Logic and Applications

The group is formed by Patrik Eklund, Ankica Babic, M.Ángeles Galán, Robert Helgesson, Ulrich Höhle, Mats Johansson, Johan Karlsson, Jari Kortelainen, Magnus Löfstrand and Michael Winter.

Traditional logic is informal and even overlapping about the production of its ingredients like, signatures, terms, sentences, entailments, models and inference rules. Traditional logic also avoids to describe how these ingredients latively appear in one and another, i.e., how terms are formally constructed from signatures, sentences proceed from terms, and so on. Our solution is to arrange logic latively, thereby providing individualization of logic, and also embracing a concept of logics in dialogue, with terms, sentences and entailments etc being transformed when communicated from one logic to the other.

Lative logic is a generalized framework and a universal structure, where specific logics of all kind can be incorporated. Lative logic uses signatures as a fundamental atomic structure, and category theory is its metalanguage. This also leads to a lative logic specific type theory, where our three-level arrangement of signatures is fundamental for a wide variety of applications. Logic in dialogue and social logic is important also for internal and external views of systems-of-systems.

Our approach to logic is also tightly coupled with logical methodology for computational intelligence. Bayesian, neural and similar methods, typically based only on rudimentary statistics and numerics, will not suffice for application development that require contextual decision-making. Our logically enriched computational intelligence provides a logical scope going far beyond traditional approaches to logic and ontology, and can be seen in our applications in the public and private sectors.

Logic
algebra and topology in logic
category theory as a metalanguage
computational intelligence
foundations of mathematics
lative logic
logic-based medicine
many-valued logic
social logic
type theory

Applications
active and healthy ageing
analytics in private and public sectors
clean energy
engineering systems and industrial engineering
financial engineering
industrial systems availability
social and health care classification, nomenclature and ontology
social choice