Deductive logic is a section of logic in which the methods of reasoning are examined, which guarantee the truth of the conclusion with the truth of the premises. Deductive logic is sometimes identified with formal logic. Outside the deductive logic are the so-called. plausible reasoning and inductive methods. It explores the ways of reasoning with standard, standard statements; these methods are designed in the form of logical systems, or calculus. Historically, the first system of deductive logic was the syllogism of Aristotle. In turn, the Stoics were the first to attempt to construct deductive logic in the form of logic of utterance. G. Frege and C. Pearce widened the scope of this logic – as typical statements, statements about relationships began to be considered and quantifiers were introduced.
The most important system of deductive logic is the classical logic of predicates of the first order. Within the framework of this system, the relation of logical sequence can be completely formalized, and the methods of reasoning can be described purely syntactically. Second-order predicate logic and higher-order systems were also constructed. However, according to Goedel’s theorem, the relation of logical sequencing of the second-order predicate logic is, in principle, unformalizable. At the present time, systems of deductive logic, between the first-order and second-order logics, systems with generalized quantifiers, with the epsilon-symbol, and also systems with non-finite rules (such as the rule of infinite induction) are intensively studied.
The desire to take into account the specifics of cognizable objects in reasoning, the factor of growth and accumulation of knowledge, the uncertainty of the concept of the truth of utterances, the ability to think of contradictory objects and situations led to the construction of various systems of so-called. (deductive) nonclassical logics, intuitionistic, modal, multivalued, relevant, paraconsistent. We began to investigate logical systems with truth failures and satiated vertex estimates. At the same time, various semantic methods are widely used, for example, the theory of models, the semantics of possible worlds, operational semantics, as well as various syntactic methods: axiomatic calculi, natural deduction, sequent calculus, analytical tables.
In a number of nonclassical systems of deductive logic, pragmatic aspects of reasoning are taken into account. In deductive logic, the methods of not only reasoning, but also the introduction of concepts (for example, the procedure for determining), as well as methods to the procedure for finding evidence, are investigated. Recently, on the basis of nonclassical deductive logic, the so-called. Dynamic logic and programming logic, focused on the problems of computer science. In addition, logic of actions, norms, imperatives and preferences are developed, oriented not only to the problems of artificial intelligence, but also to application in the field of ethics and law.
Deductive logic is unified, and the variety of its systems is determined by the fact that by parts the methods of reasoning based on different types of statements are used and applied in different contexts. Different systems use different formalized languages, more or less strong abstractions and idealizations are accepted, different knowledge characteristics are taken into account or not taken into account. In deductive logic, its relationships with various other (non-inductive) logical systems are also investigated and their semantic-epistemological justification is given.