Analyzing the selection of the herbrand base process for building a Smart Semantic Tree Theorem Prover

Traditionally, semantic trees have played an important role in proof theory for validating the unsatisfiability of sets of clauses. More recently, they have also been used to implement more practical tools for verifying the unsatisfiability of clause sets in first-order predicate logic. The method ultimately relies on the Herbrand Base, a set used in building the semantic tree. The Herbrand Base is used together with the Herbrand Universe, which stems from the initial clause set in a particular theorem. When searching for a closed semantic tree, the selection of suitable atoms from the Herbrand Base is very important and should be carried out carefully by educated guesses in order to avoid building a tree using atoms which are irrelevant for the proof. In an effort to circumvent the creation of irrelevant ground instances, a novel approach is investigated in this dissertation. As opposed to creating the ground instances of the clauses in S in a strict syntactic order, the values will be established through calculations which are based on relevance for the problem at hand. This idea has been applied and accordingly tested with the use of the Smart Semantic Tree Theorem Prover (SSTTP), which provides an algorithm for choos- ing prominent atoms from the Herbrand Base for utilisation in the generation of closed semantic trees. Part of this study is an empirical investigation of this prover performance on first-order problems without equality, as well as whether or not it is able to compete with modern theorem provers in certain niches. The results of the SSTTP are promising in terms of finding proofs in less time than some of the state-of-the-art provers. However, it can not compete with them in terms of the total number of the solved problems

Logic and the Foundations of Game and Decision Theory (LOFT 7)

This volume collects together revised papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2006). LOFT is a key venue for presenting research at the intersection of logic, economics and computer science, and the present collection gives a lively and wide-ranging view of an exciting and rapidly growing area

Fluid Flow Simulation and Optimisation with Lattice Boltzmann Methods on High Performance Computers - Application to the Human Respiratory System

An overall strategy for numerical simulations of the full human respiratory system is introduced. The integrative approach takes advantage of numerical simulation, high performance computing and newly developed mathematical optimisation techniques, all based on a mesoscopic model description and on lattice Boltzmann methods as discretisation strategies. Validated numerical results are presented for the simulation of respirations in a real human lung and nose geometry captured by CT

Proceedings of the 2nd Conference on Production Systems and Logistics (CPSL 2021)

Proceedings of the CPSL 202

DARWIN ≥ MARX - ECO/LOGICAL R/EVOLUTION

Eco/logical R/evolution, is the story of mankind, told with words of a great and wonderful subjective odyssey, the never-ending quest; for objective truths and collective Eudaimonia. The author raises the issues; of political weakness and widespread confusion, about logical analytical errors, of which we find many of in Old Marxist Ideology. As a conscious effort, is thus made, to expel the mental subjugation of Platonic Idealism, away from the clenches Aristotelian Realism, and its bastard offspring; Old Historical Materialism. The book identifies, in the works of Darwin and Marx, a wide range of worrying philosophical incompatibilities, such that are clearly found; in their respective theories and research methodologies. We hereby propose; that a New Marxist Philosophy of Science, stands a probable chance; at unifying the Natural and Social Sciences. As the convergence of truths is manifest, thus, it is mapped out in detail by the author, out of necessity. It invokes, a Marxist Metaphysical Identity, for the sole purpose off; presenting a teleological framework, for New Marxist Theory. NOTE: Reader must look up each word in a dictionary, which they see on both sides of the "/" when found in the middle of a word

Emergence through conflict : the Multi-Disciplinary Design System (MDDS)

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2009.Includes bibliographical references (p. 413-430).This dissertation proposes a framework and a group of systematic methodologies to construct a computational Multi-Disciplinary Design System (MDDS) that can support the design of complex systems within a variety of domains. The way in which the resulting design system is constructed, and the capabilities it brings to bare, are totally different from the methods used in traditional sequential design. The MDDS embraces diverse areas of research that include design science, systems theory, artificial intelligence, design synthesis and generative algorithms, mathematical modeling and disciplinary analyses, optimization theory, data management and model integration, and experimental design among many others. There are five phases to generate the MDDS. These phases involve decomposition, formulation, modeling, integration, and exploration. These phases are not carried out in a sequential manner, but rather in a continuous move back and forth between the different phases. The process of building the MDDS begins with a top-down decomposition of a design concept. The design, seen as an object, is decomposed into its components and aspects, while the design, seen as a process, is decomposed into developmental levels and design activities. Then based on the process decomposition, the architecture of the MDDS is formulated into hierarchical levels each of which comprises a group of design cycles that include design modules at different degrees of abstraction. Based on the design object decomposition, the design activities which include synthesis, analysis, evaluation and optimization are modeled within the design modules.(cont.) Subsequently through a bottom-up approach, the design modules are integrated into a data flow network. This network forms MDDS as an integrated system that acts as a holistic structured functional unit that explores the design space in search of satisfactory solutions. The MDDS emergent properties are not detectable through the properties and behaviors of its parts, and can only be enucleated through a holistic approach. The MDDS is an adaptable system that is continuously dependent on, and responsive to, the uncertainties of the design process. The evolving MDDS is thus characterized a multi-level, multi-module, multi-variable and multi-resolution system. Although the MDDS framework is intended to be domain-independent, several MDDS prototypes were developed within this dissertation to generate exploratory building designs.by Anas Alfaris.Ph.D

Automatic proof assistant of theorems

U ovom radu proučavamo automatski dokazivač teorema HERBY. Najprije se bavimo teorijskom pozadinom njegovog rada i uvodimo pojmove Herbrandove baze i Herbarandovog univerzuma da bi došli do ključnog rezultata, Herbrandovog teorema. Iz jedne verzije Herbrandovog teorema dobivamo način na koji program HERBY dokazuje teoreme, tj. konstrukcijom zatvorenog semantičkog stabla. Zatim proučavamo reprezentaciju logike prvog reda unutar programa HERBY te pretvaranje formula logike prvog reda u klauzule kako bismo mogli programu HERBY teorem zadati u željenom obliku. Opisujemo nekoliko heuristika koje čine konstrukciju zatvorenog semantičkog stabla efikasnijom. Napokon pokrećemo program HERBY te pomoću njega dokazujemo dva teorema. Za svaki teorem skiciramo zatvoreno semantičko stablo pomoću kojeg smo ga dokazali.In this paper we present the proof assistant HERBY. Firstly, we take a look into the theoretical basis of its work. We introduce the Herbrand base and the Herbrand universe to arrive at the key conjecture, Herbrand theorem. One version of the theorem serves as an insight into the method HERBY uses to prove theorems, which is by constructing closed semantic trees. We then present a representation of first order logic formulas within HERBY and we study the transformation of first order logic formulas into clauses as they are the form theorems need to take to be used as input. We observe some of the heuristics that are used for efficiency reasons in constructing a closed semantic tree. Finally, we run and test HERBY by proving two theorems. For each of the theorems we offer a sketch of the closed semantic tree used to prove it