BK-lattices. Algebraic Semantics for Belnapian Modal Logics

Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK-lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK-lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK. Finally, we describe invariants determining a twist-structure over a modal algebra.     

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.     

The Varieties Defined by P-compatible Identities of Modular Ortholattices

In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOL _Ex defined by so called externally compatible identities of modular ortholattices.     

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.     

Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic

The variety \({\mathcal{SH}}\) of semi-Heyting algebras was introduced by H. P. Sankappanavar (in: Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress, Universidad Nacional del Sur, Bahía Blanca, 2008) [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo (Studia Logica 98(1–2):9–25, 2011) [6]. In this article we introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this presentation of the logic is that we can prove a cut-elimination theorem for GsH that allows us to prove the decidability of the logic. As a direct consequence, we also obtain the decidability of the equational theory of semi-Heyting algebras.     

Semi-intuitionistic Logic

The purpose of this paper is to define a new logic ${\mathcal {SI}}$ called semi-intuitionistic logic such that the semi-Heyting algebras introduced in [4] by Sankappanavar are the semantics for ${\mathcal {SI}}$ . Besides, the intuitionistic logic will be an axiomatic extension of ${\mathcal {SI}}$ .     

Reasoning About Games

A mixture of propositional dynamic logic and epistemic logic that we call PDL + E is used to give a formalization of Artemov??s knowledge based reasoning approach to game theory, (KBR), [4, 5]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.     

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.     

The Lattice of Subvarieties of {\sqrt{\prime}} quasi-MV Algebras

In the present paper we continue the investigation of the lattice of subvarieties of the variety of ${\sqrt{\prime}}$ quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D _r is not finitely based, and we provide an infinite equational basis for the same variety.     

Semantic plasticity and epistemicism

This paper considers the connections between semantic shiftiness (plasticity), epistemic safety and an epistemic theory of vagueness as presented and defended by Williamson (1996a, b, 1997a, b). Williamson explains ignorance of the precise intension of vague words as rooted in insensitivity to semantic shifts: one??s inability to detect small shifts in intension for a vague word results in a lack of knowledge of the word??s intension. Williamson??s explanation, however, falls short of accounting for ignorance of intension.     

Beyond Original Sin: A Paradigm Shift for the Age of Neuroscience

In this article I explore the implications of Jesus?? location of the kingdom of heaven in the lived experience of the individual and of the findings of neuroscientific research for a paradigm shift in Christian theology, one that moves us beyond the Adamic myth and belief in original sin. Support for a theological paradigm shift based on lived experience is provided by Capps (1993) and for this particular paradigm shift by Pagels (1989) and Ricoeur (2004). I point out that the doctrine of original sin supports and fosters the negativity bias of the brain and inhibits the resculpting of the brain. Drawing on Hanson??s (2009) evidence in support of the brain??s neuroplasticity (i.e., its capacity to change itself) and on Brach??s (2003) critique of the ??trance of unworthiness,?? I make the case for meditative and mindful awareness practices in Christianity and other religious traditions as proven methods for the resculpting of the brain in order that individuals may experience greater joy, contentment, and awareness of the goodness of life and of God??s creation. A longitudinal neuroscientific research study of Roman Catholic nuns (Newberg and Waldman 2009) provides evidence in support of the role of contemplative prayer and meditation in generating the joy and serenity that Jesus?? allusion to the hidden treasure envisions.     

Kripke Sheaf Completeness of some Superintuitionistic Predicate Logics with a Weakened Constant Domains Principle

The completeness w.r.t. Kripke frames with equality (or, equivalently, w.r.t. Kripke sheaves, [8] or [4, Sect. 3.6]) is established for three superintuitionistic predicate logics: (Q-H + D*), (Q-H + D*&K), (Q-H + D*&K&J). Here Q-H is intuitionistic predicate logic, J is the principle of the weak excluded middle, K is Kuroda’s axiom, and D* (cf. [12]) is a weakened version of the well-known constant domains principle D. Namely, the formula D states that any individual has ancestors in earlier worlds, and D* states that any individual has ${\neg\neg}$ -ancestors (i.e., ancestors up to ${\neg\neg}$ -equality) in earlier worlds. In particular, the logic (Q-H + D*&K&J) is the Kripke sheaf completion of (Q-H + E&K&J), where E is a version of Markov’s principle (cf. [12]). On the other hand, we show that the logic (Q-H + D*&J) is incomplete w.r.t. Kripke sheaves.     

Predictions from a model of global psychophysics about differences between perceptual and physical matches

A well-known phenomenon is that ??matched?? successive signals do not result in physical identity. This phenomenon has mostly been studied in terms of how much the second of two signals varies from the first, which is called the time-order error (TOE). Here, theoretical predictions led us to study the more general question of how much the matching signal differs from the standard signal, independent of the position of the matching signal as the first or second in a presentation. This we call non-equal matches (NEM). Using Luce??s (Psychological Review, 109, 520?C532, 2002, Psychological Review, 111, 446?C454, 2004, Psychological Review, 115, 601, 2008, Psychological Review, 119, 373?C387, 2012) global psychophysical theory, we predicted NEM when an intensity z is perceived to be ??1 times a standard signal x.?? The theory predicts two different types of individual behaviors for the NEM, and these predictions were evaluated and confirmed in an experiment. We showed that the traditional definition of TOE precludes the observation, and thus the study, of the NEM phenomenon, and that the NEM effect is substantial enough to alter conclusions based on data that it affects. Furthermore, we demonstrated that the custom of averaging data over individuals clearly leads to quite misleading results. An important parameter in this modeling is a reference point that plays a central role in creating variability in the data, so that the key to obtaining regular data from respondents is to stabilize the reference point.     

Information Density and Dependency Length as Complementary Cognitive Models

Certain English constructions permit two syntactic alternations.

1. a. I looked up the number. b. I looked the number up.
2. a. He is often at the office. b. He often is at the office.

This study investigates the relationship between syntactic alternations and processing difficulty. What cognitive mechanisms are responsible for our attraction to some alternations and our aversion to others? This article reviews three psycholinguistic models of the relationship between syntactic alternations and processing: Maximum Per Word Surprisal (building on the ideas of Hale, in Proceedings of the 2nd Meeting of the North American chapter of the association for computational linguistics. Association for Computational Linguistics, Pittsburgh, PA, pp 159–166, 2001), Uniform Information Density (UID) (Levy and Jaeger in Adv Neural Inf Process Syst 19:849–856, 2007; inter alia), and Dependency Length Minimization (DLM) (Gildea and Temperley in Cognit Sci 34:286–310, 2010). Each theory makes predictions about which alternations native speakers should favor. Subjects were recruited using Amazon Mechanical Turk and asked to judge which of two competing syntactic alternations sounded more natural. Logistic regression analysis on the resulting data suggests that both UID and DLM are powerful predictors of human preferences. We conclude that alternations that approach uniform information density and minimize dependency length are easier to process than those that do not.     

Discussions with Bocheński concerning Soviet Marxism–Leninism, 1952–1986

Boche??ski??s lucid, unpartisan, and judiciously critical discussion of Soviet Marxism?CLeninism in his book Der sowjetrussische dialektische Materialismus (1950) filled a major gap in our understanding of that influential movement. Prior to its publication there had been only two works on the subject in English, John Somerville??s Soviet Philosophy (1946) and the Handbook of Philosophy (1949), edited and adapted by Howard Selsam from the Kratkij filosofskij slovar?? (2nd ed. 1940). Both are marked by strong partisanship and ideological bias. Somerville is uncritically pro-Soviet and abjectly Stalinist. Selsam, although he tones down the adulation of Marx, Stalin et al. of the KFS, retains that work??s abuse of such ??reactionary?? and ??idealist?? thinkers as Plato and such ??reactionary?? and ??bourgeois?? thinkers as Hegel. The benign influence of Boche??ski??s work increased with the publication of the English translation, Soviet Russian Dialectical Materialism, in 1963.     

The importance of perceived autonomy support for the psychological health and work satisfaction of health professionals: Not only supervisors count, colleagues too!

Previous studies show that supervisors?? autonomy-supportive style predicts greater psychological health (Baard et al. in J Appl Soc Psychol 34:2045?C2068, 2004; Blais and Brière 1992; Lynch et al. in Prof Psychol Res Pract 36:415?C425, 2005) and lower psychological distress (Deci et al. in Personal Soc Psychol Bull 27:930?C942, 2001). The goal of the present study is to extend these results and investigate the contribution of colleagues?? perceived autonomy support in the prediction of health professionals?? work satisfaction and psychological health. The combined impact of supervisors?? and colleagues?? perceived autonomy support is also examined. A sample of 597 health professionals from the province of Quebec (Canada) completed a questionnaire, which included measures of perceived supervisors?? and colleagues?? autonomy support and outcome variables. Results confirm that supervisors?? and colleagues?? perceived autonomy support predict health professionals?? work satisfaction and psychological health. Results also show that colleagues?? perceived autonomy support adds to the prediction of health professionals?? work satisfaction, subjective well-being, and suicidal ideation above and beyond supervisors?? perceived autonomy support.