Dual Systems of Sequents and Tableaux for Many-Valued Logics

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and the exclusion of the opposite truth value describe the same situation.

Elimination of Cuts in First-order Finite-valued Logics

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information

Systematic construction of natural deduction systems for many-valued logics

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems

The image torque operator: A new tool for mid-level vision

Contours are a powerful cue for semantic image understanding. Objects and parts of objects in the image are delineated from their surrounding by closed contours which make up their boundary. In this paper we introduce a new bottom-up visual operator to capture the concept of closed contours, which we call the ’Torque ’ operator. Its computation is inspired by the mechanical definition of torque or moment of force, and applied to image edges. The torque operator takes as input edges and computes over regions of different size a measure of how well the edges are aligned to form a closed, convex contour. We explore fundamental properties of this measure and demonstrate that it can be made a useful tool for visual attention, segmentation, and boundary edge detection by verifying its benefits on these applications. 1