The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łukasiewicz’s 3-Valued Logic Ł3

25 p.We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix (with both only one and two designated values) and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova (Rep Math Log 47:173–182, 2012).S

Modeling the interaction of computer errors by four-valued contaminating logics

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics

Construct validation of a non-exercise measure of cardiorespiratory fitness in older adults

<p>Abstract</p> <p>Background</p> <p>Cardiorespiratory fitness (CRF) is associated with a decreased risk of all-cause mortality but is rarely assessed in medical settings due to burdens of time, cost, risk, and resources. The purpose of this study was to test the construct validity of a regression equation developed by Jurca and colleagues (2005) to estimate CRF without exercise testing in community dwelling older adults.</p> <p>Methods</p> <p>Participants (n = 172) aged 60 to 80 years with no contraindications to submaximal or maximal exercise testing completed a maximal graded exercise test (GXT) and the submaximal Rockport 1-mile walk test on separate occasions. Data included in the regression equation (age, sex, body mass index, resting heart rate, and physical activity) were obtained via measurement or self-report. Participants also reported presence of cardiovascular conditions.</p> <p>Results</p> <p>The multiple R for the regression equation was .72, <it>p < .001 </it>and CRF estimated from this equation was significantly correlated with the MET value from the GXT (<it>r </it>= 0.66) and with CRF estimated from submaximal field testing (<it>r </it>= 0.67). All three CRF indices were significantly and inversely associated with reporting more cardiovascular conditions.</p> <p>Conclusions</p> <p>This research provides preliminary evidence that a non-exercise estimate of CRF is at least as valid as field test estimates of CRF and represents a low-risk, low-cost, and expedient method for estimating fitness in older adults.</p