The Higher-Order Prover Leo-II.

Leo-II is an automated theorem prover for classical higher-order logic. The prover has pioneered cooperative higher-order-first-order proof automation, it has influenced the development of the TPTP THF infrastructure for higher-order logic, and it has been applied in a wide array of problems. Leo-II may also be called in proof assistants as an external aid tool to save user effort. For this it is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants. Recent progress in this direction is reported for the Isabelle/HOL system.The Leo-II project has been supported by the following grants: EPSRC grant EP/D070511/1 and DFG grants BE/2501 6-1, 8-1 and 9-1.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10817-015-9348-y

Public Announcement Logic in HOL

A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic. It is demonstrated (i) how meta-theoretical studies can be automated this way, and (ii) how non-trivial reasoning in the target logic (public announcement logic), required e.g. to obtain a convincing encoding and automation of the wise men puzzle, can be realized. Key to the presented semantical embedding -- in contrast, e.g., to related work on the semantical embedding of normal modal logics -- is that evaluation domains are modeled explicitly and treated as additional parameter in the encodings of the constituents of the embedded target logic, while they were previously implicitly shared between meta logic and target logic.Comment: 3rd DaL\'i Workshop, Dynamic Logic: New Trends and Applications, Online, 9-10 October 202

Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories

The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expressive power of Church's type theory as a meta-logic to semantically embed a combination of quantified non-classical logics, our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive encodings of complex ethical theories and their automation on the computer are no longer antipodes.Comment: 14 page

Cloning, annotation and developmental expression of the chicken intestinal MUC2 gene

Intestinal mucin 2 (MUC2) encodes a heavily glycosylated, gel-forming mucin, which creates an important protective mucosal layer along the gastrointestinal tract in humans and other species. This first line of defense guards against attacks from microorganisms and is integral to the innate immune system. As a first step towards characterizing the innate immune response of MUC2 in different species, we report the cloning of a full-length, 11,359 bp chicken MUC2cDNA, and describe the genomic organization and functional annotation of this complex, 74.5 kb locus. MUC2 contains 64 exons and demonstrates distinct spatiotemporal expression profiles throughout development in the gastrointestinal tract; expression increases with gestational age and from anterior to posterior along the gut. The chicken protein has a similar domain organization as the human orthologue, with a signal peptide and several von Willebrand domains in the N-terminus and the characteristic cystine knot at the C-terminus. The PTS domain of the chicken MUC2 protein spans ~1600 amino acids and is interspersed with four CysD motifs. However, the PTS domain in the chicken diverges significantly from the human orthologue; although the chicken domain is shorter, the repetitive unit is 69 amino acids in length, which is three times longer than the human. The amino acid composition shows very little similarity to the human motif, which potentially contributes to differences in the innate immune response between species, as glycosylation across this rapidly evolving domain provides much of the musical barrier. Future studies of the function of MUC2 in the innate immune response system in chicken could provide an important model organism to increase our understanding of the biological significance of MUC2 in host defense and highlight the potential of the chicken for creating new immune-based therapies

Automating Access Control Logics in Simple Type Theory with LEO-II

Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory (which is also known as higher-order logic) and we have demonstrated that the higher-order theorem prover LEO-II can automate reasoning in and about them. In this paper we combine these results and describe a sound and complete embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEO-II can be applied to automate reasoning in prominent access control logics.Comment: ii + 20 page

The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency

Computer-supported Exploration of a Categorical Axiomatization of Modeloids

A modeloid, a certain set of partial bijections, emerges from the idea to abstract from a structure to the set of its partial automorphisms. It comes with an operation, called the derivative, which is inspired by Ehrenfeucht-Fra\"iss\'e games. In this paper we develop a generalization of a modeloid first to an inverse semigroup and then to an inverse category using an axiomatic approach to category theory. We then show that this formulation enables a purely algebraic view on Ehrenfeucht-Fra\"iss\'e games.Comment: 24 pages; accepted for conference: Relational and Algebraic Methods in Computer Science (RAMICS 2020