A 2-categorial Generalization of the Concept of Institution

After defining, for each many-sorted signature Σ = (S, Σ), the category Ter(Σ), of generalized terms for Σ (which is the dual of the Kleisli category for \mathbb T_S{\mathbb {T}_{\bf \Sigma}}, the monad in Set ^S determined by the adjunction T_S \dashv G_S{{\bf T}_{\bf \Sigma} \dashv {\rm G}_{\bf \Sigma}} from Set ^S to Alg(Σ), the category of Σ-algebras), we assign, to a signature morphism d from Σ to Λ, the functor d_à{{\bf d}_\diamond} from Ter(Σ) to Ter(Λ). Once defined the mappings that assign, respectively, to a many-sorted signature the corresponding category of generalized terms and to a signature morphism the functor between the associated categories of generalized terms, we state that both mappings are actually the components of a pseudo-functor Ter from Sig to the 2-category Cat. Next we prove that there is a functor Tr^Σ, of realization of generalized terms as term operations, from Alg(Σ) × Ter(Σ) to Set, that simultaneously formalizes the procedure of realization of generalized terms and its naturalness (by taking into account the variation of the algebras through the homomorphisms between them). We remark that from this fact we will get the invariance of the relation of satisfaction under signature change. Moreover, we prove that, for each signature morphism d from Σ to Λ, there exists a natural isomorphism θ ^d from the functor Tr^L °(Id ×d_à){{{\rm Tr}^{\bf {\bf \Lambda}} \circ ({\rm Id} \times {\bf d}_\diamond)}} to the functor Tr^S °(d^* ×Id){{\rm Tr}^{\bf \Sigma} \circ ({\bf d}^* \times {\rm Id})}, both from the category Alg(Λ) × Ter(Σ) to the category Set, where d* is the value at d of the arrow mapping of a contravariant functor Alg from Sig to Cat, that shows the invariant character of the procedure of realization of generalized terms under signature change. Finally, we construct the many-sorted term institution by combining adequately the above components (and, in a derived way, the many-sorted specification institution), but for a strict generalization of the standard notion of institution.     

Proof theory and mathematical meaning of paraconsistent C-systems

A proof-theoretic analysis and new arithmetical semantics are proposed for some paraconsistent C-systems, which are a relevant sub-class of Logics of Formal Inconsistency (LFIs) introduced by W.A. Carnielli et al. (2002, 2005) [8] and [9]. The sequent versions BC, CI, CIL of the systems bC, Ci, Cil presented in Carnielli et al. (2002, 2005) [8] and [9] are introduced and examined. BC, CI, CIL admit the cut-elimination property and, in general, a weakened sub-formula property. Moreover, a formal notion of constructive paraconsistent system is given, and the constructivity of CI is proven. Further possible developments of proof theory and provability logic of CI-based arithmetical systems are sketched, and a possible weakened Hilbert?s program is discussed. As to the semantical aspects, arithmetical semantics interprets C-system formulas into Provability Logic sentences of classical Arithmetic PA (Artemov and Beklemishev (2004) [2], Japaridze and de Jongh (1998) [19], Gentilini (1999) [15], Smorynski (1991) [22]): thus, it links the notion of truth to the notion of provability inside a classical environment. It makes true infinitely many contradictions B∧¬B and falsifies many arbitrarily complex instances of non-contradiction principle ¬(A∧¬A). Moreover, arithmetical models falsify both classical logic LK and intuitionistic logic LJ, so that a kind of metalogical completeness property of LFI-paraconsistent logic w.r.t. arithmetical semantics is proven. As a work in progress, the possibility to interpret CI-based paraconsistent Arithmetic PACI into Provability Logic of classical Arithmetic PA is discussed, showing the role that PACIarithmetical models could have in establishing new meta-mathematical properties, e.g. in breaking classical equivalences between consistency statements and reflection principles.     

On the Closure Properties of the Class of Full G-models of a Deductive System

In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACS_s A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACS_s A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples. Dedicated to the memory of Willem Johannes Blok     

Development and Evaluation of a Decision Aid About Prenatal Testing for Women of Advanced Maternal Age

Objective: To develop and evaluate a decision aid designed to prepare patients of advanced maternal age for counseling about prenatal diagnostic testing. Setting: A regional genetics center. Design: A before/after study. Interventions: Participants used an audioguided workbook to learn about options and outcomes and to clarify personal risks, values, questions, and predispositions. Subjects: 21 women of advanced maternal age and 17 spouses. Main outcome measures: Knowledge of prenatal testing alternatives, decisional conflict, level of anxiety, and acceptability of the decision aid. Results: After using the decision aid, participants had significantly reduced decisional conflict (uncertainty) and a significant increase in knowledge. There was no effect on state or trait anxiety. More than three-quarters of participants were satisfied with the length, clarity, balance, and acceptability of the decision aid. Conclusions: The decision aid shows promise as a useful aid for preparing couples for counseling.     

Varieties of Three-Valued Heyting Algebras with a Quantifier

This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q ₃ of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q ₃ and we construct the lattice of subvarieties (Q ₃ ) of the variety Q ₃ .     

On the Existence of Continua of Logics Between Some Intermediate Predicate Logics

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.     

A Rule-Extension of the Non-Associative Lambek Calculus

An extension L ⁺ of the non-associative Lambek calculus Lis defined. In L ⁺ the restriction to formula-conclusion sequents is given up, and additional left introduction rules for the directional implications are introduced. The system L ⁺ is sound and complete with respect to a modification of the ternary frame semantics for L.     

On the Representation of N4-Lattices

N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. Finally, subdirectly irreducible N4-lattices are described.     

The Incompleteness of RGL

RGLis a version of the modal logic GLbased on the relevant logic R. It is shown that the class of RKframes that verify all theorems of RGLalso verify a scheme that we call (!). If RGLhas (!) as a theorem, however, it is not a relevant logic. I go on to show that not all instances of (!) are theorems of RGL, hence this logic is not complete over any class of RKframes.     

A Negationless Interpretation of Intuitionistic Theories. I

The present work contains an axiomatic treatment of some parts of the restricted version of intuitionistic mathematics advocated by G. F. C. Griss, also known as negationless intuitionistic mathematics. Formal systems NPC, NA, and FIM ^N for negationless predicate logic, arithmetic, and analysis are proposed. Our Theorem 4 in Section 2 asserts the translatability of Heyting's arithmetic HAinto NA. The result can in fact be extended to a large class of intuitionistic theories based on HAand their negationless counterparts. For instance, in Section 3 this is shown for Kleene's system of intuitionistic analysis FIMand our FIM ^N . This revised version was published online in June 2006 with corrections to the Cover Date.     

Statement of Removal

The Journal, Publisher and Author have agreed to remove this article having received expressions of concern regarding the representation of certain clinical data.

For more information, please contact the Publisher or Editor of this Journal.

Article title: Thinking Developmentally: A Contemporary Psychoanalytic Perspective

Authors: Sally Bloom-Feshbach

Journal: Journal of Infant, Child, and Adolescent Psychotherapy

Citation information: Volume 17, Number 2, pages 91–95

Version of Record Published Online: 31 May 2018

DOI: http://dx.doi.org/10.1080/15289168.2018.1456122     

The countable homogeneous universal model of B 2

We give a detailed account of the Algebraically Closed and Existentially Closed members of the second Lee class B ₂ of distributive p-algebras, culminating in an explicit construction of the countable homogeneous universal model of B ₂. The axioms of Schmid [7], [8] for the AC and EC members of B ₂ are reduced to what we prove to be an irredundant set of axioms. The central tools used in this study are the strong duality of Clark and Davey [3] for B ₂ and the method of Clark [2] for constructing AC and EC algebras using a strong duality. Applied to B ₂, this method transfers the entire discussion into an equivalent dual category X ₂ of Boolean spaces which carry a pair of tightly interacting orderings. The doubly ordered spaces of X ₂ prove to be much more readily constructed and analyzed than the corresponding algebras in B ₂.     

Causal explanations for lack of pregnancy applying the common sense model of illness representation to the fertility context

Abstract

Objectives: The current study explored causal explanations for lack of pregnancy and association with help-seeking behaviour. Differences based on gender and country Human Development Index were examined.

Design: A mixed method design was used.

Main outcome measures: Data were drawn from the International Fertility Decision-Making Study, a cross-sectional study of 10,045 individuals (1690 men; 8355 women) from 79 countries. Respondents rated to what extent they believed their lack of pregnancy was due to something they or their partner had done/not done or other factors and described their reasons for making this rating.

Results: Respondents were aged 18–50 (M?=?31.83) years, partnered and had been trying to achieve a pregnancy/father a child for over six months (M?=?2.8 years). Men and women primarily believed their lack of pregnancy was due to medical problems or chance/bad luck. Thematic analysis of textual responses from 29.7% of the sample found that respondents focused on their personal experience or a salient life event when describing the cause of their lack of pregnancy. Women expressed more regret and helplessness about causes than men. Significant country differences were observed.

Conclusions: Individuals may develop inaccurate causal explanations based on their personal experiences. Access to accurate information is necessary to facilitate timely help-seeking.     

Reducing demand for ineffective health remedies: overcoming the illusion of causality

Abstract

Objective: We tested a novel intervention for reducing demand for ineffective health remedies. The intervention aimed to empower participants to overcome the illusion of causality, which otherwise drives erroneous perceptions regarding remedy efficacy.

Design: A laboratory experiment adopted a between-participants design with six conditions that varied the amount of information available to participants (N?=?245). The control condition received a basic refutation of multivitamin efficacy, whereas the principal intervention condition received a full contingency table specifying the number of people reporting a benefit vs. no benefit from both the product and placebo, plus an alternate causal explanation for inefficacy over placebo.

Main outcome measures: We measured participants’ willingness to pay (WTP) for multivitamin products using two incentivized experimental auctions. General attitudes towards health supplements were assessed as a moderator of WTP. We tested generalisation using ratings of the importance of clinical-trial results for making future health purchases.

Results: Our principal intervention significantly reduced participants’ WTP for multivitamins (by 23%) and increased their recognition of the importance of clinical-trial results.

Conclusion: We found evidence that communicating a simplified full-contingency table and an alternate causal explanation may help reduce demand for ineffective health remedies by countering the illusion of causality.     

An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency

In this paper, I present the modal adaptive logic AJ ^r (based on S5) as well as the discussive logic D ^r ₂ that is defined from it. D ^r ₂ is a (non-monotonic) alternative for Jaśkowski’s paraconsistent system D ₂ . Like D ₂ , D ^r ₂ validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, D ^r ₂ moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D ₂ , this does not require the introduction of discussive connectives. It is argued that this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions.*Research for this paper was indirectly supported by the Flemish Minister responsible for Science and Technology (contract BIL1/8). The author is indebted to Leon Horsten, Jo?o Marcos, Jerzy Perzanowski, Liza Verhoeven, and especially to the referee and to Diderik Batens for comments and suggestions.     

Light Affine Set Theory: A Naive Set Theory of Polynomial Time

In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.In this paper, we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST.     

Constructive Logic with Strong Negation is a Substructural Logic. I

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL _ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL _ew . Presented by Heinrich Wansing     

The role of philosophy and ethics at the edges of medicine

Background

The purpose of this study is to make a philosophical argument against the phenomenological critique of standardization in clinical ethics. We used the context of clinical ethics in Saudi Arabia to demonstrate the importance of credentialing clinical ethicists.

Methods

Philosophical methods of argumentation and conceptual analysis were used.

Results

We found the phenomenological critique of standardization to be flawed because it relies on a series of false dichotomies.

Conclusions

We concluded that the phenomenological framing of the credentialing debate relies upon two extreme views to be navigated between, not chosen among, in the credentialing of clinical ethicists.

     

The effects of scenario-based risk information on perceptions of susceptibility to Chlamydia and HIV

Abstract

Objectives: The Self-Report Habit Index (SRHI) was originally reported as one-dimensional; however, habit has been described as characterised by several features. Moreover, one-dimensional models for the SRHI have demonstrated poor fit. Therefore, we aimed to compare multidimensional models with a one-dimensional model in both snacking and physical activity habits, besides examining further instrument characteristics.

Design: A cross-sectional study was conducted with high school and university students (n?=?555).

Main outcome measure: The SRHI adapted for physical activity and for snaking habits was applied at one time point.

Results: Nested models with one factor, two factors and three factors were compared. Next, a hierarchical second-order model was tested, and further validity issues, as well as invariance between habits, were examined. Three-dimensional models represented a better fit for both habits. However, fit was still inadequate in the snacking version. In addition, discriminant validity concerns emerged for the physical activity SRHI. Moreover, invariance between the snacking and the physical activity versions was not confirmed.

Conclusions: Considering the SRHI as composed by the dimensions of ‘lack of awareness’, ‘lack of control’ and ‘history of behavioural repetition’ seems to be more accurate. Nevertheless, our findings suggest that further research is needed.     

A modal sequent calculus for a fragment of arithmetic

Global properties of canonical derivability predicates (the standard example is Pr() in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, interpolation and the fixed point theorem.The second author holds a grant from the Consiglio Nazionale delle Ricerche, gruppo G.N.S.A.G.A.