Projects / Programmes
On Linear Logic and Its Extensions
| Code |
Science |
Field |
Subfield |
| 1.01.06 |
Natural sciences and mathematics |
Mathematics |
Probability and statistics |
| Code |
Science |
Field |
| P110 |
Natural sciences and mathematics |
Mathematical logic, set theory, combinatories |
linear logic, n-contraction, n-weakening, free algebra, game semantics, cut-elimination, decidability, interpolation, set theory, dynamic intensional logic.
Researchers (1)
| no. |
Code |
Name and surname |
Research area |
Role |
Period |
No. of publicationsNo. of publications |
| 1. |
05954 |
PhD Andreja Prijatelj |
Mathematics |
Head |
1998 - 1999 |
0 |
Organisations (1)
Abstract
This project consists of six open problems that, with a single exception, arise from linear logic. With the birth of linear logic, J. - Y. Girard presented new foundations of mathematical logic. Its flourishing development up till now has connected the research in logic with a number of other branches in Mathematics (i.e. algebra, linear algebra, category theory, set theory) as well as with theoretical computer science and artificial intelligence. One of the central, still nowadays open problems of linear logic is to determine a corresponding complete
semantics yielding a natural interpretation of exponentials. Our proposal to this end is to extend the systems of linear logic with bounded structural rules of n-contraction and n-weakening (with n > 1). In this extended systems, both linear modalities can be defined solely by corresponding multiplicative connectives. It turns out, that this is a bridge to be crossed in order to find a corresponding complete semantics in terms of game theory on a suitable free lattice structure. However, the extended linear systems do not enjoy the cut-elimination property. Thus, there are no standard proof-theoretic methods to investigate their meta-properties. Instead, our successful approach is the use of algebraic models, in particular free
ordered algebraic structures, the constructions of which present new results in algebra
itself. The next research topics deal with decidability and interpolation problems for the
cut-free systems of extended linear logic and the consistency problem of the unrestricted
comprehension scheme in set theory based on linear logic. The final ''isolated'' problem,
arising from 1987, presents a representation theorem for models of dynamic intentensinal logic.
