In the eld of inductive theorem proving syntactical diierences between the induction hypothesis and induction conclusion are used in order to guide the proof BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent synt...

This article covers the issues of remodeling breast milk’s protective properties during creating infant milk formulas. First all, this concerns conditions for normal intestinal microbiota development in growing organism. Its quantitative and qualitative features are trigger either sanogenetic, or pathological immune metabolic reactions, also determine gut-brain axis functioning. The significanc...

We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counter-example guided inductive synthesis principle (CEGIS) and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely ...

In legal reasoning systems, a typical application of normative reasoning, partial information plays an important role in the representation and reasoning of legal knowledge. To construct a legal knowledge-base with partial information, many features are required of knowledge representation languages. In this paper, we discuss the representation of knowledge-bases and their re nement through our...

This paper studies an extension of inductive de nitions in the context of a type-free theory. It is a kind of simultaneous inductive de nition of two predicates where the de ning formulas are monotone with respect to the rst predicate, but not monotone with respect to the second predicate. We call this inductive de nition half-monotone in analogy of Allen's term half-positive. We can regard thi...

In two earlier papers we derived congruence formats for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation. Here this work is extended with important stability a...