Sport bodies: An examination of positive body image,sport-confidence,and subjective sport performance in Jamaican athletes

Guided by the Sport-Confidence Model, this study examined the associations among a positive body image, sport-confidence, and sport performance evaluations. Using a cross-sectional design, a purposive sample of 314 Jamaican athletes (male = 70.7%; $M_{age}$ = 22.85; SD = 4.89) completed measures of body and functionality appreciation, sport-confidence, and subjective sport performance. Results from path analysis provided evidence for good model-data fit. Body (B = 9.03, p < .001) and functionality (B = 4.93, p = .036) appreciation exerted direct effects on sport-confidence. Sport-confidence exerted a direct effect on sport performance evaluations (B = 0.09, p < .001). Body (B = 0.79, CI_95% [0.44, 1.17]) and functionality (B = 0.43, CI_95% [0.05, 0.92]) appreciation exerted indirect effects on sport performance evaluations through sport-confidence. Results indicate that supporting the development of a positive body image in athletes may contribute to feelings of sport-confidence and positive performance outcomes.     

Logic programming as classical inference

We propose a denotational semantics for logic programming based on a classical notion of logical consequence which is apt to capture the main proposed semantics of logic programs. In other words, we show that any of those semantics can be viewed as a relation of the form $T{\models }^{\star }X$ where T is a theory which naturally represents the logic program under consideration together with a set of formulas playing the role of “hypotheses”, in a way which is dictated by that semantics, ${\models }^{\star }$ is a notion of logical consequence which is classical because negation, disjunction and existential quantification receive their classical meaning, and X represents what can be inferred from the logic program, or an intended interpretation of that logic program (such as an answer-set, its well-founded model, etc.). The logical setting we propose extends the language of classical modal logic as it deals with modal operators indexed by ordinals. We make use of two kinds of basic modal formulas: ${\square }_{\alpha }\phi$ which intuitively means that the logical program can generate φ by stage α of the generation process, and ${◇}_{\alpha }{\square }_{\beta }\phi$ with $\alpha >\beta$, which intuitively means that φ can be used as a hypothesis from stage β of the generation process onwards, possibly expecting to confirm φ by stage α (so expecting ${\square }_{\alpha }\phi$ to be generated). This allows us to capture Rondogiannis and Wadge's version of the well-founded semantics [27] where a member of the well-founded model is a closed atom which receives an ordinal truth value of ${\mathtt{true}}_{\alpha }$ or ${\mathtt{false}}_{\alpha }$ for some ordinal α: in our framework, this corresponds to having $T{\models }^{\star }{\square }_{\alpha }\phi$ or $T{\models }^{\star }{\square }_{\alpha }\neg \phi$, respectively, with T being the natural representation of the logic program under consideration and the right set of “hypotheses” as dictated by the well-founded semantics. The framework we present goes much beyond the proposed traditional semantics for logic programming, as it can for instance let us investigate under which conditions a set of hypotheses can be minimal, with each hypothesis being activated as late as possible and confirmed as soon as possible, setting the theoretical foundation to sophisticated ways of making local use of hypotheses in knowledge-based systems, while still being theoretically grounded in a classical notion of logical consequence.     

A family of Gödel hybrid logics

In this paper, we define a family of fuzzy hybrid logics that are based on Gödel logic. It is composed of two infinite-valued versions called ${\mathsf{GH}}_{\infty }$ and ${\mathsf{WGH}}_{\infty }$, and a sequence of finitary valued versions ${({\mathsf{GH}}_n)}_{0<n<\infty }$. We define decision procedures for both ${\mathsf{WGH}}_{\infty }$ and ${({\mathsf{GH}}_n)}_{0<n<\infty }$ that are based on particular sequents and on a set of proof rules dealing with such sequents. As these rules are strongly invertible the procedures naturally allow one to generate countermodels. Therefore we prove the decidability and the finite model property for these logics. Finally, from the decision procedure of ${\mathsf{WGH}}_{\infty }$, we design a sound and complete sequent calculus for this logic.     

Bridging Curry and Church's typing style

There are two versions of type assignment in the λ-calculus: Church-style, in which the type of each variable is fixed, and Curry-style (also called “domain free”), in which it is not. As an example, in Church-style typing, ${\lambda }_{x:A}.x$ is the identity function on type A, and it has type $A\to A$ but not $B\to B$ for a type B different from A. In Curry-style typing, ${\lambda }_x.x$ is a general identity function with type $C\to C$ for every type C. In this paper, we will show how to interpret in a Curry-style system every Pure Type System (PTS) in the Church-style without losing any typing information. We will also prove a kind of conservative extension result for this interpretation, a result which implies that for most consistent PTSs of the Church-style, the corresponding Curry-style system is consistent. We will then show how to interpret in a system of the Church-style (a modified PTS, stronger than a PTS) every PTS-like system in the Curry style.