Frontal Operators in Weak Heyting Algebras

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation ${\tau(a) \leq b \vee (b \rightarrow a)}$ , for all ${a, b \in A}$ . These operators were studied from an algebraic, logical and topological point of view by Leo Esakia in [10]. We will study frontal operators in weak Heyting algebras and we will consider two examples of them. We will give a Priestley duality for the category of frontal weak Heyting algebras in terms of relational spaces ${\langle X, \leq, T, R \rangle}$ where ${\langle X, \leq, T \rangle}$ is a WH-space [6], and R is an additional binary relation used to interpret the modal operator. We will also study the WH-algebras with successor and the WH-algebras with gamma. For these varieties we will give two topological dualities. The first one is based on the representation given for the frontal weak Heyting algebras. The second one is based on certain particular classes of WH-spaces.     

On a Definition of a Variety of Monadic ℓ-Groups

In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL ₀ of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor ${{\mathsf{K}^\bullet}}$ , motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category ${MV^{\bullet}}$ of monadic MV-algebras induced by “Kalman’s functor” ${\mathsf{K}^\bullet}$ . Moreover, we extend the construction to ?-groups introducing the new category of monadic ?-groups together with a functor ${\Gamma ^\sharp}$ , that is “parallel” to the well known functor ${\Gamma}$ between ? and MV-algebras.     

Classical Modal De Morgan Algebras

In this note we introduce the variety ${{\mathcal C}{\mathcal D}{\mathcal M}_\square}$ of classical modal De Morgan algebras as a generalization of the variety ${{{\mathcal T}{\mathcal M}{\mathcal A}}}$ of Tetravalent Modal algebras studied in [11]. We show that the variety ${{\mathcal V}_0}$ defined by H. P. Sankappanavar in [13], and the variety S of Involutive Stone algebras introduced by R. Cignoli and M. S de Gallego in [5], are examples of classical modal De Morgan algebras. We give a representation theory, and we study the regular filters, i.e., lattice filters closed under an implication operation. Finally we prove that the variety ${{{\mathcal T}{\mathcal M}{\mathcal A}}}$ has the Amalgamation Property and the Superamalgamation Property.     

Importing Logics

The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and exogenous enrichment.     

Margaret R. Miles’ Augustine and the Fundamentalist’s Daughter: An Eriksonian Perspective

My perspective on Margaret R. Miles’s Augustine and the Fundamentalist’s Daughter is informed by Erik H. Erikson’s life cycle model (Erikson 1950, 1959, 1963, 1964, 1968a, b, 1982; Erikson and Erikson 1997) and, more specifically, by my relocation of his life stages and their accompanying human strengths (Erikson 1964) according to decades (Capps 2008). I interpret Miles’s account of her life from birth to age forty as revealing the selves that comprise the composite Self (Erikson 1968a) that come into their own during the first four decades of the life cycle, i.e., the hopeful, willing, purposeful, and competent selves     

Exemplification as molecular function

Since the publication of Universals and Scientific Realism (Armstrong 1978a, b) until Sketch for a Systematic Metaphysics (Armstrong 2010), via Universals: An Opinionated Introduction (Armstrong 1989), a World of States of Affairs (Armstrong 1997), and Truth and Truthmakers (Armstrong 2004), David Armstrong has developed one of the most influential theories of instantiation in contemporary analytic metaphysics (see, for example, Lewis, in Aust J Phil 61(4), 343–377, 1983; Baxter in Aust J Phil, 79, 449–464, 2001; Forrest, in Aust J Phil, 83, 213–228, 2006). Instantiation has been advocated by Armstrong to give a solution to what he has called the “pressing problem” of “the multiple location of property universals” (Armstrong, in Universals: An opinionated introduction. University Press, Cambridge, 1989, pp. 89–90). Here I argue that Armstrong’s theory of instantiation fails to solve the problem because it involves two kinds of instantiation to account for particulars “having” and “sharing” universals. As a viable alternative to Armstrong’s theory, I propose a theory of instantiation capable of accounting for both phenomena in a univocal way.     

Disrupting the Coloniality of Being: Toward De-colonial Ontologies in Philosophy of Education

This essay works to bridge conversations in philosophy of education with decolonial theory. The author considers Margonis?? (1999, 2011a, b) use of Rousseau (1979) and Heidegger (1962) in developing an ontological attitude that counters social hierarchies and promotes anti-colonial relations. While affirming this effort, the essay outlines a coloniality of being at work in Rousseau and Heidegger through thier reliance on the colonial conceptualization of African Americans and Native Americans as savage and primitive. The essay turns to decolonial theory and the work of Maldenado-Torres (Cult Stud 21(2?C3):240?C270, 2007, 2009) to highlight how a decolonial attitude complicates, yet enriches Margonis?? philosophical framework.     

An Introduction to Issues of Gender in Stalking Research

Stalking research has increased substantially in the past 20?years. This special issue is intended to contribute to this literature by using gender as a focus point in 1) applying new theoretical perspectives that incorporate the role of gender to the study of stalking perpetration (Davis et al. 2010; Duntley and Buss 2010), 2) addressing divergent findings regarding gender in experiences of victims (Sheridan and Lyndon 2010) and perpetrators (Thompson et al. 2010), and 3) furthering the study of how gender influences perceptions of stalking (Cass and Rosay 2011; Dunlap et al. 2011; Sinclair 2010; Yanowitz and Yanowitz 2010). To place this special issue in context of the current state of knowledge on gender and stalking, we review the state of the existing research as it relates to the domains covered by articles present in this issue.     

Decidability of General Extensional Mereology

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.     

25 years of research on the use of geometry in spatial reorientation: a current theoretical perspective

The purpose of this article is to review and evaluate the range of theories proposed to explain findings on the use of geometry in reorientation. We consider five key approaches and models associated with them and, in the course of reviewing each approach, five key issues. First, we take up modularity theory itself, as recently revised by Lee and Spelke (Cognitive Psychology, 61, 152–176, 2010a; Experimental Brain Research, 206, 179–188, 2010b). In this context, we discuss issues concerning the basic distinction between geometry and features. Second, we review the view-matching approach (Stürzl, Cheung, Cheng, & Zeil, Journal of Experimental Psychology: Animal Behavior Processes, 34, 1–14, 2008). In this context, we highlight the possibility of cross-species differences, as well as commonalities. Third, we review an associative theory (Miller & Shettleworth, Journal of Experimental Psychology: Animal Behavior Processes, 33, 191–212, 2007; Journal of Experimental Psychology: Animal Behavior Processes, 34, 419–422, 2008). In this context, we focus on phenomena of cue competition. Fourth, we take up adaptive combination theory (Newcombe & Huttenlocher, 2006). In this context, we focus on discussing development and the effects of experience. Fifth, we examine various neurally based approaches, including frameworks proposed by Doeller and Burgess (Proceedings of the National Academy of Sciences of the United States of America, 105, 5909–5914, 2008; Doeller, King, & Burgess, Proceedings of the National Academy of Sciences of the United States of America, 105, 5915–5920, 2008) and by Sheynikhovich, Chavarriaga, Strösslin, Arleo, and Gerstner (Psychological Review, 116, 540–566, 2009). In this context, we examine the issue of the neural substrates of spatial navigation. We conclude that none of these approaches can account for all of the known phenomena concerning the use of geometry in reorientation and clarify what the challenges are for each approach.     

Gender and Leadership: A Frame Analysis of University Home Web Page Images

With calls for (business) leaders to contribute to greater global fairness and social justice (BAWB 2006; Maak and Pless Journal of Business Ethics, 88, 537–550, 2009), this paper considers gender equality on University home web page images as one means of communicating equal access to leadership roles for both men and women. Although there are many paths for leadership development, one important purpose of Universities is to create people who will potentially become leaders in our society (Shapiro 2005). We analyzed the home web pages at 24 leading universities to identify implicit messages about gender roles, building on implicit leadership theory and leadership prototypes. Using an adapted version of Goffman’s frame analysis (1979), our results suggest depiction of gender equality in university home web pages, in contrast to studies of print advertisements (cf., Kang Sex Roles, 37(11/12), 979–996, 1997; Lindner Sex Roles, 51(7/8), 409–421, 2004). Our results also identify specific opportunities to depict greater equity and to continue to expand the potential for both women and men to be seen as being capable and belonging on this leadership path.     

Rational intuition and understanding

Rational intuitions involve a particular form of understanding that gives them a special epistemic status. This form of understanding and its epistemic efficacy are not explained by several current theories of rational intuition, including Phenomenal Conservatism (Huemer, Skepticism and the veil of perception, 2001; Ethical intuitionism, 2005; Philos Phenomenol Res 74:30–55, 2007), Proper Functionalism (Plantinga, Warrant and proper function, 1993), the Competency Theory (Bealer Pac Philos Q 81:1–30, 2000; Sosa, A virtue epistemology, 2007) and the Direct Awareness View (Conee, Philos Phenomenol Res 4:847–857, 1998; Bonjour, In defense of pure reason, 1998). Some overlook it; others try to account for it but fail. We can account for the role of understanding in rational intuition by returning to the view of some of the early Rationalists, e.g. Descartes and Leibniz. While that view carries a prohibitive cost, it does contain an insight that may help us solve the problem of giving understanding its due.     

New Directions for Research on the Role of Parents and Teachers in the Development of Gender-Related Math Attitudes: Response to Commentaries

We frame our response to the commentaries by Cheryan (2011), Lane (2011), and Shapiro and Williams (2011), in terms of two broad points made by Lane (2011). First, we agree that the various constructs that we termed “math attitudes”—including math-gender stereotypes, math anxiety, math self-concepts, and achievement motivation in math—are in fact distinct (Gunderson et al. 2011b). Nevertheless, we argue that investigating common mechanisms underlying the transmission of these constructs from adults to children is a productive approach because it can lead to general interventions to boost children’s performance and dispositions toward math. Second, we argue that research on the development of gender-related math attitudes exists at the intersection of multiple research areas, including research on attitudes (broadly defined), math, gender, social learning, and child development, and that drawing on well-developed theories in these areas can lead to novel research questions and predictions. The three excellent commentaries broaden the scope of our article on gender-related math attitudes to include the transmission of implicit attitudes from adults to children, stereotype threat, and gender roles in math-related careers (Cheryan 2011; Gunderson et al. 2011b; Lane 2011; Shapiro and Williams 2011).     

Dependence and Independence

We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using = ${(\vec{x}, \vec{y})}$ have.     

Pereboom’s Frankfurt case and derivative culpability

Pereboom has formulated a Frankfurt-style counterexample in which an agent is alleged to be responsible despite the fact that there are only non-robust alternatives present (Pereboom, Moral responsibility and alternative possibilities: essays on the importance of alternative possibilities, 2003; Phil Explor 12(2):109–118, 2009). I support Widerker’s objection to Pereboom’s Tax Evasion 2 example (Widerker, J Phil 103(4):163–187, 2006) (which rests on the worry that the agent in this example is derivatively culpable as opposed to directly responsible) against Pereboom’s recent counterarguments to this objection (Pereboom 2009). Building on work by Moya (J Phil 104:475–486, 2007; Critica 43(128):3–26, 2011) and Widerker (Widerker 2006), I argue that there is good reason to measure the robustness of alternatives in terms of comparative, rather than non-comparative likelihood of exemption, where the important factor for blame is whether the agent is “doing her reasonable best” to avoid blameworthy behaviour. I maintain that an agent only ever appears responsible when alternatives are robust in this sense. In Pereboom’s examples, both Tax Evasion 2, and his more recent version, Tax Evasion 3 (Pereboom 2009), I maintain the robustness of the alternatives, so understood, is unclear. We can clear up any ambiguity by sharpening the examples, and the result is that the agent appears responsible when the alternatives are made clearly robust, and does not appear responsible when alternatives appear clearly non-robust. The comparative nature of our judgements about blame, I maintain helps to explain the continuing appeal of the “leeway-incompatibilist” viewpoint.     

Monsters in Kaplan’s logic of demonstratives

Kaplan (1989a) insists that natural languages do not contain displacing devices that operate on character—such displacing devices are called monsters. This thesis has recently faced various empirical challenges (e.g., Schlenker 2003; Anand and Nevins 2004). In this note, the thesis is challenged on grounds of a more theoretical nature. It is argued that the standard compositional semantics of variable binding employs monstrous operations. As a dramatic first example, Kaplan’s formal language, the Logic of Demonstratives, is shown to contain monsters. For similar reasons, the orthodox lambda-calculus-based semantics for variable binding is argued to be monstrous. This technical point promises to provide some far-reaching implications for our understanding of semantic theory and content. The theoretical upshot of the discussion is at least threefold: (i) the Kaplanian thesis that “directly referential” terms are not shiftable/bindable is unmotivated, (ii) since monsters operate on something distinct from the assertoric content of their operands, we must distinguish ingredient sense from assertoric content (cf. Dummett 1973; Evans 1979; Stanley 1997), and (iii) since the case of variable binding provides a paradigm of semantic shift that differs from the other types, it is plausible to think that indexicals—which are standardly treated by means of the assignment function—might undergo the same kind of shift.     

Propositional Reasoning that Tracks Probabilistic Reasoning

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method ${\sf B}_{p}$ , which specifies an initial belief state ${\sf B}_{p}(\top)$ that is revised to the new propositional belief state ${\sf B}(E)$ upon receipt of information E. An acceptance rule tracks Bayesian conditioning when ${\sf B}_{p}(E) = {\sf B}_{p|_{E}}(\top)$ , for every E such that p(E)?>?0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The ??Lockean?? rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1?C2):221?C262, 1975; Alchourrón et al., J Symb Log 50:510?C530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987).     

Tempo and Temperament: A Music Lesson on the Significance of Time for the Art of Pastoral Care

This article will focus on the relationship between tempo and temperament and the power of music to facilitate healing, especially for individuals who struggle with temperament or mood disorders, by examining briefly how individuals diagnosed with depression may be helped by listening to or performing music as a form of treatment. Current research into the “science” of music is providing concrete evidence for the reality that musicians and music therapists have long intuited to be true–music does have the capacity to facilitate healing by influencing brain activity and altering moods (Cambell and Doman 2011; Levitin 2007, 2008; Mannes 2011; Powell 2010; Pruyser 1983; Rose 2004). Insofar as music is an integral part of most worship traditions, it provides a common ground for conversation that may seem more natural and less formidable to ministers and lay people alike than the structures of conventional counseling or care-giving relationships, especially for those who have a tendency to be suspicious of all things psychological.     

The representation of Takeuti's\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} -operator

Gaisi Takeuti has recently proposed a new operation on orthomodular latticesL, \(\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} \) :P(L)»L. The properties of \(\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} \) suggest that the value of \(\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} \) (A) (A) \( \subseteq \) L) corresponds to the degree in which the elements ofA behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular latticesL and the existence of two-valued homomorphisms onL.