Formalization as the Immanent Part of Logical Solving

Abstract

The work is devoted to the logical analysis of the problem solving by logical means. It starts from general characteristic of the applied logic as a tool: 1. to bound logic with its applications in theory and practice; 2. to import methods and methodologies from other domains into logic; 3. to export methods and methodologies from logic into other domains. The precise solving of a precisely stated logical problem occupies only one third of the whole process of solving real problems by logical means. The formalizing precedes it and the deformalizing follows it. The main topic when considering formalization is a choice of a logic. The classical logic is usually the best one for a draft formalization. The given problem and peculiarities of the draft formalization could sometimes advise us to use some other logic. If axioms of the classical formalization have some restricted form this is often the advice to use temporal, modal or multi-valued logic. More precisely, if all binary predicates occur only in premises of implications then it is possible sometimes to replace a predicate classical formalization by a propositional modal or temporal in the appropriate logic. If all predicates are unary and some of them occur only in premises then the classical logic maybe can replaced by a more adequate multi-valued. This idea is inspired by using Rosser–Turkette operator $J_i$in the book [22]. If we are interested not in a bare proof but in construction it gives us it is often to transfer to an appropriate constructive logic. Its choice is directed by our main resource (time, real values, money or any other imaginable resource) and by other restrictions.Logics of different by their nature resources are mutually inconsistent (e.g. nilpotent logics of time and linear logics of money). Also it is shown by example how Arnold’s principle works in logic: too “precise” formalization often becomes less adequate than more “rough”. DOI: 10.21146/2074-1472-2018-24-1-129-145