23,068 research outputs found
A decidable weakening of Compass Logic based on cone-shaped cardinal directions
We introduce a modal logic, called Cone Logic, whose formulas describe
properties of points in the plane and spatial relationships between them.
Points are labelled by proposition letters and spatial relations are induced by
the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening
of Venema's Compass Logic. We prove that, unlike Compass Logic and other
projection-based spatial logics, its satisfiability problem is decidable
(precisely, PSPACE-complete). We also show that it is expressive enough to
capture meaningful interval temporal logics - in particular, the interval
temporal logic of Allen's relations "Begins", "During", and "Later", and their
transposes
Protention and retention in biological systems
This paper proposes an abstract mathematical frame for describing some
features of cognitive and biological time. We focus here on the so called
"extended present" as a result of protentional and retentional activities
(memory and anticipation). Memory, as retention, is treated in some physical
theories (relaxation phenomena, which will inspire our approach), while
protention (or anticipation) seems outside the scope of physics. We then
suggest a simple functional representation of biological protention. This
allows us to introduce the abstract notion of "biological inertia".Comment: This paper was made possible only as part of an extended
collaboration with Francis Bailly (see references), a dear friend and
"ma\^itre \'a penser", who contributed to the key ideas. Francis passed away
in february 2008: we continue here our inspiring discussions and joint wor
- …