Controlling redundancy in large search spaces: Argonne-style theorem proving through the years

Author(s):  
Ewing L. Lusk
1986 ◽  
Author(s):  
Martin Abadi ◽  
Zohar Manna
Keyword(s):  

Engevista ◽  
2014 ◽  
Vol 17 (2) ◽  
pp. 152
Author(s):  
Radael De Souza Parolin ◽  
Pedro Paulo Gomes Watts Rodrigues ◽  
Antônio J. Silva Neto

The quality of a given water body can be assessed through the analysis of a number of indicators. Mathematical and computational models can be built to simulate the behavior of these indicators (observable variables), in such a way that different scenarios can be generated, supporting decisions regarding water resources management. In this study, the transport of a conservative contaminant in an estuarine environment is simulated in order to identify the position and intensity of the contaminant source. For this, it was formulated an inverse problem, which was solved through computational intelligence methods. This approach required adaptations to these methods, which had to be modified to relate the source position to the discrete mesh points of the domain. In this context, two adaptive techniques were developed. In one, the estimated points are projected to the grid points, and in the other, points are randomly selected in the iterative search spaces of the methods. The results showed that the methodology here developed has a strong potential in water bodies’ management and simulation.


Author(s):  
Mark Wilson

Scientists have developed various collections of specialized possibilities to serve as search spaces in which excessive reliance upon speculative forms of lower dimensional modeling or other unwanted details can be skirted. Two primary examples are discussed: the search spaces of machine design and the virtual variations utilized within Lagrangian mechanics. Contemporary appeals to “possible worlds” attempt to imbed these localized possibilities within fully enunciated universes. But not all possibilities are made alike and these reductive schemes should be resisted, on the grounds that they render the utilities of everyday counterfactuals and “possibility” talk incomprehensible. The essay also discusses whether Wittgenstein’s altered views in his Philosophical Investigations reflect similar concerns.


2021 ◽  
pp. 1-15
Author(s):  
Geoff Sutcliffe

The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-J10 was the twenty-fifth competition in the CASC series. Twenty-four ATP systems and system variants competed in the various competition divisions. This paper presents an outline of the competition design, and a commentated summary of the results.


1993 ◽  
Vol 19 (3-4) ◽  
pp. 275-301
Author(s):  
Andrzej Biela

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.


2015 ◽  
Vol 65 (2) ◽  
Author(s):  
M. R. Darnel ◽  
W. C. Holland ◽  
H. Pajoohesh

AbstractIn this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.


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