We generalize two well-known model-theoretic characterization theorems from propositional modal logic to first-order modal logic. We first study FML-definable frames and give a version of the Goldblatt–Thomason theorem for this logic. The advantage of this result, compared with the original Goldblatt–Thomason theorem, is that it does not need the condition of ultrafilter reflection and uses only closure under bounded morphic images, generated subframes and disjoint unions. We then investigate Lindström type theorems for first-order modal logic. We show that FML has (...) the maximal expressive power among the logics extending FML which satisfy compactness, bisimulation invariance and the Tarski union property. (shrink)

In Part I of this paper we presented a Hilbert-style system $\Sigma _D$ axiomatizing stit logic of justification announcements interpreted over models with discrete time structure. In this part, we prove three frame definability results for $\Sigma _D$ using three different definitions of a frame plus another version of completeness result.

Bermúdez claims that agents think about framed outcomes, not outcomes themselves; and that seemingly incoherent preferences can be rational, once defined over framed outcomes. However, the agents in his examples know that alternative frames describe the same outcome, neutrally understood. This undermines the restriction of their preferences to framed outcomes and, in turn, the argument for rational framing effects.

We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas (...) which are satisfiable under any valuation (the so‐called existential validity). Continuing previous work in which model theoretic characterization for this type of definability of elementary classes was proved, we give an analogous general result without the assumption of the first‐order definability. Furthermore, we outline relationships between sets of existentially valid formulas corresponding to several well‐known modal logics. (shrink)

In the basic modal language and in the basic modal language with the added universal modality, first-order definability of all formulas over the class of all frames is shown. Also, it is shown that the problems of modal definability of first-order sentences over the class of all frames in the languages and are both PSPACE-complete.

It is nearly impossible to open a textbook on Newtonian mechanics without encountering the concept of inertial frames: the frames that are privileged by the theory’s dynamics. In this paper, I argue that extant definitions of inertial frames are unsatisfactory. I criticise two common definitions of inertial frames: law-based definitions, according to which inertial frames are simply those in which the laws are true, and structure-based definitions, according to which inertial frames are those that are ‘adapted’ to spatiotemporal structure. I (...) then offer a new, symmetry-based definition of inertial frames. This definition offers a non-conventional way of specifying the dynamically privileged frames. The result clarifies the foundations of Newtonian mechanics and accounts for the empirical success of coordinate-dependent formulations of it. (shrink)

According to a seminal paper by Barsalou , frames are attribute-value-matrices for representing exemplars or concepts. Frames have been used as a tool for reconstructing scientific concepts as well as conceptual change within scientific revolutions . In the frame-based representations of scientific concepts developed so far the semantic content of concepts is determined by a set of attribute-specific values. This way of representing semantic content works best for prototype concepts and defined concepts of a conceptual taxonomy satisfying the no-overlap (...) principle. In addition to the semantic content of prototype concepts and defined concepts, frames can also contain empirical knowledge that is represented as constraints between the values of the frame. Beside prototype concepts and defined concepts, theoretical concepts that are multiply operationalized play an important role in science. However, so far no frame-based representation of theoretical concepts has been proposed. In this paper, it will be shown that theoretical concepts can be represented by frames and that frame-based representations of prototype concepts and defined concepts have another structure than frame-based representations of theoretical concepts. In order to explicate this difference, we will develop a frame-based method for representing all three kinds of concepts by means of mathematical graph-theory. One important consequence will be that the constraints of a frame representing a theoretical concept are entailed by the structure of the frame, as opposed to a frame representing defined or prototype concepts. (shrink)

The main result is that is no effective algorithmic answer to the question:how to recognize whether arbitrary modal formula has a first-order equivalent on the class of finite frames. Besides, two known problems are solved: it is proved algorithmic undecidability of finite frame consequence between modal formulas; the difference between global and local variants of first-order definability of modal formulas on the class of transitive frames is shown.

The framework of quantum frames can help unravel some of the interpretive difficulties i the foundation of quantum mechanics. In this paper, I begin by tracing the origins of this concept in Bohr's discussion of quantum theory and his theory of complementarity. Engaging with various interpreters and followers of Bohr, I argue that the correct account of quantum frames must be extended beyond literal space–time reference frames to frames defined by relations between a quantum system and the exosystem or external (...) physical frame, of which measurement contexts are a particularly important example. This approach provides superior solutions to key EPR-type measurement and locality paradoxes. (shrink)

In two experiments, participants had to choose between a sure and a risky option. The sure option was presented either in a gain or a loss frame. Need was defined as a minimum score the participants had to reach. Moreover, choices were made under two different time constraints and with three different levels of induced need to be reached within a fixed number of trials. The two experiments differed with respect to the specific amounts to win and the need (...) levels. The $$2 \times 2 \times 3$$2×2×3 design was a within-subject design. Data were evaluated on an overall and on a group level, the latter based on participants’ stated risk preference and on revealed preferences using cluster analysis across subjects. Overall, the results showed riskier behavior when the choice options were presented as losses as compared to gains and when the induced need was highest. Time limits enhanced the framing effect. (shrink)

Social entrepreneurship is perceived as a legitimate and innovative solution to social problems. Yet, when one looks at the literature one finds that the social problems that the SE movement seeks to address and how these problems are identified and defined are not studied. This lack of attention to the defining of social problems in SE has implications for the domain for problems do not exist unless they are recognized and defined, and those that define problems have influence on how (...) these will eventually be addressed. Our paper presents an analysis of framing activities in SE done by the actors involved in the development and promotion of the SE movement. Our analysis reveals that these actors are concerned with creating an ecosystem to support social entrepreneurs. Critical analysis of discourses of these actors reveals a powerful mobilization discourse, one that supports social entrepreneurs as the agents of change. We also find that as the SE movement emerged at the beginning of a cycle of protest against capitalist systems, their framing of SE as system changing of these very systems therefore finds strong resonance with a wide variety of actors. (shrink)

We introduce frame-equivalence games tailored for reasoning about the size, modal depth, number of occurrences of symbols and number of different propositional variables of modal formulae defining a given frame property. Using these games, we prove lower bounds on the above measures for a number of well-known modal axioms; what is more, for some of the axioms, we show that they are optimal among the formulae defining the respective class of frames.

The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So, a notion of "polymodal base" arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper's main paradigm. The modal definability (in the spirit of van Benthem's correspondence theory) of arbitrary and ~-elementary classes of frames in this base and in (...) some of its extensions, e.g., £(R,-R,R-1 ,_R-1), £(R,-R,=I=) etc., is described, and numerous examples of conditions definable there, as well as undefinable ones, are adduced. (shrink)

In his recent article ‘Nudging, Informed Consent and Bullshit’, William Simkulet1 convincingly argues that certain types of nudging satisfy Frankfurt’s criteria of bullshit. As a prelude to this argument, Simkulet considers whether recommendations and framing are types of nudging and whether they satisfy the requirement of adequate disclosure essential for a valid informed consent. He defines nudging as the systematic attempt at altering behaviour by non-rational means, and describes adequate disclosure as providing the patient with true information that enables an (...) understanding of treatment options and their risks and benefits. Simkulet argues that recommendations and framing are types of rational persuasion in that they potentially enhance patients’ understanding of treatment options and their risks and benefits. Therefore, not only do they not qualify as nudging, but they may be required in order to secure adequate disclosure. In this brief comment, I focus on Simkulet’s considerations of framing and show that framing may be nudging and that it may violate the requirements of informed consent. The framing of medical information may influence patients’ preferences for treatment. It has been shown that framing information about a risky medical intervention in chance of survival rather than risk of death increases patients’ preferences for the intervention.2 3 In his exploration of framing, Simkulet contends that the fact that people respond differently to …. (shrink)

In his recent article ‘Nudging, Informed Consent and Bullshit’, William Simkulet 1 convincingly argues that certain types of nudging satisfy Frankfurt’s criteria of bullshit. As a prelude to this argument, Simkulet considers whether recommendations and framing are types of nudging and whether they satisfy the requirement of adequate disclosure essential for a valid informed consent. He defines nudging as the systematic attempt at altering behaviour by non-rational means, and describes adequate disclosure as providing the patient with true information that enables (...) an understanding of treatment options and their risks and benefits. Simkulet argues that recommendations and framing are types of rational persuasion in that they potentially enhance patients’ understanding of treatment options and their risks and benefits. Therefore, not only do they not qualify as nudging, but they may be required in order to secure adequate disclosure. In this brief comment, I focus on Simkulet’s considerations... (shrink)

In this paper we define the notion of frame based formulas. We show that the well-known examples of formulas arising from a finite frame, such as the Jankov-de Jongh formulas, subframe formulas and cofinal subframe formulas, are all particular cases of the frame based formulas. We give a criterion for an intermediate logic to be axiomatizable by frame based formulas and use this criterion to obtain a simple proof that every locally tabular intermediate logic is axiomatizable (...) by Jankov-de Jongh formulas. We also show that not every intermediate logic is axiomatizable by frame based formulas. (shrink)

In the philosophy of science, the frame model is used in order to represent and analyze scientific concepts and conceptual change. However, the potential of the frame model is far from being fully exploited: Up to now, the frame model is only applied to a rather small set of different kinds of concepts and important advantages of the frame model for reconstructing and analyzing concepts have been neglected. In this article, we will essentially extend the (...) class='Hi'>frame model in the following way: We will develop a frame-based approach for representing a comprehensive class of different kinds of concepts including conjunctively and disjunctively defined concepts, family resemblance concepts, prototype concepts, operationalized concepts, dual concepts integrating two different ways of concept determination, and theoretical concepts. In order to do so, we will define different kinds of frames with respect to the logical structure of the kind of concept that is represented by a particular frame. We will exemplify our approach by means of ten frames applied to standard cases of conceptual analyses in philosophy and cognitive science as well as to scientific concepts of political science, psychology, linguistics and physics. (shrink)

For Knox, ‘spacetime’ is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays theoperationalrole of spacetime—i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields—we identify in this paper important limitations of her approach: these limitations are based upon the fact that there is a (...) gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox’s spacetime functionalism might be amended in light of these issues. (shrink)

A grafted frame is a new kind of frame which combines a modal frame and some relevance frames. A grafted model consists of a grafted frame and a truth-value assignment. In this paper, the grafted frame and the grafted model are constructed and used to show the completeness of S1. The implications of S1-completeness are discussed. A grafted frame does not combine two kinds of frames simply by putting relations defined in the components together. (...) That is, the resulting grafted frame is not in the form of $\langle W, R, R'\rangle$ , or more generally, in the form of $\langle W, R, R', R'',...\rangle$ , which consists of a non-empty set with several relations defined on it. Rather, it resembles the construction of fibering proposed by D. M. Gabbay and M. Finger (see [4] and [3]). On a grafted frame, some modal worlds, which belong to the initial modal frame, are attached by some relevance frames. However, these two semantics have important differences. Consider the combined semantics involving semantics of relevance logic and modal logic. A fibred model and a grafted model proposed in this paper differ in the following respects. First, a fibred model is constructed from a class of modal models and a class of relevance models. A grafted model consists of a grafted frame and a truth-value assignment, where the grafted frame is constructed from a modal frame and some relevance frames, and the assignment is a union of a modal truth-value assignment V M and some relevance truth-value assignments V R . V M (V R ) defined in this paper is not the same as the assignment contained in a modal (relevance) model. Second, in a fibred model each relevance world is associated (or fibred) with a modal model and each modal world with a relevance model. To be the grafted frame on which a grafted model is based, it is enough to have some modal worlds attached by some relevance frames. Moreover, no relevance world is associated with a modal frame in the grafted frame. Third, fibred models are intended to provide an appropriate semantics to combined logics. Grafted frames and grafted models are inspired to characterize S1, which, containing only one modality □, is not a combined logic. It is shown in this paper that S1 is sort of a meta-logic of the intersection of S0.4 and F, where S0.4, a new system proposed in this paper, is in turn a meta-logic of the relevance logic. (shrink)

A grafted frame is a new kind of frame which combines a modal frame and some relevance frames. A grafted model consists of a grafted frame and a truth-value assignment. In this paper, the grafted frame and the grafted model are constructed and used to show the completeness of S1. The implications of S1-completeness are discussed. A grafted frame does not combine two kinds of frames simply by putting relations defined in the components together. (...) That is, the resulting grafted frame is not in the form of $\langle W, R, R'\rangle$, or more generally, in the form of $\langle W, R, R', R'',...\rangle$, which consists of a non-empty set with several relations defined on it. Rather, it resembles the construction of fibering proposed by D. M. Gabbay and M. Finger. On a grafted frame, some modal worlds, which belong to the initial modal frame, are attached by some relevance frames. However, these two semantics have important differences. Consider the combined semantics involving semantics of relevance logic and modal logic. A fibred model and a grafted model proposed in this paper differ in the following respects. First, a fibred model is constructed from a class of modal models and a class of relevance models. A grafted model consists of a grafted frame and a truth-value assignment, where the grafted frame is constructed from a modal frame and some relevance frames, and the assignment is a union of a modal truth-value assignment V$_M$ and some relevance truth-value assignments V$_R$. V$_M$ defined in this paper is not the same as the assignment contained in a modal model. Second, in a fibred model each relevance world is associated with a modal model and each modal world with a relevance model. To be the grafted frame on which a grafted model is based, it is enough to have some modal worlds attached by some relevance frames. Moreover, no relevance world is associated with a modal frame in the grafted frame. Third, fibred models are intended to provide an appropriate semantics to combined logics. Grafted frames and grafted models are inspired to characterize S1, which, containing only one modality $\square$, is not a combined logic. It is shown in this paper that S1 is sort of a meta-logic of the intersection of S0.4 and F, where S0.4, a new system proposed in this paper, is in turn a meta-logic of the relevance logic. (shrink)

The concept of vulnerability is widely used in human rights policy documents, reports, and case law focusing on the impacts of climate change on human rights. In academic discussions, the concept, however, has also sparked a discussion on its benefits and challenges for the advancement of human rights, especially concerning the principles of equality and non-discrimination. This article aims at contributing to this debate from a frame-analytical perspective. In social sciences, frame-analysis is a form of discourse analysis which (...) focuses on the consequences of different concepts for legal, political, and social discussions and norms. With the example of selected UN documents on different human rights issues in the context of climate change, the article, firstly, analyzes whether and how the concept of vulnerability is defined in the documents and why it is used in the documents. Secondly, it is elaborated to which individuals and groups the concept is applied. Thirdly, it is discussed how vulnerability is conceptualized in relation to or in distinction to the concepts of inequality and discrimination. In a further section it is analyzed what narratives are mobilized by the frame of vulnerability. The article concludes that from a discourse-analytical perspective the frame of vulnerability mobilizes problematic narratives which has gendered and racialized implications for those labeled vulnerable. (shrink)

This essay seeks to develop and illustrate an approach to comparison based on "ad hoc" frames. A frame is defined by a question, to which dif- ferent thinkers can be seen as offering complementary and/or competing responses. Pursuing a middle ground between universalist conceptions of comparison and particularist rejections of comparison, this approach brings various positions into dialogue in a manner that is not inherently totalizing. The article draws extensively on Hegel's philosophy of religion to articulate this approach to (...) comparison and its presuppositions. The sec- ond section of the essay seeks to illustrate the value of this approach by using the question of how traditional practices are inherited to frame a comparison of Hegel on habit and the Confucian thinker Xunzi on ritual. This comparison functions principally to indicate the process of comparison and suggest the value of pursuing this comparison in greater depth. (shrink)

In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the (...) canonical extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in [FIT 92a]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. (shrink)

This article deals with frames and schemata in news reporting. It distinguishes frames and schemata in newsroom discourse and news reports. On the individual cognitive level, a frame is defined as a set of schemata for different aspects of reality. They emerge in newsroom discourse and in exchange with other discourses, i. e., they are not idiosyncratic but shared among those working in a newsroom. It is supposed that news report structures correspond to these newsroom frames and schemata. The (...) article discusses these considerations in regard to related explanations of news production, especially attitudinal approaches such as news bias. While the latter assume that journalists prefer information consistent with their own attitudes or that news reporting is ‘synchronized’ with editorial tendencies, the framing approach proposes that information in routine news reports correspond to newsroom frames. In this study I will use xenophobia as an example to identify newsroom frames in a qualitative frame analysis. In the second part of the study, quantitative analysis of news framing examines whether news report information correlates with newsroom frames. Finally, I will present empirical evidence that shows that newsroom frames play a role in news reporting. (shrink)

We define and study the notion of an indexed frame. This is a bi-dimensional structure consisting of a Cartesian product equipped with relations which only relate pairs if they coincide in one of their components. We show that these structures are quite ubiquitous in modal logic, showing up in the literature as products of Kripke frames, subset spaces, or temporal frames for STIT logics. We show that indexed frames are completely characterised by their ‘orthogonal’ relations, and we provide their (...) sound and complete logic. Using these ‘orthogonality’ results, we provide necessary and sufficient conditions for an arbitrary Kripke frame to be isomorphic to certain well-known bi-dimensional structures. (shrink)

The development of autonomous, robotic weaponry is progressing rapidly. Many observers agree that banning the initiation of lethal activity by autonomous weapons is a worthy goal. Some disagree with this goal, on the grounds that robots may equal and exceed the ethical conduct of human soldiers on the battlefield. Those who seek arms-control agreements limiting the use of military robots face practical difficulties. One such difficulty concerns defining the notion of an autonomous action by a robot. Another challenge concerns how (...) to verify and monitor the capabilities of rapidly changing technologies. In this article we describe concepts from our previous work about autonomy and ethics for robots and apply them to military robots and robot arms control. We conclude with a proposal for a first step toward limiting the deployment of autonomous weapons capable of initiating lethal force. (shrink)

The concept of moral distress comes from nursing ethics, and was initially defined as ‘…when one knows the right thing to do, but institutional constraints make it nearly impossible to pursue the right course of action’. There is a large body of literature associated with moral distress, yet multiple definitions now exist, significantly limiting its usefulness. We undertook a systematic review of the argument-based bioethics literature on this topic as the basis for a critical appraisal, identifying 55 papers for analysis. (...) We found that moral distress is most frequently framed around individual experiences of distress in relation to local practices and constraints, and understood in terms of power relations and workplace hierarchies. This understanding is directly derived from, and often still seen as specific to, nursing. Frequently the perspective of the morally distressed individual is privileged. Understandings of moral distress have evolved towards an ‘occupational health approach’, with the assumption that moral distress should be measured and prevented. Counter-perspectives were identified, highlighting conceptual problems. Based on our review, we propose a redefinition of moral distress: ‘Ethical unease or disquiet resulting from a situation where a clinician believes they have contributed to avoidable patient or community harm through their involvement in an action, inaction or decision that conflicts with their own values’. This definition is specific enough for research use, anchored in clinicians’ professional responsibilities and concerns about harms to patients, framed relationally rather than hierarchically, and amenable to multiple perspectives on any given morally distressing situation. (shrink)

A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have a relational semantics provided by structures based on polarities. Such structures have associated complete lattices of stable subsets, and these have been used to construct canonical extensions of lattice-based algebras. We study classes of structures that are closed under ultraproducts and whose (...) stable set lattices have additional operators that are first-order definable in the underlying structure. We show that such classes generate varieties of algebras that are closed under canonical extensions. The proof makes use of a relationship between canonical extensions and MacNeille completions. (shrink)

One of the common and commonsensical ways to distinguish cinema from every other art and semiotic system, and to define the property of its uniqueness, is to claim that cinema is the only art/”language” that links images. This “linking” can imply three different yet complementary operations. First, cinema links individual still photographs into an apparently continuous sequence of movement by pushing the individual frames or photographs through a camera or projector at sixteen or twenty-four or however many frames per second. (...) Second, cinema links images by editing , by splicing together individual shots, which are continuous chains of linked frames. Finally, cinema links images with sounds, synchronously or otherwise. The only problem with such an apparently unrestrictive and unprescriptive definition of cinema and the “cinematic” is that it obscures an essentially cinematic operation that precedes the linking of cinema images: the image must first be framed before it can be linked with another.But is framing unique to cinema? Don’t paintings have frames? Aren’t photographs frames? Isn’t the theater’s proscenium arch a frame? A consequence of such perfectly sensible questions is a consistent undervaluing of the cinema frame as an essentially and uniquely cinematic tool, unlike that of any other art, producing serious errors in the writing of film theory and serious misunderstandings of the processes of film history. The goal of this article is to diagnose some of these errors so they might someday be cured. Gerald Mast is professor of English and general in the humanities at the University of Chicago. Among his many books are A Short History of the Movies, The Comic Mind: Comedy and the Movies, Film/Cinema/Movie, The Movies in Our Midst, and Howard Hawks, Storyteller. His previous contributions to Critical Inquiry are “What Isn’t Cinema?” and “Kracauer’s Two Tendencies and the Early History of Film Narrative”. (shrink)

The recent construction of “gender equality” as a defining value of European societies has shaped the policy goals of immigrant integration programs. This focus on “gender equality” may function, paradoxically, to exclude immigrants, if immigrant integration policies rely on stereotypical representations of immigrants and fail to acknowledge the multiple, intersecting forms of inequality that immigrant women face. This article contributes to the critical scholarship on the role of “gender equality” in the field of immigrant integration policy by examining the framing (...) of this concept in the policy documents and implementation of the French civic integration program. Using ethnographic observations and field interviews, I illustrate how frontline workers, many of whom were women of immigrant origin, interacted with participants to frame “gender equality” in exclusionary and inclusionary ways, and how “gender equality” functioned as a racial boundary within the program. The tensions in the discourses of frontline workers mirrored those of the political context in which the policy developed; they were constrained by a difference-blind ideology of French republicanism as they insisted on “gender equality” as the pathway to belonging in France. (shrink)

The simplest bimodal combination of unimodal logics \ and \ is their fusion, \, axiomatized by the theorems of \ for \ and of \ for \, and the rules of modus ponens, necessitation for \ and for \, and substitution. Shehtman introduced the frame product \, as the logic of the products of certain Kripke frames: these logics are two-dimensional as well as bimodal. Van Benthem, Bezhanishvili, ten Cate and Sarenac transposed Shehtman’s idea to the topological semantics and (...) introduced the topological product \, as the logic of the products of certain topological spaces. For almost all well-studies logics, we have \, for example, \. Van Benthem et al. show, by contrast, that \. It is straightforward to define the product of a topological space and a frame: the result is a topologized frame, i.e., a set together with a topology and a binary relation. In this paper, we introduce topological-frame products \ of modal logics, providing a complete axiomatization of \, whenever \ is a Kripke complete Horn axiomatizable extension of the modal logic D: these extensions include \ and \, but not \ or \. We leave open the problem of axiomatizing \, \, and other related logics. When \, our result confirms a conjecture of van Benthem et al. concerning the logic of products of Alexandrov spaces with arbitrary topological spaces. (shrink)

New techniques in genome editing have led to a controversial debate about the opportunities and uncertainties they present for agricultural food production and consumption. In July 2018, the Court of Justice of the European Union defined genome editing as a new process of mutagenesis, which implies that the resulting organisms count as genetically modified and are subject, in principle, to the obligations of EU Directive 2001/18/EG. This paper examines how key protagonists from academia, politics, and the economy strategically framed the (...) debate around genome editing in agriculture in Germany prior to its legal classification by the Court of Justice. It is based on an analysis of 96 official statements, including position papers, press releases, and information brochures. Our study reveals eight strategic frames used in the discourse on genome editing and uncovers the strategies used to disconnect from or connect with the previous discourse on green genetic engineering in the 1970s, 1980s and 1990s. Building on competitive framing theory, the study provides explanations for the use and emergence of counter-framing strategies and their success or failure in the debate around genome editing. (shrink)

In his paper 'Generalised Ortho Negation' [2] J.Michael Dunn mentions a claim of mine to the effect that there is no condition on 'perp frames' equivalent to the holding of double negation elimination ∼∼A ⊩ A. That claim is wrong. In this paper I correct my error and analyse the behaviour of conditions on frames for negations which verify a number of different theses.

Hilbert-style axiomatic systems are presented for versions of the modal logics K, where {D, 4, 5}, with noncontingency as the sole modal primitive. The classes of frames characterized by the axioms of these systems are shown to be first-order definable, though not equal to the classes of serial, transitive, or euclidean frames. The canonical frame of the noncontingency logic of any logic containing the seriality axiom is proved to be nonserial. It is also shown that any class of frames (...) definable in the noncontingency language contains the class of functional frames, and dually, there exists a greatest consistent normal noncontingency logic. (shrink)

The paper generalises Goldblatt's completeness proof for Lemmon–Scott formulas to various modal propositional logics without classical negation and without ex falso, up to positive modal logic, where conjunction and disjunction, andwhere necessity and possibility are respectively independent.Further the paper proves definability theorems for Lemmon–Scottformulas, which hold even in modal propositional languages without negation and without falsum. Both, the completeness theorem and the definability theoremmake use only of special constructions of relations,like relation products. No second order logic, no general (...) frames are involved. (shrink)

Concussion and Mild Traumatic Brain Injury affect millions of people worldwide. mTBI has been called the “signature injury” of the recent conflicts in Iraq and Afghanistan, affecting thousands of active duty service men and women, and veterans. Sport-related concussion represents a significant public health problem, with elite and professional athletes, and millions of youth and amateur athletes worldwide suffering concussions annually. These brain injuries have received scant attention from neuroethicists, and the focus of this special issue is on defining the (...) ethical considerations and developing and elucidating the neuroethical contributions to the discussion about concussion and mTBI. (shrink)

An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain (...) types of Finsler space, and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed. (shrink)

A possible world structure consist of a set W of possible worlds and an accessibility relation R. We take a partial function r(·,·) to the unit interval [0, 1] instead of R and obtain a Kripke frame with graded accessibility r Intuitively, r(x, y) can be regarded as the reliability factor of y from x We deal with multimodal logics corresponding to Kripke frames with graded accessibility in a fairly general setting. This setting provides us with a framework for (...) fuzzy possible world semantics. The basic propositional multimodal logic gK (grated K) is defined syntactically. We prove that gK is sound and complete with respect to this semantics. We discuss some extensions of gK including logics of similarity relations and of fuzzy orderings. We present a modified filtration method and prove that gK and its extensions introduced here are decidable. (shrink)

This article examines and presents examples of contemporary advertising within the medical and health professions that continue the process and organisation of knowledge about women and their reproductive bodies. It draws on feminist and poststructural perspectives to inform a critical evaluation of the visual representations of menopausal women and hormone replacement therapy. These representations work to construct certain definitions of the feminine that sustain and support existing contradictory cultural meanings and values about menopause. I argue that the images continue to (...) misrepresent and define what forms of femininity and sexual gender are desirable and acceptable for menopausal women. The article addresses the problems of gender discrimination and bias within the advertising industry, and illustrates the ways in which readers of visual texts may be influenced by stereotypic assumptions concerning a woman's lived experience of menopause. It illustrates how specific symbolic images directed towards men and women for hormone replacement therapy, testosterone deficiency and sexual dysfunction influence the viewer's decision making and action responses. (shrink)

The advocate of modal logic or relevant logic has traditionally argued that her preferred system offers the best regimentation of the theory of entailment. Essential to the projects of modal and relevant logic is the importation of non-truth-functional expressive resources into the object language on which the logic is defined. The most elegant technique for giving the semantics of such languages is that of frame semantics, a variation on which features the device of partitioned frames that divide 'points of (...) evaluation' into two types: normal points and abnormal points. This essay attempts to provide satisfying philosophical interpretations of the partitioned frame semantics for some weak modal logics and relevant logics. According to the current best interpretation, partitioned frame semantics are a kind of possible worlds semantics that appeal to 'logically impossible worlds' where the laws of logic may fail to hold. This is undermined by the fact that all of the target logics fail to satisfy criteria of expressibility needed to support the thesis that laws of logic fail to hold at abnormal points. This suggests that we should not look for a monistic interpretive paradigm for partitioned frame semantics. (shrink)

For Knox, ‘spacetime’ is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays the operational role of spacetime—i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields—we identify in this paper important limitations of her approach: these limitations are based upon the fact that there (...) is a gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox’s spacetime functionalism might be amended in light of these issues. (shrink)

The stability theory of first order theories was initiated by Saharon Shelah in 1969. The classification of abstract elementary classes was initiated by Shelah, too. In several papers, he introduced non-forking relations. Later, Shelah [17, II] introduced the good non-forking frame, an axiomatization of the non-forking notion.We improve results of Shelah on good non-forking frames, mainly by weakening the stability hypothesis in several important theorems, replacing it by the almost λ-stability hypothesis: The number of types over a model of (...) cardinality λ is at most λ+.We present conditions on Kλ, that imply the existence of a model in Kλ+n for all n. We do this by providing sufficiently strong conditions on Kλ, that they are inherited by a properly chosen subclass of Kλ+. What are these conditions? We assume that there is a ‘non-forking’ relation which satisfies the properties of the non-forking relation on superstable first order theories. Note that here we deal with models of a fixed cardinality, λ.While in Shelah [17, II] we assume stability in λ, so we can use brimmed models, here we assume almost stability only, but we add an assumption: The conjugation property.In the context of elementary classes, the superstability assumption gives the existence of types with well-defined dimension and the ω-stability assumption gives the existence and uniqueness of models prime over sets. In our context, the local character assumption is an analog to superstability and the density of the class of uniqueness triples with respect to the relation ≼bs is the analog to ω-stability. (shrink)

In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be precise, we will define four special kinds of Kripke frames, namely, geometric frames, irreducible geometric frames, complete geometric frames and quantum Kripke frames; and we will show that they correspond to (...) pure orthogeometries, irreducible pure orthogeometries, Hilbertian geometries and irreducible Hilbertian geometries, respectively. The discovery of these correspondences raises interesting research topics and will enrich the study of logic. (shrink)

Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the (...) combination of implicit definability and reducibility. The three notions of definability are characterized semantically using algebras. The use of algebras, rather than frames, is shown to be necessary for these characterizations. (shrink)

Chiappe and Kukla argue that relevance theory fails to solve the frame problem as defined by Fodor. They are right. They are wrong, however, to take Fodor’s frame problem too seriously. Fodor’s concerns, on the other hand, even though they are wrongly framed, are worth addressing. We argue that Relevance thoery helps address them.

In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need to (...) be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface. (shrink)