A Hybrid Method for Modeling and Solving Supply Chain Optimization Problems with Soft and Logical Constraints

This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful for modeling problems resulting from commercial agreements, contracts, competition, technology, safety, and environmental conditions. Two programming and solving environments, mathematical programming (MP) and constraint logic programming (CLP), were combined in the hybrid method. This integration, hybridization, and the adequate multidimensional transformation of the problem (as a presolving method) helped to substantially reduce the search space of combinatorial models for supply chain optimization problems. The operation research MP and declarative CLP, where constraints are modeled in different ways and different solving procedures are implemented, were linked together to use the strengths of both. This approach is particularly important for the decision and combinatorial optimization models with the objective function and constraints, there are many decision variables, and these are summed (common in manufacturing, supply chain management, project management, and logistic problems). The ECLiPSe system with Eplex library was proposed to implement a hybrid method. Additionally, the proposed hybrid transformed model is compared with the MILP-Mixed Integer Linear Programming model on the same data instances. For illustrative models, its use allowed finding optimal solutions eight to one hundred times faster and reducing the size of the combinatorial problem to a significant extent

The 1900 Turn in Bertrand Russell’s Logic, the Emergence of his Paradox, and the Way Out

Russell’s initial project in philosophy (1898) was to make mathematics rigorous reducing it to logic. Before August 1900, however, Russell’s logic was nothing but mereology. First, his acquaintance with Peano’s ideas in August 1900 led him to discard the part-whole logic and accept a kind of intensional predicate logic instead. Among other things, the predicate logic helped Russell embrace a technique of treating the paradox of infinite numbers with the help of a singular concept, which he called ‘denoting phrase’. Unfortunately, a new paradox emerged soon: that of classes. The main contention of this paper is that Russell’s new conception only transferred the paradox of infinity from the realm of infinite numbers to that of class-inclusion. Russell’s long-elaborated solution to his paradox developed between 1905 and 1908 was nothing but to set aside of some of the ideas he adopted with his turn of August 1900: (i) With the Theory of Descriptions, he reintroduced the complexes we are acquainted with in logic. In this way, he partly restored the pre-August 1900 mereology of complexes and simples. (ii) The elimination of classes, with the help of the ‘substitutional theory’, and of propositions, by means of the Multiple Relation Theory of Judgment, completed this process

Tool support for reasoning in display calculi

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, that allows us to adapt the tool for a wide variety of user defined calculi

Crisis of Fundamentality → Physics, Forward → Into Metaphysics → The Ontological Basis of Knowledge: Framework, Carcass, Foundation

The present crisis of foundations in Fundamental Science is manifested as a comprehensive conceptual crisis, crisis of understanding, crisis of interpretation and representation, crisis of methodology, loss of certainty. Fundamental Science "rested" on the understanding of matter, space, nature of the "laws of nature", fundamental constants, number, time, information, consciousness. The question "What is fundametal?" pushes the mind to other questions → Is Fundamental Science fundamental? → What is the most fundamental in the Universum?.. Physics, do not be afraid of Metaphysics! Levels of fundamentality. The problem №1 of Fundamental Science is the ontological justification (basification) of mathematics. To understand is to "grasp" Structure ("La Structure mère"). Key ontological ideas for emerging from the crisis of understanding: total unification of matter across all levels of the Universum, one ontological superaxiom, one ontological superprinciple. The ontological construction method of the knowledge basis (framework, carcass, foundation). The triune (absolute, ontological) space of eternal generation of new structures and meanings. Super concept of the scientific world picture of the Information era - Ontological (structural, cosmic) memory as "soul of matter", measure of the Universum being as the holistic generating process. The result of the ontological construction of the knowledge basis: primordial (absolute) generating structure is the most fundamental in the Universum

Using Qualitative Hypotheses to Identify Inaccurate Data

Identifying inaccurate data has long been regarded as a significant and difficult problem in AI. In this paper, we present a new method for identifying inaccurate data on the basis of qualitative correlations among related data. First, we introduce the definitions of related data and qualitative correlations among related data. Then we put forward a new concept called support coefficient function (SCF). SCF can be used to extract, represent, and calculate qualitative correlations among related data within a dataset. We propose an approach to determining dynamic shift intervals of inaccurate data, and an approach to calculating possibility of identifying inaccurate data, respectively. Both of the approaches are based on SCF. Finally we present an algorithm for identifying inaccurate data by using qualitative correlations among related data as confirmatory or disconfirmatory evidence. We have developed a practical system for interpreting infrared spectra by applying the method, and have fully tested the system against several hundred real spectra. The experimental results show that the method is significantly better than the conventional methods used in many similar systems.Comment: See http://www.jair.org/ for any accompanying file

Return of Logos: Ontological Memory → Information → Time

Total ontological unification of matter at all levels of reality as a whole, its “grasp” of its dialectical structure, space dimensionality and structure of the language of nature – “house of Being” [1], gives the opportunity to see the “place” and to understand the nature of information as a phenomenon of Ontological (structural) Memory (OntoMemory), the measure of being of the whole, “the soul of matter”, qualitative quantity of the absolute forms of existence of matter (absolute states). “Information” and “time” are multivalent phenomena of Ontological Memory substantiating the essential unity of the world on the “horizontal” and “vertical”. Ontological constructing of dialectics of Logos self-motion, total unification of matter, “grasp” of the nature of information leads to the necessity of introducing a new unit of information showing the ideas of dialectical formation and generation of new structures and meanings, namely Delta-Logit (Δ-Logit), qualitative quantum-prototecton, fundamental organizing, absolute existential-extreme. The simplest mathematical symbol represents the dialectical microprocessor of the Nature. Ontological formula of John A. Wheeler «It from Bit» [2] is “grasped” as the first dialectic link in the chain of ontological formulas → “It from Δ-Logit” → “It from OntoMemory” → “It from Logos, Logos into It”. Ontological Memory - core, semantic attractor of the new conceptual structure of the world of the Information Age, which is based on Absolute generating structure («general framework structure»), the representant of onto-genetic code and algorithm of the Universe