Between Logic and Heuristic :: Calculus Mathematics Essays

Between Logic and Heuristic*ABSTRACT This article aims to rebuild a new type of logical calculi-logical heuristic calculus which contains the means of reducing complete search. Such a heuristic component of calculus is reached with the uphold of meta-level means. The principal means for reducing search is structural in stochastic variableation about information about contrary literals of formula. There are two major approaches to perusal the process of think (problem-solving). On one hand, it is necessary to discover and investigate correct modes of reasoning in which the property of truth is preserved. This task which can be formulated as the point what is a correct reasoning (proof)? is considered in Logic. In order to decide this problem, Logic is based upon the concept of logical form. There is a special syntactical method to deal with this conceptthe method of construction of a logical calculus. In this respect, the calculus in question is a black box which guarantees the t rue conclusion under the true premisses. Thus, Logic (logical form) gives the answer for the question about correct reasoning the correct reasoning is a proof. But logical syntax, as a black box calculus, isnt interested in the real process of derivation building, in studying the question about methods of proof-search, in studying and construction a more manageable and efficient machinery of truth preserving. Availability of any method of pure(a) (complete) search, e.g. British museum algorithm, is quite enough for Logic (logical form). On the other hand, the process of problem-solving can be investigated in the light of the following question how is it manageable to build a piece of correct reasoning?. This task is considered in Heuristic. Heuristic investigates general principles and methods of problem-solving. Computer Heuristic (computer heuristic method) is a system of rules (a rule) for internal reducing the complete search, i.e. heuristic methods are opposed to exhaustive search methods. The area of intersection of Logic and Computer Heuristic is proof-seach theory (PST), which investigates realizable methods of problem-solving (how is it possible to build a proof?) in some calculus. PST deals with the heuristic component of proof systems. More precisely, the aim of proof-search theory can be defined as follows discovering, on the basis of a calculus and an entity in the calculus in question of the structure of a possible derivation of this entity, a derivation which is kindle in some respect.(1) Thus, proof-search theory can be included into the logical pragmatic (look at Fig.