A Strong Completeness Theorem for the Gentzen systems associated with finite algebras
ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems.
Live Graphical Computing Logic, Virtual Trees, and Visualization
The paper is a preliminary overview to a virtual tree computing logic with applications to Virtual Reality. Meta-contextual logic is combined with Morph Gentzen, a new computing logic the author presented in 1997. It has applications towards Virtual RealityVR computing since the trees on the languages can carry visual structures via functions. Designated functions define agents, as specific function symbols, to represent languages with only abstract definition known at syntax. The languages are called “Intelligent” in the sense that there are designated function symbols on the syntax with explicit signature annotations, for example having to have 1-1 functions only on a subsignture. Generic diagrams for models are defined as yet a second order lift from context. The techniques allowed us to define a computational linguistics and model theory for “intelligent languages,” i.e. agent augmented languages. Applications to visual computing with agent JAVA are alluded to. * Prjekakdmkrd.tripod.com Academic E-mail cyrusfn@alum.mit.edu
Heat Recovery Systems
Geothermal energy is recovered from an underground zone of relatively hot strata via a borehole into which is inserted a heat pipe system containing a working fluid, the heat pipe system comprising an assembly of two tubes in concentric relation, the inner tube being constituted by a relatively small diameter capillary for the return of working fluid to the vicinity of the zone of the relatively hot strata. The working fluid is preferably assisted in its return under gravity by means of a pump. The system includes heat exchange means operable to recover thermal energy from the working fluid. A third and outermost tube may be used to reduce heat losses, this third tube enclosing the two tubes over all but that part of their length which is in the zone of relatively hot strata.