Abstract interpretation (AI) is one of the most scalable automated approaches to program verification available today. To achieve efficiency, many steps of the analysis, e.g., joins and widening, lose precision. As a result, AI often produces false alarms, coming from the inability to find a safe inductive invariant even when it exists in a chosen abstract domain. To tackle this problem, we pre...

Proof of Craig’s Theorem: Assume that S is a deductively closed set of sentences, whose elements may be recursively enumerated thus F(0), F(1), ..., F(n), ..., where F is a recursive function from natural numbers to sentences (we assume that expressions, sentences, etc., have been Gödel-coded in some manner). The set of theorems of an axiomatic theory is automatically recursively enumerable. Bu...

s Review Panel Gerry Altmann, Sachiko Aoshima, Jennifer Arnold, William Badecker, Markus Bader, Ellen Gurman Bard, Julie Boland, Ina Bornkessel-Schlesewsky, Dianne Bradley, Holly Branigan, Diane Brentari, Sarah Brown-Schmidt, Marc Brysbaert, Petra Burkhardt, Helen Cairns, Katy Carlson, Manuel Carreiras, Craig G. Chambers, Harald Clahsen, Charles Clifton, David Corina, Martin Corley, Seana Couls...

Christian apologists, like Willian Lane Craig and Stephen T. Davis, argue that belief in Jesus’ resurrection is reasonable because it provides the best explanation of available evidence. In this article, I refute thesis. To do so, lay out how logic inference to (IBE) operates, including what good explanations must be by definition, then apply IBE issue at hand. Multiple explanations—including (...

Theorem 3.2 A consequence system (L,`) enjoys Craig interpolation with respect to an L-function var, if (i) there is a Craig generalized translation schema from (L,`) to another consequence system (L′,`′) with respect to var and an L′-function var′; (ii) (L′,`′) enjoys Craig interpolation with respect to var′. Proof: Let (h1, h2, h) be a Craig generalized translation schema from (L,`) to (L′,`′...

Image analysis is an image processing technique that aims to extract features or information from images. Image analysis in medicine has a special place because is a basis for disease diagnosis for physicians. Electrophoresis is a laboratory separating technique. Electrophoresis images are created during the electrophoresis process. Serum protein and hemoglobin electrophoresis test are the ...