The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a deductive inference method for PC(ID), its propositional fragment. We introduce a formal proof system based on the sequent calculus (Gentzen-style deductive system) for this logic. As PC(ID) is an integration of classical propositional logic a...

The run-time verification logic Eagle is equipped with two forms of binary cut operator, sequential composition ( ; ) and concatenation (·). Essentially, a concatenation formula F1 · F2 holds on a trace if that trace can be cut into two non-overlapping traces such that F1 holds on the first and F2 on the second. Sequential composition differs from concatenation in that the two traces must overl...

Hilbert’s epsilon substitution method provides a technique for showing that a theory is consistent by producing progressively more accurate computable approximations to the non-computable components of a proof. If it can be shown that this process eventually halts with a sufficiently good approximation, the theory is consistent. Here we produce a new formulation of the method for the theory ID1...

We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation affine logic into intuitionistic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict non-strict order pairs, cut-valued metrics, spaces. also explain the bifurcation some classical using choice ...

The rapid increase of non-linear loads in the last three decades has caused electrical quantities such as voltages and currents in 3-phase distribution systems to become distorted waveforms. This paper reviews, explains and discusses some new concepts, definitions and new available theory in the unbalanced and distorted systems. The usefulness of the proposed practical definitions is investigat...