https://en.wikipedia.org/wiki/Resolution_(logic)
https://ru.wikipedia.org/wiki/Правило_резолюций
https://en.wikipedia.org/wiki/Unification_(computer_science)
https://ru.wikipedia.org/wiki/Частный_случай_формулы
John Alan Robinson used first-order syntactical unification as a basic building block of his resolution procedure for first-order logic
1965, J. A. Robinson, A Machine-Oriented Logic Based on the Resolution
Traditionally, a single step in a deduction has been required, for pragmatic and psychological reasons, to be simple enough, broadly speaking, to be apprehended
as correct by a human being in a single intellectual act.
No doubt this custom originates in the desire that each single step of a deduction should be indubitable, even though the deduction as a whole may consist of a long chain of such steps. The ultimate conclusion of a deduction, if the deduction is correct, follows logically from the premisses used in the deduction; but the human mind may well find the unmediated transition from the premisses to the conclusion surprising, hence (psychologically) dubitable. Part of the point, theft, of the logical analysis
of deductive reasoning has been to reduce complex inferences, which are beyond the capacity of the human mind to grasp as single steps, to chains of simpler inferences, each of which is within the capacity of the human mind to grasp as a single transaction.From the theoretical point of view, however, an inference principle need only be sound (i.e., allow only logical consequences of premisses to be deduced from them) and effective (i.e., it must be algorithmically decidable whether an alleged application of the inference principle is indeed an application of it).
When the agent carrying out the application of an inference principle is a modern computing machine, the traditional limitation on the complexity of inference principles is
no longer very appropriate. More powerful principles, involving perhaps a much greater amount of combinatorial information-processing for a single application, become a possibility.In the system described in this paper, one such inference principle is used. It is called the resolution principle, and it is machine-oriented, rather than human-oriented, in the sense of the preceding remarks. The resolution principle is quite powerful, both in the psychological sense that it condones single inferences which are often beyond the ability of the human to grasp (other than discursively), and in the theoretical sense that it alone, as sole inference principle, forms a complete system of first-order logic. While this latter property is of no great importance, it is interesting that (as far as the author is aware) no other complete system of first-order logic has consisted of just one inference principle, if one construes the device of introducing a logical axiom, given outright, or by a schema, as a (premiss-free) inference principle. The main advantage of the resolution principle lies in its ability to allow us to avoid one of the major combinatorial obstacles to efficiency which have plagued earlier theorem-proving procedures.
Отредактировано Лис (2019-11-24 14:51:02)