We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono’s algebraic approach to substructural logics. We propose generalized BI algebras (GBI-algebras) as a common framework for algebras arising via “declarative resource reading”, intuitionistic generalizations of relation algebras and arrow logics and the distributive Lambek cal...

some appropriate axioms (for details see [7]). These axioms imply that the relation ≈ on A defined by: a ≈ b if and only if a → b = 1 and b → a = 1, 1)/ ≈ is a Heyting algebra. For a given Heyting algebra B there always exists a Nelson algebra A such that A h is isomorphic to B: the Fidel-Vakarelov construction of the Nelson algebra N (B) (see e.g. [8]) yields an example of such an algebra. In ...

disease. One first-class original contribution, by John Brooke, compares the images of Whewell and Priestley as nineteenth-century caricatures embellished by twentieth-century sociologists. McEvoy summarizes his well-documented analysis of Priestley. Many ofthe other papers, based on exegesis ofparticular sides of Priestley's complex thoughts, connect perhaps too little with the original signif...

in this paper, we try to determine the status of the relation between dahr world and matrial world. the conclusion shows the subjective duality and objective unity of dahr and material entities. two interpretations of this duality can be suggested. in the first interpretation, this unity, and the duality supposed, are explained on the basis of different intellectual cognition of immaterial and ...

This study compares four different potential evapotranspiration equations according to Priestley Taylor, Kimberly Penman, Penman Monteith (FAO-56) and Hargreaves on a global basis to demonstrate their difference, and assess their impact on the calculation of stream flows. The various equations of potential evapotranspiration show great differences in magnitude. But due to the limited availabili...

1 Problem Show that the electric field vanishes inside a perfect conductor according to " all " definitions of this concept, while the interior magnetic field vanishes only under some definitions. This problem depends on the concept of a conductor, and of a perfect conductor. The phenomenon of conduction of electricity may have been first reported by Gray in 1731 [1], who described experiments ...

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".