We present a basis for a category-theoretic account of Mendler-style inductive types. The account is based on suitably defined concepts of Mendler-style algebra and algebra homomorphism; Mendler-style inductive types are identified with initial Mendler-style algebras. We use the identification to obtain a reduction of conventional inductive types to Mendler-style inductive types and a reduction...

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limi...

Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning, reaching the important conclusion that it is at least as powerful as inductive reasoning (specifically, they showed that each inductive proof can be translated into a cyclic proof). We add to their investigation by proving the converse of this result, namely that each inductive proof can be translated into an ...

Inductive learning techniques can be utilised to build a set of IF-THEN rules from a given example data set. This paper presents a new technique for inductive learning called GAIL (Genetic Algorithm for Inductive Learning) which is based on Genetic Algorithms. Common algorithms for inductive learning are briefly reviewed. The GAIL algorithm is described and results are shown for two benchmark d...

background: basil (ocimum basilicum l.), a member of the lamiaceae family, has traditionally been used as a medicinal plant in the treatment of headaches, coughs, diarrhea, constipation, warts, worms, and kidney malfunctions. objective: to investigate the foliar application effects of bio-stimulators and bio-fertilizers on morphological and phytochemical traits of basil (ocimum basilicum l.). m...

objective: the aim of present study was to evaluate the quality, density and thickness of newly formed bone in experimental defects treated with combi-pack®, bio-oss® and biostite®. materials and methods: eight new zealand white rabbits were included in this randomized,blinded study. four equal 3×6 mm bone defects were created on the frontal and parietal bones of each animal and three were imme...

the co-inoculation of mulberry with phosphate solubilizing micro-organisms, nitrogen fixing bacteria and arbuscular mycorrhiza has influenced its macronutrient uptake through leaf. the data revealed that maximum nitrogen (484.12 kg /ha) , phosphorus (59.83 kg /ha) and potassium (244.61 kg/ha) uptake through leaf has taken place due to co-inoculation treatments as compared to the un inoculated t...

background: bio aerosols include airborne micro-organisms such as bacteria, fungi, viruses, etc and their products. exposure to a bio aerosol is linked with a broad spectrum of health problems, including infectious diseases, acute toxic effects, allergies, and cancer. the aim of this study was to evaluate the quality and quantity of bio aerosols found in the air of different wards in valiasr ho...

This is the fourth in a series of papers extending Martin-Löf’s meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of cubical inductive types, inductive types whose constructors may take dimension parameters and may have specified boundaries. Using this schema, we are able to speci...