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

Late Smithian microbial deposits and their lateral marine fossiliferous limestones (Early Triassic, Hurricane Cliffs, Utah, USA)

International audienceRecurrent microbialite proliferations during the Early Triassic are usually explained by ecological relaxation and abnormal oceanic conditions. Most Early Triassic microbialites are described as single or multiple lithological units without detailed ecological information about lateral and coeval fossiliferous deposits. Exposed rocks along Workman Wash in the Hurricane Cliffs (southwestern Utah, USA) provide an opportunity to reconstruct the spatial relationships of late Smithian microbialites with adjacent and contemporaneous fossiliferous sediments. Microbialites deposited in an intertidal to subtidal interior platform are intercalated between inner tidal flat dolosiltstones and subtidal bioturbated fossiliferous limestones. Facies variations along these fossiliferous deposits and microbialites can be traced laterally over a few hundreds of meters. Preserved organisms reflect a moderately diversified assemblage, contemporaneous to the microbialite formation. The presence of such a fauna, including some stenohaline organisms (echinoderms), indicates that the development of these late Smithian microbial deposits occurred in normal-marine waters as a simple facies belt subject to relative sea-level changes. Based on this case study, the proliferation of microbialites cannot be considered as direct evidence for presumed harsh environmental conditions