machine-based computers that can perform some non-Turing computable feats by utilising the geometry of a particular kind of general relativistic spacetime. It is shown that SADn can decide n-quantifier arithmetic but not (n+1)-quantifier arithmetic, a result that reveals how neatly the SADn family maps into the Kleene arithmetical hierarchy. Introduction Axiomatising computers The power of SAD computers Remarks regarding the concept of computability.

We show that various fragments of the intuitionistic/constructive theory of the reals are decidable.

Qualitative Reasoning (QR) is an area of research within Artificial Intelligence that automates reasoning and problem solving about the physical world. QR research aims to deal with representation and reasoning about continuous aspects of entities without the kind of precise quantitative information needed by conventional numerical analysis techniques. Order-of-magnitude Reasoning (OMR) is an approach in QR concerned with the analysis of physical systems in terms of relative magnitudes. In this paper we consider the logic OMR_N for order-of-magnitude reasoning with the (...) bidirectional negligibility relation. It is a multi-modal logic given by a Hilbert-style axiomatization that reflects properties and interactions of two basic accessibility relations (strict linear order and bidirectional negligibility). Although the logic was studied in many papers, nothing was known about its decidability. In the paper we prove decidability of OMR N by showing that the logic has the strong finite model property. (shrink)

For $\Bbb {F}$ the field of real or complex numbers, let $CG(\Bbb {F})$ be the continuous geometry constructed by von Neumann as a limit of finite dimensional projective geometries over $\Bbb {F}$ . Our purpose here is to show the equational theory of $CG(\Bbb {F})$ is decidable.

Mele's chapter addresses two primary aims. The first is to develop an experimentally useful conception of conscious deciding. The second is to challenge a certain source of skepticism about free will: the belief that conscious decisions and intentions are never involved in producing corresponding overt actions. The challenge Mele develops has a positive dimension that accords with the aims of this volume: It sheds light on a way in which some conscious decisions and intentions do seem to be efficacious.

Discussions about assisted suicide have hitherto been based on accounts of dignity conceived only as an inherent value or as a status; accounts of dignity in which it appears as a (contingent) attitude, by contrast, have been neglected. Yet there are two good reasons to consider dignity to be an attitude. First, this concept of dignity best allows us to grasp a crucial aspect of everyday language: people often express fears of losing their dignity—and it is not possible to explain (...) this with an account in which dignity is inherent. Second, such a concept allows us to adduce new argumentation where the argument based on status ends. Dignity considered as a status provides grounds to argue for the moral permissibility of assisted suicide, in the sense that in such an account individuals possess the normative power to waive their right to life. But the question then remains of how to decide what counts as a good reason for assisted suicide—and this is where an argument based on dignity as an attitude can provide illumination. (shrink)

This paper extends the investigations into logical properties of the quantified argument calculus (Quarc) by suggesting a series of proper subsystems which, although retaining the entire vocabulary of Quarc, restrict quantification in such a way as to make the result decidable. The proof of decidability is via a procedure that prunes the infinite branches of a derivation tree in what is a syntactic counterpart of semantic filtration. We demonstrate an application of one of these systems by showing that Aristotle’s (...) assertoric syllogistic is embeddable within, thus also providing another method of showing its decidability. (shrink)

We show that the Axiom of Foundation, as well as the Antifoundation Axiom AFA, plays a crucial role in determining the decidability of the following problem. Given a first-order theory T over the language , and a sentence F of the form with quantifier-free in the same language, are there models of T in which F is true? Furthermore we show that the Extensionality Axiom is quite irrelevant in that respect.

The species of indeterminist tense logic called Peircean by A. N. Prior is proved to be recursively decidable.

A definition is given for formulae $A_1,\ldots,A_n$ in some theory $T$ which is formalized in a propositional calculus $S$ to be (in)dependent with respect to $S$. It is shown that, for intuitionistic propositional logic $\mathbf{IPC}$, dependency (with respect to $\mathbf{IPC}$ itself) is decidable. This is an almost immediate consequence of Pitts' uniform interpolation theorem for $\mathbf{IPC}$. A reasonably simple infinite sequence of $\mathbf{IPC}$-formulae $F_n(p, q)$ is given such that $\mathbf{IPC}$-formulae $A$ and $B$ are dependent if and only if at least (...) on the $F_n(A, B)$ is provable. (shrink)

Since Plato’s massive critique of the Sophists rhetoric’s ill repute runs through the history of western philosophy denunciating methods of rhetoric as in large part dishonest persuasion strategies which are at most marginally interested in dealing with truths. This judgement falls way too short insofar as it distorts the historically grown stock labeled “rhetoric” not only in the Aristotelian work. With reference to Olaf Müller’s philosophical book addressing the “controversy” between Goethe and Newton about the nature of light, I will (...) study the different rhetorical models and methods used by Newton and Goethe and also Müller himself. It becomes apparent that even works attempting to decide who was right in the long run do far more than trying to evoke true “representations” of facts or truths in the reader. The specific use of language patterns provides deeper insight into an author’s mindset towards the subject area discussed in his work and generally speaking the investigation of the rhetoric of science and philosophy leads to a better understanding of different epistemic cultures both in philosophy and science. (shrink)

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...) disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier theory. These criteria are applied not only to the weak truth-table degrees of the recursively enumerable sets but also to various substructures of the polynomial many-one (pm) degrees of the recursive sets. These applications to the pm degrees require no new complexity-theoretic results. The fact that the pm-degrees of the recursive sets have a decidable two-quantifier theory answers a question raised by Shore and Slaman in [21]. (shrink)

ABSTRACT The question of axiomatizability of first-order temporal logics is studied w.r.t. different semantics and several restrictions on the language. The validity problem for logics admitting flexible interpretations of the predicate symbols or allowing at least binary predicate symbols is shown to be ?1 1-complete. In contrast, it is decidable for temporal logics with rigid monadic predicate symbols but without function symbols and identity.

The ways in which we exercise intentional agency are varied. I take the domain of intentional agency to include all that we intentionally do versus what merely happens to us. So the scope of our intentional agency is not limited to intentional action. One can also exercise some intentional agency in omitting to act and, importantly, in producing the intentional outcome of an intentional action. So, for instance, when an agent is dieting, there is an exercise of agency both with (...) respect to the agent’s actions and omissions that constitute her dieting behavior and in achieving the intended outcome of losing weight. In our mental lives we exercise intentional agency both in performing mental actions and when we intentionally produce certain outcomes at which our mental actions are aimed. The nature and scope of our intentional agency in our mental lives with respect to controlling the acquisition of mental states such as belief, desire, and intention is a topic that is of interest in its own right. In this essay, I will focus solely on our control over coming to believe. Understanding what sort of control we have our beliefs has far-reaching implications. For instance, theorizing about self-deception and wishful thinking is aided by theorizing about what if any intentional agency we can exercise with respect to acquiring beliefs. Another often mentioned concern that motivates thinking about doxastic agency comes from religion (when conversion requires a change of belief). We also hold persons morally and epistemically responsible for beliefs they have or fail to have. Finally, some deontological theories of epistemic justification require that agents be able to exercise a robust form of doxastic control. Fruitful work on any of these problems requires that we have an account of our intentional agency in acquiring beliefs. There are at least three loci of doxastic control. The first is over acquiring beliefs. The second is over maintaining beliefs. The third is over how we use our beliefs. I am chiefly concerned with the first locus of doxastic control in this essay, but I will say something about the second locus along the way. Also, I will only consider one way we might exercise control over acquiring beliefs. Specifically, I will present an argument against direct doxastic voluntarism (DDV). By “DDV” I mean to refer to the thesis that it is conceptually possible for agents to consciously exercise the same sort of direct voluntary control over coming to acquire a doxastic attitude—such as belief, suspension of belief, and disbelief—that they exercise over uncontroversial basic actions. If DDV is correct, then coming to believe can be a basic action-type. DDV, or something very close to it, was Bernard Williams’ target in his 1973 paper, “Deciding to Believe.” Williams’s argument is widely regarded as having been a failure. But I think that Williams was on to something in his paper. Hence, in this paper, while I do not attempt to resurrect Williams’s argument, I develop and defend a revised argument for a thesis that is quite close to Williams’s. I will proceed as follows. First, I will discuss Bernard Williams’ (1973) failed attempt at showing that DDV is conceptually impossible. This will be followed by a discussion of some constraints on our belief-forming activities. I will then clarify my target a bit more than Williams does in his original paper. Finally, I will present my own argument against the conceptual possibility of DDV. (shrink)

Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.

Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any sentence A containing only bounded quantifiers and functions in F, and any positive rational number delta, decides either “A is true”, or “a delta-strengthening of A is false”. Moreover, if F can be computed in complexity class C, then under mild assumptions, this “delta-decision problem” for bounded Sigma k-sentences resides in Sigma k. The results stand in sharp contrast to the (...) well-known undecidability of the general first-order theories with these functions, and serve as a theoretical basis for the use of numerical methods in decision procedures for formulas over the reals. (shrink)

We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (LAN) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging LAN , we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the three (...) categories and evaluate their validity vis-à-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property. (shrink)

Book reviewed in this article: The Concept of Moral Consensus: The Case of Technological Interventions into Human Reproduction. Edited by Kurt Bayertz. Deciding Together: Bioethics and Moral Consensus. By Jonathan D. Moreno.

We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...) of set theory that is in one of the following forms: ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns distinct values to all of the variables y1,…,yl, ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns the same value to all of the variables y1,…,yl. (shrink)

Let HF be the collection of the hereditarily finite well-founded sets and let the primitive language of set theory be the first-order language which contains binary symbols for equality and membership only. As announced in a previous paper by the authors, "Truth in V for ∃*∀∀-sentences is decidable," truth in HF for ∃*∀∀-sentences of the primitive language is decidable. The paper provides the proof of that claim.

We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V-modules is decidable.

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

During the first wave of the COVID-19 pandemic in Italy, practitioners had to make tragic decisions regarding the allocation of scarce resources in the ICU. The Italian debate has paid a lot of attention to identifying the specific regulatory criteria for the allocation of resources in the ICU; in this paper, however, we argue that deciding such criteria is not enough for the implementation of fair and transparent allocative decisions. In this respect, we discuss three ethical issues: (a) in the (...) Italian context, the treating physician, rather than a separate committee, was generally the one responsible for the allocation decision; (b) although many allocative guidelines have supported moral equivalence between withholding and withdrawing treatments, some health professionals have continued to consider it a morally problematic aspect; and (c) the health workers who have had to make the aforementioned decisions or even only worked in ICU during the pandemic often experienced moral distress. We conclude by arguing that, even if these problems are not directly related to the above-mentioned issues of distributive justice, they can nevertheless directly affect the quality and ethics of the implementation of allocative criteria, regardless of those chosen. (shrink)

BackgroundEverybody has the right to decide whether to receive specific medical treatment or not and to provide their free, prior and informed consent to do so. As dementia progresses, people with Alzheimer’s dementia (PwAD) can lose their capacity to provide informed consent to complex medical treatment. When the capacity to consent is lost, the autonomy of the affected person can only be guaranteed when an interpretable and valid advance directive exists. Advance directives are not yet common in Germany, and their (...) validity is often questionable. Once the dementia diagnosis has been made, it is assumed to be too late to write an advance directive. One approach used to support the completion of advance directives is ‘Respecting Choices’®—an internationally recognised, evidence-based model of Advance Care Planning (ACP), which, until now, has not been evaluated for the target group of PwAD. This study’s aims include (a) to investigate the proportion of valid advance directives in a memory clinic population of persons with suspected AD, (b) to determine the predictors of valid advance directives, and (c) to examine whether the offer of ACP can increase the proportion of valid advance directives in PwAD.MethodWe intend to recruit at leastN = 250 participants from two memory clinics in 50 consecutive weeks. Of these, the first 25 weeks constitute the baseline phase (no offer of ACP), the following 25 weeks constitute the intervention phase (offer of ACP). The existence and validity of an advance directive will be assessed twice (before and after the memory clinic appointment). Moreover, potential predictors of valid advance directives are assessed.DiscussionThe results of this study will enhance the development of consent procedures for advance directives of PwAD based on the ACP/Respecting Choices (R) approach. Therefore, this project contributes towards increasing the autonomy and inclusion of PwAD and the widespread acceptance of valid advance directives in PwAD.Trial RegistrationDRKS, DRKS00026691, registered 15th of October 2021,https://www.drks.de/drks_web/navigate.do?navigationId=trial.HTML&TRIAL_ID=DRKS00026691. (shrink)

If X is set and L a lattice, then an L-subset or fuzzy subset of X is any map from X to L, [11]. In this paper we extend some notions of recursivity theory to fuzzy set theory, in particular we define and examine the concept of almost decidability for L-subsets. Moreover, we examine the relationship between imprecision and decidability. Namely, we prove that there exist infinitely indeterminate L-subsets with no more precise decidable versions and classical subsets whose (...) unique shaded decidable versions are the L-subsets almost-everywhere indeterminate. (shrink)

We consider McCarthy's notions of predicate circumscription and formula circumscription. We show that the decision problems “does θ have a countably infinite minimal model” and “does φ hold in every countably infinite minimal model of θ” are complete Σ 1 2 and complete π 1 2 over the integers, for both forms of circumscription. The set of structures definable as first order definable subsets of countably infinite minimal models is the set of structures which are Δ 1 2 over the (...) integers, for both forms of circumscription. Thus, restricted to countably infinite structures, predicate and formula circumscription define the same sets and have equally difficult decision problems. With general formula circumscription we can define several infinite cardinals, so the decidability problems are dependent upon the axioms of set theory. (shrink)

Realism is the claim that truth may transcend all possible verification. The familiar Dummettian argument against that modal claim is that there is no way to manifest an understanding of it in actual linguistic practice. The Dummettian anti-realist's provisional conclusion is that the modal claim must be false. ;The attack on truth-conditional semantics and on the principle of bivalence are familiar ingredients of the anti-realist negative programme. I agree that, whether mathematical formulae or ordinary sentences in the past tense are (...) concerned, we cannot manifest a knowledge of the truth-conditions of particular instances of 'It is possible that ' by deciding their truth. There is nevertheless a way to argue in favour of specific instances of the modal claim when s is a sentence in the past tense. The proposed argument does not appeal to the recognitional abilities which, in the standard anti-realist perspective, constitute grasp of meaning. It does not commit one to the endorsement of the principle of bivalence, although the principle implies the modal claim. ;Our understanding of the workings of nature, whether grounded on scientific theories or on common sense, implies the modal claim. Since we are only contingently connected to the evidence pro or con past events and since the existence of evidence is itself a contingent matter, sentences which say that those events occurred could be true whether or not we can, at any point in time, detect that they are true. The possibility that truths about past facts transcend all possible verification is a purely natural possibility, grounded on what we know of the workings of nature. ;This implies that decidable statements in the past tense are not immune to the realism vs. anti-realism debate. Although they do not transcend verifiability, they could transcend whatever our recognitional abilities, no matter how extended, would allow us to establish at any point in time, either in the past, right now, or in an indefinitely extensible future. (shrink)