Conjunction and Disjunction in Infectious Logics

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction

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

Logics based on linear orders of contaminating values

A wide family of many-valued logics - for instance, those based on the weak Kleene algebra - includes a non-classical truth-value that is 'contaminating' in the sense that whenever the value is assigned to a formula $arphi$, any complex formula in which $arphi appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behaviour is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper

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

Silver nanoparticles deposited on calcium hydrogenphosphate – silver phosphate matrix; biological activity of the composite

The composite containing nanosilver uniformly deposited on matrix composed of CaHPO4  x 2H2 O (brushite, ca 89 mass %), CaHPO4  (monteonite, ca 9.5 mass%), and Ag3 PO4  (0.5 mas%) was obtained by addition of calcium nitrate and silver nitrate aqueous solution at 30:1 Ca:Ag molar ratio into excess of (NH4 )2 PO4  solution at pH 5.0 – 5.5. The isolated solid was characterized by STEM, XRD, and LDI mass spectrometry. It has been found that nanosilver was uniformly distributed within composite as 3 PO4  as identified by XRD method. The composite showed strong growth inhibition in E. coli and P. aeruginosa strains, and moderate towards S. aureus. The C. albicans cells were the most resistant to the tested material, although still composite was moderately cytostatic for the yeast

Silver nanoparticles deposited on calcium hydrogenphosphate – silver phosphate matrix; biological activity of the composite

The composite containing nanosilver uniformly deposited on matrix composed of CaHPO4  x 2H2 O (brushite, ca 89 mass %), CaHPO4  (monteonite, ca 9.5 mass%), and Ag3 PO4  (0.5 mas%) was obtained by addition of calcium nitrate and silver nitrate aqueous solution at 30:1 Ca:Ag molar ratio into excess of (NH4 )2 PO4  solution at pH 5.0 – 5.5. The isolated solid was characterized by STEM, XRD, and LDI mass spectrometry. It has been found that nanosilver was uniformly distributed within composite as 3 PO4  as identified by XRD method. The composite showed strong growth inhibition in E. coli and P. aeruginosa strains, and moderate towards S. aureus. The C. albicans cells were the most resistant to the tested material, although still composite was moderately cytostatic for the yeast

Evolutionary rates of Jurassic ammonites in relation to sea-level fluctuations

An analysis is presented of the diversity and faunal turnover of Jurassic ammonites related to transgressive /regressive events. The data set contained 400 genera and 1548 species belonging to 67 ammonite zones covering the entire Jurassic System. These data were used in the construction of faunal turnover curves and ammonite diversities, that correlate with sea-level fluctuation curves. Twenty-four events of ammonite faunal turnover are analyzed throughout the Jurassic. The most important took place at the Sinemurian-Carixian boundary, latest Carixian-Middle Domerian, Domerian-Toarcian boundary, latest Middle Toarcian-Late Toarcian, Toarcian-Aalenian boundary, latest Aalenian-earliest Bajocian, latest Early Bajocian-earliest Late Bojocian, Early Bathonian-Middle Bathonian boundary, latest Middle Bathonian-earliest Late Bathonian, latest Bathonian-Early Callovian, earliest Early Oxfordian-Middle Oxfordian, earliest Late Oxfordian-latest Oxfordian, latest Early Kimmeridgian, Late Kimmeridgian, middle Early Tithonian and Early Tithonian-Late Tithonian boundary. More than 75 percent of these turnovers correlate with regressive-transgressive cycles in the Exxon, and /or Hallam's sea-level curves. Inmost cases the extinction events coincide with regressive intervals, whereas origination and radiation events are related to transgressive cycles. The turnovers frequently coincide with major or minor discontinuities in the Subbetic basin (Betic Cordillera)