"Logic leaps and boundaries: how logic benefits from, and furthers, interdisciplinary research"
Nik Sultana
Development in logic arises from a dialogue between philosophy, mathematics, and computing.
Each of these areas has nurtured logic with new questions and each has contributed fresh ideas that often
emerge from an area's unique viewpoint. For instance, philosophy tends to explore high-level ideas
whereas mathematics makes ideas precise and carries out a rigorous exploration of the theory.
Computing sometimes overlaps with mathematics, but it tends to emphasise the mechanisation of
mathematical ideas. Developments in computational logic liberate us from tedious, repetitive tasks
and calculations -- consequently this frees up energy to explore new areas.
Logic's inherent interdisciplinarity has benefited all three areas and is reinforced by the circulation of
people and ideas between them. The general theme of logic in all three areas remains the study of
correct reasoning, but the specific technical points being explored are richly varied and their
scope within reasoning is often far from obvious.
Other than the three subjects mentioned above, logic also interacts with a broad variety of other subjects
including engineering, law, and medicine, in which logic is applied to solve concrete problems,
and from which logic could draw ideas for further generalisation. Furthermore, new opportunities for
interaction with logic are being opened up as branches of empirical sciences are becoming more formal.
This is because logic is instrumental in establishing a bedrock for theoretical developments of any nature.
Due to logic's interdisciplinarity, there are many ways of measuring progress in the field. Examples of
activities that contribute to progress in logic include: defining new logics, deriving new theorems,
discovering new methods, formalising existing theories, and so on. There is no shortage of open
questions in logic. One of the most general and persistent questions is how to reason about complex artefacts.
Such artefacts include aeroplane control software, and it is desirable to rigorously show them to possess
certain properties -- such as "correctness". The solution of such problems benefits from collaborative,
interdisciplinary effort and its practical consequences include increased security and safety in society.