‘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.

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)

This book stands at the intersection of two topics: the decidability and computational complexity of hybrid logics, and the deductive systems designed for them. Hybrid logics are here divided into two groups: standard hybrid logics involving nominals as expressions of a separate sort, and non-standard hybrid logics, which do not involve nominals but whose expressive power matches the expressive power of binder-free standard hybrid logics.The original results of this book are split into two parts. This division reflects the division of (...) the book itself. The first type of results concern model-theoretic and complexity properties of hybrid logics. Since hybrid logics which we call standard are quite well investigated, the efforts focused on hybrid logics referred to as non-standard in this book. Non-standard hybrid logics are understood as modal logics with global counting operators ) whose expressive power matches the expressive power of binder-free standard hybrid logics. The relevant results comprise: 1. Establishing a sound and complete axiomatization for the modal logic K with global counting operators ), which can be easily extended onto other frame classes, 2. Establishing tight complexity bounds, namely NExpTime-completeness for the modal logic with global counting operators defined over the classes of arbitrary, reflexive, symmetric, serial and transitive frames ), MT), MD), MB), MK4) with numerical subscripts coded in binary. Establishing the exponential-size model property for this logic defined over the classes of Euclidean and equivalential frames ), MS5).Results of the second type consist of designing concrete deductive systems for standard and non-standard hybrid logics. More precisely, they include: 1. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for a rich class of binder-free standard hybrid logics. An interesting feature of indicated calculi is the nonbranching character of the rule, 2. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for non-standard hybrid logics. The internalization technique applied to a tableau calculus for the modal logic with global counting operators is novel in the literature, 3. Devising the first hybrid algorithm involving an inequality solver for modal logics with global counting operators. Transferring the arithmetical part of reasoning to an inequality solver turned out to be sufficient in ensuring termination.The book is directed to philosophers and logicians working with modal and hybrid logics, as well as to computer scientists interested in deductive systems and decision procedures for logics. Extensive fragments of the first part of the book can also serve as an introduction to hybrid logics for wider audience interested in logic.The content of the book is situated in the areas of formal logic and theoretical computer science with some elements of the theory of computational complexity. (shrink)

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)

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)

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...

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)

Western society today is less unified by a set of core values than ever before. Undoubtedly, the concept of moral consensus is a difficult one in a liberal, democratic and pluralistic society. But it is imperative to avoid a rigid majoritarianism where sensitive personal values are at stake, as in bioethics. Bioethics has become an influential part of public and professional discussions of health care. It has helped frame issues of moral values and medicine as part of a more general (...) effort to find consensus about some of the most perplexing questions of our time. But why is it thought that a moral consensus is important or that it deserves respect? How does moral consensus acquire legitimacy in a society that includes diverse value systems? How is moral consensus possible and how do small groups help create or distort consensus processes? Written by a medical school professor trained in philosophy, this timely work tackles these questions from philosophical, historical, and social scientific standpoints. It begins by describing the traditional ambivalence about consensus in Western culture as well as the uncertain relationship in modernity between consensus and expertise. After outlining the current bioethical consensus, the book gives philosophical and political analyses of the idea of consensus, then assesses the role of consensus in national ethics commissions and in the ethics committee movement. Moreno constructs an original, naturalistic philosophy of moral consensus, referred to as "bioethical naturalism", and then applies sociology and social psychology to actual consensus processes. The book concludes with an account of bioethics as a consensus-oriented social reform movement. This insightful volume will be essential reading for bioethicists, philosophers, physicians, members of ethics committees, and all those concerned with ethical and social issues in health care. (shrink)

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

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)

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)

The purpose of this paper is to prove the decidability ofstit theory (a logic of seeing to it that) with a single agent andRefref Equivalence. This result is obtained through an axiomatization of the theory and a proof that it has thefinite model property. A notion ofcompanions to stit formulas is introduced and extensively used in the proof.

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)

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)

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.

The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.

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)

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)

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)

The present paper has three objectives: Presenting an actualization of a proof of the decidability of monadic predicates logic in the contemporary model theory context; Show examples of decidable and undecidable fragments inside First order logic, offering an original proof of the following theorem: Any formula of First of order logic is decidable if its prenex normal form is in the following form: ∀x1,…,∀xn∃y1,…,∃ymφ; Presenting a theorem that characterizes the validity of First order logic by the tautologicity of Propositional logic, (...) said result is interesting since immediately arises the doubt of how to conciliate said characterization with Alonzo Church’s Undecidability Theorem for First Order Logic. (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.

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.

Let $L = \langle, +, h_q, 1\rangle_{q \in \mathbb{Q}}$ where $\mathbb{Q}$ is the set of rational numbers and $h_q$ is a one-place function symbol corresponding to multiplication by $q$. Then the $L$-theory of Scott's model for intuitionistic analysis is decidable.

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)

The paper considers the set ML 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 ML 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.

In this paper, John Tillson defends an approach to deciding the aims and content of public schooling from the critique of Public Reason Liberalism. The approach that he defends is an unrestricted pairing of the Epistemic Criterion and of the Momentousness Criterion. On the Epistemic Criterion, public schooling should align students' credence with credibility. On the Momentousness Criterion, public schooling ought to include content that it is costly for children to lack the correct view about, where they are otherwise (...) unlikely to have it. Public Reason Liberals seek to restrict both the Epistemic and Momentousness Criteria to within a range that is acceptable to politically reasonable citizens. In response, Tillson argues, first, that the considerations that encourage Public Reason Liberalism instead motivate unrestricted versions of the Epistemic and Momentousness Criteria; and, second, that Public Reason Liberalism faces a dilemma, that it either entails absurd consequences or must undermine itself in addressing these. (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)

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.

In classical propositional logic, a theory T is prime iff it is complete. In Łukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free ℓ -groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory (...) over countably many variables. (shrink)

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)

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

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.

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.

Three classes of decidable discrete linear orders with varying degrees of effectiveness are investigated. We consider how a classical order type may lie in relation to these three classes, and we characterize by their order types elements of these classes that have effective nontrivial self-embeddings.

I issue a challenge for the view that deciding‐to‐A is rendered intentional by an intention or other pro‐attitude towards deciding. Either such an attitude cannot rationalize my deciding specifically to A for a reason I take to support doing A, or, fixing for this, cannot accommodate deciding without entertaining alternatives. If successful, the argument motivates the search for an account that does not source the intentionality of deciding in a rationalizing pro‐attitude.

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)

In this paper I argue that even if one accepts non-cognitivism about trust, the view that trust is not a species of and does not require belief, one should reject voluntarism about trust, the view that we can trust directly at will. There is good reason to think that we cannot trust directly at will, in the way that we can act, and this is so regardless of whether trust requires belief.

We study the class of l-groups of the form C with X an essential P-space. Many such l-groups are non-projectable and their elementary theories may often be reduced to that of an associated Boolean algebra with distinguished ideal. In this paper we establish the decidability of the theories of two classes of such l-groups via corresponding results for the associated structures.

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. (shrink)

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a (...) constant. (shrink)